%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL896+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:50:45 AM UTC 2026
% Result : Theorem 11.68s 2.00s
% Output : Proof 11.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL896+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 17:10:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.68/2.00 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.68/2.00
% 11.68/2.00 % SZS status Theorem
% 11.68/2.00
% 11.68/2.01 % SZS output start Proof
% 11.68/2.01 Axiom 1 (sos_02): X + Y = Y + X.
% 11.68/2.01 Axiom 2 (sos_03): X + 0 = X.
% 11.68/2.01 Axiom 3 (sos_04): X >= X = true.
% 11.68/2.01 Axiom 4 (sos_08): X >= 0 = true.
% 11.68/2.01 Axiom 5 (sos_01): (X + Y) + Z = X + (Y + Z).
% 11.68/2.01 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 11.68/2.01 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 11.68/2.01 Axiom 8 (sos_12): (X + (X ==> Y)) + ((X + (X ==> Y)) ==> Z) = X + (X ==> (Y + (Y ==> Z))).
% 11.68/2.01 Axiom 9 (sos_09): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 11.68/2.01 Axiom 10 (sos_07): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 11.68/2.01 Axiom 11 (sos_07_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 11.68/2.01 Axiom 12 (sos_06): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 11.68/2.01
% 11.68/2.01 Lemma 13: X + (X ==> (Y + (Y ==> X))) = X + (X ==> Y).
% 11.68/2.01 Proof:
% 11.68/2.01 X + (X ==> (Y + (Y ==> X)))
% 11.68/2.01 = { by axiom 8 (sos_12) R->L }
% 11.68/2.01 (X + (X ==> Y)) + ((X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 12 (sos_06) R->L }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(((X + (X ==> Y)) ==> X) >= 0, true, ifeq2(0 >= ((X + (X ==> Y)) ==> X), true, 0, (X + (X ==> Y)) ==> X), (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 4 (sos_08) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(true, true, ifeq2(0 >= ((X + (X ==> Y)) ==> X), true, 0, (X + (X ==> Y)) ==> X), (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 7 (ifeq_axiom) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(0 >= ((X + (X ==> Y)) ==> X), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 6 (ifeq_axiom) R->L }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(true, true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 9 (sos_09) R->L }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(ifeq((0 + (X ==> Y)) >= 0, true, ((0 + (X ==> Y)) + X) >= (0 + X), true), true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 1 (sos_02) R->L }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(ifeq((0 + (X ==> Y)) >= 0, true, ((0 + (X ==> Y)) + X) >= (X + 0), true), true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 2 (sos_03) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(ifeq((0 + (X ==> Y)) >= 0, true, ((0 + (X ==> Y)) + X) >= X, true), true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 4 (sos_08) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(ifeq(true, true, ((0 + (X ==> Y)) + X) >= X, true), true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 6 (ifeq_axiom) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq(((0 + (X ==> Y)) + X) >= X, true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.01 = { by axiom 1 (sos_02) }
% 11.68/2.01 (X + (X ==> Y)) + ifeq2(ifeq((X + (0 + (X ==> Y))) >= X, true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.02 = { by axiom 1 (sos_02) R->L }
% 11.68/2.02 (X + (X ==> Y)) + ifeq2(ifeq((X + ((X ==> Y) + 0)) >= X, true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.02 = { by axiom 5 (sos_01) R->L }
% 11.68/2.02 (X + (X ==> Y)) + ifeq2(ifeq(((X + (X ==> Y)) + 0) >= X, true, 0 >= ((X + (X ==> Y)) ==> X), true), true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.02 = { by axiom 11 (sos_07_1) }
% 11.68/2.02 (X + (X ==> Y)) + ifeq2(true, true, 0, (X + (X ==> Y)) ==> X)
% 11.68/2.02 = { by axiom 7 (ifeq_axiom) }
% 11.68/2.02 (X + (X ==> Y)) + 0
% 11.68/2.02 = { by axiom 2 (sos_03) }
% 11.68/2.02 X + (X ==> Y)
% 11.68/2.02
% 11.68/2.02 Goal 1 (goals_13): x17 + (x17 ==> x18) = x18 + (x18 ==> x17).
% 11.68/2.02 Proof:
% 11.68/2.02 x17 + (x17 ==> x18)
% 11.68/2.02 = { by axiom 7 (ifeq_axiom) R->L }
% 11.68/2.02 ifeq2(true, true, x17 + (x17 ==> x18), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 10 (sos_07) R->L }
% 11.68/2.02 ifeq2(ifeq((x17 ==> (x18 + (x18 ==> x17))) >= (x17 ==> (x18 + (x18 ==> x17))), true, (x17 + (x17 ==> (x18 + (x18 ==> x17)))) >= (x18 + (x18 ==> x17)), true), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 3 (sos_04) }
% 11.68/2.02 ifeq2(ifeq(true, true, (x17 + (x17 ==> (x18 + (x18 ==> x17)))) >= (x18 + (x18 ==> x17)), true), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 6 (ifeq_axiom) }
% 11.68/2.02 ifeq2((x17 + (x17 ==> (x18 + (x18 ==> x17)))) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17))
% 11.68/2.02 = { by lemma 13 }
% 11.68/2.02 ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 7 (ifeq_axiom) R->L }
% 11.68/2.02 ifeq2(true, true, ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17)), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 10 (sos_07) R->L }
% 11.68/2.02 ifeq2(ifeq((x18 ==> (x17 + (x17 ==> x18))) >= (x18 ==> (x17 + (x17 ==> x18))), true, (x18 + (x18 ==> (x17 + (x17 ==> x18)))) >= (x17 + (x17 ==> x18)), true), true, ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17)), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 3 (sos_04) }
% 11.68/2.02 ifeq2(ifeq(true, true, (x18 + (x18 ==> (x17 + (x17 ==> x18)))) >= (x17 + (x17 ==> x18)), true), true, ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17)), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 6 (ifeq_axiom) }
% 11.68/2.02 ifeq2((x18 + (x18 ==> (x17 + (x17 ==> x18)))) >= (x17 + (x17 ==> x18)), true, ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17)), x18 + (x18 ==> x17))
% 11.68/2.02 = { by lemma 13 }
% 11.68/2.02 ifeq2((x18 + (x18 ==> x17)) >= (x17 + (x17 ==> x18)), true, ifeq2((x17 + (x17 ==> x18)) >= (x18 + (x18 ==> x17)), true, x17 + (x17 ==> x18), x18 + (x18 ==> x17)), x18 + (x18 ==> x17))
% 11.68/2.02 = { by axiom 12 (sos_06) }
% 11.68/2.02 x18 + (x18 ==> x17)
% 11.68/2.02 % SZS output end Proof
% 11.68/2.02
% 11.68/2.02 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------