%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN553-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 01:48:05 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.34s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN553-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n001.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 16:34:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 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
% 0.20/0.34
% 0.20/0.34 % SZS status Unsatisfiable
% 0.20/0.34
% 0.20/0.34 % SZS output start Proof
% 0.20/0.34 Axiom 1 (p2_1): p2(X, X) = true.
% 0.20/0.34 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.34 Axiom 3 (p2_5): p2(f8(X, Y), f8(Y, X)) = true.
% 0.20/0.34 Axiom 4 (p2_7): p2(f8(X, f8(Y, Z)), f8(f8(X, Y), Z)) = true.
% 0.20/0.34 Axiom 5 (p2_6): ifeq(p2(X, Y), true, ifeq(p2(Z, X), true, p2(Z, Y), true), true) = true.
% 0.20/0.34 Axiom 6 (p2_8): ifeq(p2(X, Y), true, ifeq(p2(Z, W), true, p2(f8(Z, X), f8(W, Y)), true), true) = true.
% 0.20/0.34
% 0.20/0.34 Goal 1 (not_p2_9): p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))) = true.
% 0.20/0.34 Proof:
% 0.20/0.34 p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 0.20/0.34 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.34 ifeq(true, true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.34 = { by axiom 6 (p2_8) R->L }
% 0.20/0.34 ifeq(ifeq(p2(f9(c3), f9(c3)), true, ifeq(p2(f8(f9(c4), c4), f8(c4, f9(c4))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true), true), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.34 = { by axiom 1 (p2_1) }
% 0.20/0.34 ifeq(ifeq(true, true, ifeq(p2(f8(f9(c4), c4), f8(c4, f9(c4))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true), true), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.34 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.34 ifeq(ifeq(p2(f8(f9(c4), c4), f8(c4, f9(c4))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.34 = { by axiom 3 (p2_5) }
% 0.20/0.34 ifeq(ifeq(true, true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.35 ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.35 ifeq(true, true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 5 (p2_6) R->L }
% 0.20/0.35 ifeq(ifeq(p2(f8(f8(f9(c3), c4), f9(c4)), f8(f9(c4), f8(f9(c3), c4))), true, ifeq(p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 3 (p2_5) }
% 0.20/0.35 ifeq(ifeq(true, true, ifeq(p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.35 ifeq(ifeq(p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.35 ifeq(ifeq(ifeq(true, true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 4 (p2_7) R->L }
% 0.20/0.35 ifeq(ifeq(ifeq(p2(f8(f9(c3), f8(c4, f9(c4))), f8(f8(f9(c3), c4), f9(c4))), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.35 ifeq(ifeq(ifeq(p2(f8(f9(c3), f8(c4, f9(c4))), f8(f8(f9(c3), c4), f9(c4))), true, ifeq(true, true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true), true), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 3 (p2_5) R->L }
% 0.20/0.35 ifeq(ifeq(ifeq(p2(f8(f9(c3), f8(c4, f9(c4))), f8(f8(f9(c3), c4), f9(c4))), true, ifeq(p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f8(f9(c3), c4), f9(c4))), true), true), true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 5 (p2_6) }
% 0.20/0.35 ifeq(ifeq(true, true, p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.35 ifeq(p2(f8(f8(c4, f9(c4)), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true, ifeq(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))), true), true)
% 0.20/0.35 = { by axiom 5 (p2_6) }
% 0.20/0.35 true
% 0.20/0.35 % SZS output end Proof
% 0.20/0.35
% 0.20/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------