%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN562-1 : TPTP v9.3.1. Released v2.5.0.
% 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 01:48:06 PM UTC 2026
% Result : Unsatisfiable 20.73s 2.92s
% Output : Proof 20.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN562-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 16:35:18 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.73/2.92 Command-line arguments: --flatten --complete-subsets
% 20.73/2.92
% 20.73/2.92 % SZS status Unsatisfiable
% 20.73/2.92
% 20.73/2.92 % SZS output start Proof
% 20.73/2.92 Axiom 1 (p2_1): p2(X, X) = true.
% 20.73/2.92 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 20.73/2.92 Axiom 3 (p2_4): p2(f9(c11), f3(c12)) = true.
% 20.73/2.92 Axiom 4 (p10_16): p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) = true.
% 20.73/2.92 Axiom 5 (p2_15): p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) = true.
% 20.73/2.92 Axiom 6 (p10_14): ifeq(p10(X, Y), true, ifeq(p2(Y, Z), true, ifeq(p2(X, W), true, p10(W, Z), true), true), true) = true.
% 20.73/2.92
% 20.73/2.92 Goal 1 (not_p10_3): p10(X, X) = true.
% 20.73/2.92 The goal is true when:
% 20.73/2.92 X = f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))
% 20.73/2.92
% 20.73/2.92 Proof:
% 20.73/2.92 p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 20.73/2.92 = { by axiom 2 (ifeq_axiom) R->L }
% 20.73/2.92 ifeq(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)))
% 20.73/2.92 = { by axiom 3 (p2_4) }
% 20.73/2.92 ifeq(true, p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)))
% 20.73/2.92 = { by axiom 5 (p2_15) R->L }
% 20.73/2.92 ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)))
% 20.73/2.92 = { by axiom 2 (ifeq_axiom) R->L }
% 20.73/2.92 ifeq(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.92 = { by axiom 3 (p2_4) }
% 20.73/2.92 ifeq(true, p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.92 = { by axiom 4 (p10_16) R->L }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.93 = { by axiom 2 (ifeq_axiom) R->L }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.93 = { by axiom 3 (p2_4) }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(true, p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.93 = { by axiom 1 (p2_1) R->L }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.93 = { by axiom 3 (p2_4) }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.93 = { by axiom 3 (p2_4) }
% 20.73/2.93 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.94 = { by axiom 3 (p2_4) }
% 20.73/2.94 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.94 = { by axiom 3 (p2_4) }
% 20.73/2.94 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true), p2(f9(c11), f3(c12))), p2(f9(c11), f3(c12)))
% 20.73/2.94 = { by axiom 3 (p2_4) }
% 20.73/2.94 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true), true), p2(f9(c11), f3(c12)))
% 20.73/2.94 = { by axiom 3 (p2_4) }
% 20.73/2.94 ifeq(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, ifeq(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true, p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true), true), true)
% 20.73/2.94 = { by axiom 6 (p10_14) }
% 20.73/2.94 true
% 20.73/2.94 = { by axiom 3 (p2_4) R->L }
% 20.73/2.94 p2(f9(c11), f3(c12))
% 20.73/2.94 = { by axiom 3 (p2_4) }
% 20.73/2.94 true
% 20.73/2.94 % SZS output end Proof
% 20.73/2.94
% 20.73/2.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------