%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN557-1 : 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 01:48:05 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN557-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 16:29:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36 Command-line arguments: --no-flatten-goal
% 0.20/0.36
% 0.20/0.36 % SZS status Unsatisfiable
% 0.20/0.36
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 Axiom 1 (p2_1): p2(X, X) = true.
% 0.20/0.38 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.38 Axiom 3 (p2_4): p2(f3(X, Y), f3(Y, X)) = true.
% 0.20/0.38 Axiom 4 (p2_12): p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))) = true.
% 0.20/0.38 Axiom 5 (p2_10): p2(f3(X, f3(Y, Z)), f3(Y, f3(X, Z))) = true.
% 0.20/0.38 Axiom 6 (p2_8): ifeq(p2(f3(X, Y), f3(Z, Y)), true, p2(X, Z), true) = true.
% 0.20/0.38 Axiom 7 (p2_6): ifeq(p2(X, Y), true, ifeq(p2(X, Z), true, p2(Z, Y), true), true) = true.
% 0.20/0.38
% 0.20/0.38 Goal 1 (not_p2_3): p2(c6, f3(c8, f5(c9))) = true.
% 0.20/0.38 Proof:
% 0.20/0.38 p2(c6, f3(c8, f5(c9)))
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.38 ifeq(true, true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 6 (p2_8) R->L }
% 0.20/0.38 ifeq(ifeq(p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.38 ifeq(ifeq(ifeq(true, true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 7 (p2_6) R->L }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(p2(f3(c6, f5(c7)), f3(c6, f5(c7))), true, ifeq(p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 1 (p2_1) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 7 (p2_6) R->L }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c6, f5(c7)), f3(c6, f5(c7))), true, ifeq(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), true, p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true), true), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 1 (p2_1) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), true, p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true), true), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), true, p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 4 (p2_12) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.38 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 5 (p2_10) R->L }
% 0.20/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c8, f3(f5(c7), f5(c9))), f3(f5(c7), f3(c8, f5(c9)))), true, ifeq(p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true, p2(f3(c6, f5(c7)), f3(f5(c7), f3(c8, f5(c9)))), true), true), true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 7 (p2_6) }
% 0.20/0.39 ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.39 ifeq(ifeq(ifeq(p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.39 ifeq(ifeq(ifeq(p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true, ifeq(true, true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 3 (p2_4) R->L }
% 0.20/0.39 ifeq(ifeq(ifeq(p2(f3(f5(c7), f3(c8, f5(c9))), f3(c6, f5(c7))), true, ifeq(p2(f3(f5(c7), f3(c8, f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), true, p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true), true), true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 7 (p2_6) }
% 0.20/0.39 ifeq(ifeq(true, true, p2(f3(c8, f5(c9)), c6), true), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.39 ifeq(p2(f3(c8, f5(c9)), c6), true, p2(c6, f3(c8, f5(c9))), true)
% 0.20/0.39 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.39 ifeq(true, true, ifeq(p2(f3(c8, f5(c9)), c6), true, p2(c6, f3(c8, f5(c9))), true), true)
% 0.20/0.39 = { by axiom 1 (p2_1) R->L }
% 0.20/0.39 ifeq(p2(f3(c8, f5(c9)), f3(c8, f5(c9))), true, ifeq(p2(f3(c8, f5(c9)), c6), true, p2(c6, f3(c8, f5(c9))), true), true)
% 0.20/0.39 = { by axiom 7 (p2_6) }
% 0.20/0.39 true
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------