%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 0.14s 5.50s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 27 17:05:36 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.50 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/5.50
% 0.14/5.50 % SZS status Theorem
% 0.14/5.50
% 0.14/5.52 % SZS output start Proof
% 0.14/5.52 Axiom 1 (sos_04): X >= X = true.
% 0.14/5.52 Axiom 2 (sos_08): X >= 0 = true.
% 0.14/5.52 Axiom 3 (sos_02): X + Y = Y + X.
% 0.14/5.53 Axiom 4 (sos_12): X + 1 = 1.
% 0.14/5.53 Axiom 5 (sos_03): X + 0 = X.
% 0.14/5.53 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/5.53 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.14/5.53 Axiom 8 (sos_13): ((X ==> 1) ==> X) ==> X = 0.
% 0.14/5.53 Axiom 9 (sos_11): ifeq(X >= Y, true, (Z ==> X) >= (Z ==> Y), true) = true.
% 0.14/5.53 Axiom 10 (sos_09): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 0.14/5.53 Axiom 11 (sos_07): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 0.14/5.53 Axiom 12 (sos_07_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 0.14/5.53 Axiom 13 (sos_06): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 0.14/5.53
% 0.14/5.53 Lemma 14: 0 + X = X.
% 0.14/5.53 Proof:
% 0.14/5.53 0 + X
% 0.14/5.53 = { by axiom 3 (sos_02) R->L }
% 0.14/5.53 X + 0
% 0.14/5.53 = { by axiom 5 (sos_03) }
% 0.14/5.53 X
% 0.14/5.53
% 0.14/5.53 Goal 1 (goals_14): (x17 ==> 1) ==> 1 = x17.
% 0.14/5.53 Proof:
% 0.14/5.53 (x17 ==> 1) ==> 1
% 0.14/5.53 = { by axiom 13 (sos_06) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= x17, true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(true, true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 12 (sos_07_1) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(((x17 ==> 1) + x17) >= x17, true, x17 >= ((x17 ==> 1) ==> x17), true), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 6 (ifeq_axiom) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(ifeq(true, true, ((x17 ==> 1) + x17) >= x17, true), true, x17 >= ((x17 ==> 1) ==> x17), true), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 2 (sos_08) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(ifeq((x17 ==> 1) >= 0, true, ((x17 ==> 1) + x17) >= x17, true), true, x17 >= ((x17 ==> 1) ==> x17), true), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by lemma 14 R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(ifeq((x17 ==> 1) >= 0, true, ((x17 ==> 1) + x17) >= (0 + x17), true), true, x17 >= ((x17 ==> 1) ==> x17), true), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 10 (sos_09) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(true, true, x17 >= ((x17 ==> 1) ==> x17), true), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 6 (ifeq_axiom) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(true, true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 11 (sos_07) R->L }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq((((x17 ==> 1) ==> x17) ==> x17) >= (((x17 ==> 1) ==> x17) ==> x17), true, (((x17 ==> 1) ==> x17) + (((x17 ==> 1) ==> x17) ==> x17)) >= x17, true), true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 1 (sos_04) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(ifeq(true, true, (((x17 ==> 1) ==> x17) + (((x17 ==> 1) ==> x17) ==> x17)) >= x17, true), true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 6 (ifeq_axiom) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2((((x17 ==> 1) ==> x17) + (((x17 ==> 1) ==> x17) ==> x17)) >= x17, true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 8 (sos_13) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2((((x17 ==> 1) ==> x17) + 0) >= x17, true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 5 (sos_03) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ifeq2(((x17 ==> 1) ==> x17) >= x17, true, ifeq2(x17 >= ((x17 ==> 1) ==> x17), true, x17, (x17 ==> 1) ==> x17), (x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 13 (sos_06) }
% 0.14/5.53 ifeq2(((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 6 (ifeq_axiom) R->L }
% 0.14/5.53 ifeq2(ifeq(true, true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 10 (sos_09) R->L }
% 0.14/5.53 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + x17) >= (0 + x17), true), true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by lemma 14 }
% 0.14/5.53 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + x17) >= x17, true), true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 2 (sos_08) }
% 0.14/5.53 ifeq2(ifeq(ifeq(true, true, (1 + x17) >= x17, true), true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 6 (ifeq_axiom) }
% 0.14/5.53 ifeq2(ifeq((1 + x17) >= x17, true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.53 = { by axiom 3 (sos_02) }
% 0.14/5.54 ifeq2(ifeq((x17 + 1) >= x17, true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 4 (sos_12) }
% 0.14/5.54 ifeq2(ifeq(1 >= x17, true, ((x17 ==> 1) ==> 1) >= ((x17 ==> 1) ==> x17), true), true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 9 (sos_11) }
% 0.14/5.54 ifeq2(true, true, ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1), (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 7 (ifeq_axiom) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> 1), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(true, true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 10 (sos_09) R->L }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(ifeq(1 >= 0, true, (1 + (x17 + (x17 ==> 1))) >= (0 + (x17 + (x17 ==> 1))), true), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by lemma 14 }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(ifeq(1 >= 0, true, (1 + (x17 + (x17 ==> 1))) >= (x17 + (x17 ==> 1)), true), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 2 (sos_08) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(ifeq(true, true, (1 + (x17 + (x17 ==> 1))) >= (x17 + (x17 ==> 1)), true), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 6 (ifeq_axiom) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2((1 + (x17 + (x17 ==> 1))) >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 3 (sos_02) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(((x17 + (x17 ==> 1)) + 1) >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 4 (sos_12) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(1 >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(true, true, ifeq2(1 >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1)), x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 11 (sos_07) R->L }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(ifeq((x17 ==> 1) >= (x17 ==> 1), true, (x17 + (x17 ==> 1)) >= 1, true), true, ifeq2(1 >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1)), x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 1 (sos_04) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2(ifeq(true, true, (x17 + (x17 ==> 1)) >= 1, true), true, ifeq2(1 >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1)), x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 6 (ifeq_axiom) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ifeq2((x17 + (x17 ==> 1)) >= 1, true, ifeq2(1 >= (x17 + (x17 ==> 1)), true, 1, x17 + (x17 ==> 1)), x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 13 (sos_06) }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> (x17 + (x17 ==> 1))), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 3 (sos_02) R->L }
% 0.14/5.54 ifeq2(x17 >= ((x17 ==> 1) ==> ((x17 ==> 1) + x17)), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 6 (ifeq_axiom) R->L }
% 0.14/5.54 ifeq2(ifeq(true, true, x17 >= ((x17 ==> 1) ==> ((x17 ==> 1) + x17)), true), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 1 (sos_04) R->L }
% 0.14/5.54 ifeq2(ifeq(((x17 ==> 1) + x17) >= ((x17 ==> 1) + x17), true, x17 >= ((x17 ==> 1) ==> ((x17 ==> 1) + x17)), true), true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 12 (sos_07_1) }
% 0.14/5.54 ifeq2(true, true, x17, (x17 ==> 1) ==> 1)
% 0.14/5.54 = { by axiom 7 (ifeq_axiom) }
% 0.14/5.54 x17
% 0.14/5.54 % SZS output end Proof
% 0.14/5.54
% 0.14/5.54 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------