%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 0.09s 0.46s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:11:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.46 Command-line arguments: --flatten --complete-subsets
% 0.09/0.46
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46
% 0.09/0.46 % SZS output start Proof
% 0.09/0.46 Axiom 1 (sos_02): X + Y = Y + X.
% 0.09/0.46 Axiom 2 (sos_03): X + 0 = X.
% 0.09/0.46 Axiom 3 (sos_12): X + 1 = 1.
% 0.09/0.46 Axiom 4 (sos_04): X >= X = true.
% 0.09/0.46 Axiom 5 (sos_08): X >= 0 = true.
% 0.09/0.46 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.09/0.46 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.46 Axiom 8 (sos_13): (X ==> Y) ==> Y = (Y ==> X) ==> X.
% 0.09/0.46 Axiom 9 (sos_06): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 0.09/0.46 Axiom 10 (sos_09): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 0.09/0.46 Axiom 11 (sos_10): ifeq(X >= Y, true, (Y ==> Z) >= (X ==> Z), true) = true.
% 0.09/0.46 Axiom 12 (sos_07): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 0.09/0.46 Axiom 13 (sos_07_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 0.09/0.46
% 0.09/0.46 Lemma 14: 0 + X = X.
% 0.09/0.46 Proof:
% 0.09/0.46 0 + X
% 0.09/0.46 = { by axiom 1 (sos_02) R->L }
% 0.09/0.46 X + 0
% 0.09/0.46 = { by axiom 2 (sos_03) }
% 0.09/0.47 X
% 0.09/0.47
% 0.09/0.47 Goal 1 (goals_14): (x17 ==> 1) ==> 1 = x17.
% 0.09/0.47 Proof:
% 0.09/0.47 (x17 ==> 1) ==> 1
% 0.09/0.47 = { by axiom 8 (sos_13) R->L }
% 0.09/0.47 (1 ==> x17) ==> x17
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(true, true, 1 ==> x17, 0) ==> x17
% 0.09/0.47 = { by axiom 5 (sos_08) R->L }
% 0.09/0.47 ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0) ==> x17
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(true, true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 11 (sos_10) R->L }
% 0.09/0.47 ifeq2(ifeq(1 >= x17, true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 3 (sos_12) R->L }
% 0.09/0.47 ifeq2(ifeq((x17 + 1) >= x17, true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 1 (sos_02) R->L }
% 0.09/0.47 ifeq2(ifeq((1 + x17) >= x17, true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(ifeq(ifeq(true, true, (1 + x17) >= x17, true), true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 5 (sos_08) R->L }
% 0.09/0.47 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + x17) >= x17, true), true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by lemma 14 R->L }
% 0.09/0.47 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + x17) >= (0 + x17), true), true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 10 (sos_09) }
% 0.09/0.47 ifeq2(ifeq(true, true, (x17 ==> x17) >= (1 ==> x17), true), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.09/0.47 ifeq2((x17 ==> x17) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by lemma 14 R->L }
% 0.09/0.47 ifeq2((x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 9 (sos_06) R->L }
% 0.09/0.47 ifeq2(ifeq2((x17 ==> (0 + x17)) >= 0, true, ifeq2(0 >= (x17 ==> (0 + x17)), true, 0, x17 ==> (0 + x17)), x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 5 (sos_08) }
% 0.09/0.47 ifeq2(ifeq2(true, true, ifeq2(0 >= (x17 ==> (0 + x17)), true, 0, x17 ==> (0 + x17)), x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.47 ifeq2(ifeq2(0 >= (x17 ==> (0 + x17)), true, 0, x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 1 (sos_02) R->L }
% 0.09/0.47 ifeq2(ifeq2(0 >= (x17 ==> (x17 + 0)), true, 0, x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(ifeq2(ifeq(true, true, 0 >= (x17 ==> (x17 + 0)), true), true, 0, x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 4 (sos_04) R->L }
% 0.09/0.47 ifeq2(ifeq2(ifeq((x17 + 0) >= (x17 + 0), true, 0 >= (x17 ==> (x17 + 0)), true), true, 0, x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 13 (sos_07_1) }
% 0.09/0.47 ifeq2(ifeq2(true, true, 0, x17 ==> (0 + x17)) >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.47 ifeq2(0 >= (1 ==> x17), true, ifeq2((1 ==> x17) >= 0, true, 1 ==> x17, 0), 0) ==> x17
% 0.09/0.47 = { by axiom 9 (sos_06) }
% 0.09/0.47 0 ==> x17
% 0.09/0.47 = { by axiom 9 (sos_06) R->L }
% 0.09/0.47 ifeq2((0 ==> x17) >= x17, true, ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17), 0 ==> x17)
% 0.09/0.47 = { by lemma 14 R->L }
% 0.09/0.47 ifeq2((0 + (0 ==> x17)) >= x17, true, ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17), 0 ==> x17)
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(ifeq(true, true, (0 + (0 ==> x17)) >= x17, true), true, ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17), 0 ==> x17)
% 0.09/0.47 = { by axiom 4 (sos_04) R->L }
% 0.09/0.47 ifeq2(ifeq((0 ==> x17) >= (0 ==> x17), true, (0 + (0 ==> x17)) >= x17, true), true, ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17), 0 ==> x17)
% 0.09/0.47 = { by axiom 12 (sos_07) }
% 0.09/0.47 ifeq2(true, true, ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17), 0 ==> x17)
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.47 ifeq2(x17 >= (0 ==> x17), true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.47 ifeq2(ifeq(true, true, x17 >= (0 ==> x17), true), true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 10 (sos_09) R->L }
% 0.09/0.47 ifeq2(ifeq(ifeq(0 >= 0, true, (0 + x17) >= (0 + x17), true), true, x17 >= (0 ==> x17), true), true, x17, 0 ==> x17)
% 0.09/0.47 = { by lemma 14 }
% 0.09/0.47 ifeq2(ifeq(ifeq(0 >= 0, true, (0 + x17) >= x17, true), true, x17 >= (0 ==> x17), true), true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 5 (sos_08) }
% 0.09/0.47 ifeq2(ifeq(ifeq(true, true, (0 + x17) >= x17, true), true, x17 >= (0 ==> x17), true), true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.09/0.47 ifeq2(ifeq((0 + x17) >= x17, true, x17 >= (0 ==> x17), true), true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 13 (sos_07_1) }
% 0.09/0.47 ifeq2(true, true, x17, 0 ==> x17)
% 0.09/0.47 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.47 x17
% 0.09/0.47 % SZS output end Proof
% 0.09/0.47
% 0.09/0.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------