diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -3221,6 +3221,17 @@
          PredR == CmpInst::ICMP_SGT && match(RHS1, m_AllOnes())))
       return Builder.CreateIsNotNeg(Builder.CreateXor(LHS0, RHS0));
 
+    // (X > C - 1) ^ (X < C + 1) --> X != C
+    // (X < C + 1) ^ (X > C - 1) --> X != C
+    const APInt *C1, *C2;
+    if ((PredL == CmpInst::ICMP_SGT && match(LHS1, m_APInt(C1)) &&
+         PredR == CmpInst::ICMP_SLT && match(RHS1, m_APInt(C2)) &&
+         *C1 + 2 == *C2) ||
+        (PredL == CmpInst::ICMP_SLT && match(LHS1, m_APInt(C2)) &&
+         PredR == CmpInst::ICMP_SGT && match(RHS1, m_APInt(C1)) &&
+         *C1 + 2 == *C2))
+      return Builder.CreateICmpNE(LHS0,
+                                  ConstantInt::get(LHS0->getType(), *C1 + 1));
   }
 
   // Instead of trying to imitate the folds for and/or, decompose this 'xor'
diff --git a/llvm/test/Transforms/InstCombine/set.ll b/llvm/test/Transforms/InstCombine/set.ll
--- a/llvm/test/Transforms/InstCombine/set.ll
+++ b/llvm/test/Transforms/InstCombine/set.ll
@@ -220,14 +220,10 @@
   ret i1 %xor
 }
 
-; FIXME: This is (a != 5).
-
 define i1 @xor_of_icmps_to_ne(i64 %a) {
 ; CHECK-LABEL: @xor_of_icmps_to_ne(
-; CHECK-NEXT:    [[B:%.*]] = icmp sgt i64 [[A:%.*]], 4
-; CHECK-NEXT:    [[C:%.*]] = icmp slt i64 [[A]], 6
-; CHECK-NEXT:    [[XOR:%.*]] = xor i1 [[B]], [[C]]
-; CHECK-NEXT:    ret i1 [[XOR]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ne i64 [[A:%.*]], 5
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %b = icmp sgt i64 %a, 4
   %c = icmp slt i64 %a, 6
@@ -237,10 +233,8 @@
 
 define i1 @xor_of_icmps_to_ne_commute(i64 %a) {
 ; CHECK-LABEL: @xor_of_icmps_to_ne_commute(
-; CHECK-NEXT:    [[C:%.*]] = icmp sgt i64 [[A:%.*]], 4
-; CHECK-NEXT:    [[B:%.*]] = icmp slt i64 [[A]], 6
-; CHECK-NEXT:    [[XOR:%.*]] = xor i1 [[B]], [[C]]
-; CHECK-NEXT:    ret i1 [[XOR]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ne i64 [[A:%.*]], 5
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %c = icmp sgt i64 %a, 4
   %b = icmp slt i64 %a, 6
@@ -250,10 +244,8 @@
 
 define i1 @xor_of_icmps_neg_to_ne(i64 %a) {
 ; CHECK-LABEL: @xor_of_icmps_neg_to_ne(
-; CHECK-NEXT:    [[B:%.*]] = icmp sgt i64 [[A:%.*]], -6
-; CHECK-NEXT:    [[C:%.*]] = icmp slt i64 [[A]], -4
-; CHECK-NEXT:    [[XOR:%.*]] = xor i1 [[B]], [[C]]
-; CHECK-NEXT:    ret i1 [[XOR]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ne i64 [[A:%.*]], -5
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %b = icmp sgt i64 %a, -6
   %c = icmp slt i64 %a, -4