%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN565-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:48:07 PM UTC 2026
% Result : Unsatisfiable 7.41s 1.18s
% Output : Proof 7.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN565-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 16:29:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.41/1.18 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 7.41/1.18
% 7.41/1.18 % SZS status Unsatisfiable
% 7.41/1.18
% 7.68/1.20 % SZS output start Proof
% 7.68/1.20 Axiom 1 (p2_1): p2(X, X) = true.
% 7.68/1.20 Axiom 2 (p2_3): p2(f5(f7(X)), f5(X)) = true.
% 7.68/1.20 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.68/1.20 Axiom 4 (p10_10): p10(f5(X), f3(f5(f6(X, Y)), f5(Y))) = true.
% 7.68/1.20 Axiom 5 (p4_4): p4(f8(X, Y), f6(X, f7(Y))) = true.
% 7.68/1.20 Axiom 6 (p4_5): p4(f7(f8(X, Y)), f8(Y, X)) = true.
% 7.68/1.20 Axiom 7 (p2_6): ifeq(p4(X, Y), true, p2(f5(X), f5(Y)), true) = true.
% 7.68/1.20 Axiom 8 (p4_7): ifeq(p4(X, Y), true, p4(f7(X), f7(Y)), true) = true.
% 7.68/1.20 Axiom 9 (p10_13): ifeq(p10(X, f3(Y, Z)), true, p10(f9(X, Z), Y), true) = true.
% 7.68/1.20 Axiom 10 (p4_9): ifeq(p4(X, Y), true, ifeq(p4(X, Z), true, p4(Z, Y), true), true) = true.
% 7.68/1.20 Axiom 11 (p2_8): ifeq(p2(X, Y), true, ifeq(p2(X, Z), true, p2(Z, Y), true), true) = true.
% 7.68/1.20 Axiom 12 (p2_16): ifeq(p2(X, Y), true, ifeq(p2(Z, W), true, p2(f3(Z, X), f3(W, Y)), true), true) = true.
% 7.68/1.20 Axiom 13 (p10_14): ifeq(p10(X, Y), true, ifeq(p2(Y, Z), true, ifeq(p2(X, W), true, p10(W, Z), true), true), true) = true.
% 7.68/1.20
% 7.68/1.20 Goal 1 (not_p10_11): p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))) = true.
% 7.68/1.20 Proof:
% 7.68/1.20 p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 7.68/1.20 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.20 ifeq(true, true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.20 = { by axiom 11 (p2_8) R->L }
% 7.68/1.20 ifeq(ifeq(p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true, ifeq(p2(f5(f7(f6(c11, f7(c12)))), f5(f6(c11, f7(c12)))), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 2 (p2_3) }
% 7.68/1.21 ifeq(ifeq(p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true, ifeq(true, true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(ifeq(p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(true, true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 10 (p4_9) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(p4(f7(f8(c11, c12)), f8(c12, c11)), true, ifeq(p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 6 (p4_5) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true), true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 5 (p4_4) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(ifeq(p4(f8(c11, c12), f6(c11, f7(c12))), true, p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true), true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 8 (p4_7) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(true, true, p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(ifeq(ifeq(p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true, p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true), true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 7 (p2_6) }
% 7.68/1.21 ifeq(ifeq(true, true, p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(true, true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 9 (p10_13) R->L }
% 7.68/1.21 ifeq(ifeq(p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(true, true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 12 (p2_16) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(p2(f5(f7(c12)), f5(c12)), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f6(c11, f7(c12)))), true, p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 1 (p2_1) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(p2(f5(f7(c12)), f5(c12)), true, ifeq(true, true, p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(p2(f5(f7(c12)), f5(c12)), true, p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 2 (p2_3) }
% 7.68/1.21 ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.21 ifeq(ifeq(ifeq(p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 4 (p10_10) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(f7(c12)))), true, ifeq(p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.21 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.21 ifeq(ifeq(ifeq(p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(f7(c12)))), true, ifeq(p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true, ifeq(true, true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.22 = { by axiom 1 (p2_1) R->L }
% 7.68/1.22 ifeq(ifeq(ifeq(p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(f7(c12)))), true, ifeq(p2(f3(f5(f6(c11, f7(c12))), f5(f7(c12))), f3(f5(f6(c11, f7(c12))), f5(c12))), true, ifeq(p2(f5(c11), f5(c11)), true, p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(c12))), true), true), true), true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.22 = { by axiom 13 (p10_14) }
% 7.68/1.22 ifeq(ifeq(true, true, p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.22 = { by axiom 3 (ifeq_axiom) }
% 7.68/1.22 ifeq(p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true)
% 7.68/1.22 = { by axiom 3 (ifeq_axiom) R->L }
% 7.68/1.22 ifeq(p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, ifeq(true, true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true), true)
% 7.68/1.22 = { by axiom 1 (p2_1) R->L }
% 7.68/1.22 ifeq(p10(f9(f5(c11), f5(c12)), f5(f6(c11, f7(c12)))), true, ifeq(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, ifeq(p2(f9(f5(c11), f5(c12)), f9(f5(c11), f5(c12))), true, p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))), true), true), true)
% 7.68/1.22 = { by axiom 13 (p10_14) }
% 7.68/1.22 true
% 7.68/1.22 % SZS output end Proof
% 7.68/1.22
% 7.68/1.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------