%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN569-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.20s 0.35s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN569-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n017.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 16:24:21 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.35 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.35
% 0.20/0.35 % SZS status Unsatisfiable
% 0.20/0.35
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 Axiom 1 (p2_1): p2(X, X) = true.
% 0.20/0.37 Axiom 2 (p8_5): p8(c11, c14) = true.
% 0.20/0.37 Axiom 3 (p8_3): p8(c14, c12) = true.
% 0.20/0.37 Axiom 4 (p9_6): p9(c13, c15, c14) = true.
% 0.20/0.37 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.37 Axiom 6 (p10_7): ifeq(p8(X, Y), true, p10(X, Y), true) = true.
% 0.20/0.37 Axiom 7 (p2_15): p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)) = true.
% 0.20/0.37 Axiom 8 (p2_10): ifeq(p2(X, Y), true, ifeq(p2(X, Z), true, p2(Z, Y), true), true) = true.
% 0.20/0.37 Axiom 9 (p9_12): ifeq(p10(c11, X), true, ifeq(p10(X, c12), true, p9(c13, f3(X), X), true), true) = true.
% 0.20/0.37 Axiom 10 (p2_11): ifeq(p9(X, Y, Z), true, ifeq(p9(X, W, Z), true, p2(W, Y), true), true) = true.
% 0.20/0.37 Axiom 11 (p2_16): ifeq(p2(X, Y), true, ifeq(p2(Z, W), true, p2(f4(Z, X), f4(W, Y)), true), true) = true.
% 0.20/0.37
% 0.20/0.37 Goal 1 (not_p8_20): tuple(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X))), p8(X, c12), p8(c11, X)) = tuple(true, true, true).
% 0.20/0.37 The goal is true when:
% 0.20/0.37 X = c14
% 0.20/0.37
% 0.20/0.37 Proof:
% 0.20/0.37 tuple(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.37 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.37 tuple(ifeq(true, true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.37 = { by axiom 11 (p2_16) R->L }
% 0.20/0.37 tuple(ifeq(ifeq(p2(c15, f3(c14)), true, ifeq(p2(f5(c12, c11), f5(c12, c11)), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.37 = { by axiom 1 (p2_1) }
% 0.20/0.37 tuple(ifeq(ifeq(p2(c15, f3(c14)), true, ifeq(true, true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(ifeq(p2(c15, f3(c14)), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(true, true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 10 (p2_11) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(p9(c13, c15, c14), true, ifeq(p9(c13, f3(c14), c14), true, p2(f3(c14), c15), true), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 4 (p9_6) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p9(c13, f3(c14), c14), true, p2(f3(c14), c15), true), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(p9(c13, f3(c14), c14), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p9(c13, f3(c14), c14), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 6 (p10_7) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p8(c11, c14), true, p10(c11, c14), true), true, ifeq(true, true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 2 (p8_5) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p10(c11, c14), true), true, ifeq(true, true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p10(c11, c14), true, ifeq(true, true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 6 (p10_7) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p10(c11, c14), true, ifeq(ifeq(p8(c14, c12), true, p10(c14, c12), true), true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 3 (p8_3) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p10(c11, c14), true, ifeq(ifeq(true, true, p10(c14, c12), true), true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p10(c11, c14), true, ifeq(p10(c14, c12), true, p9(c13, f3(c14), c14), true), true), true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 9 (p9_12) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c14), c15), true), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(p2(f3(c14), c15), true, p2(c15, f3(c14)), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c14), c15), true, p2(c15, f3(c14)), true), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 1 (p2_1) R->L }
% 0.20/0.38 tuple(ifeq(ifeq(ifeq(p2(f3(c14), f3(c14)), true, ifeq(p2(f3(c14), c15), true, p2(c15, f3(c14)), true), true), true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 8 (p2_10) }
% 0.20/0.38 tuple(ifeq(ifeq(true, true, p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(true, true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 8 (p2_10) R->L }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(ifeq(p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11))), true, ifeq(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), true, p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), true), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 1 (p2_1) }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(ifeq(true, true, ifeq(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), true, p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), true), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(ifeq(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), true, p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 7 (p2_15) }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(ifeq(true, true, p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), true), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 5 (ifeq_axiom) }
% 0.20/0.38 tuple(ifeq(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), true, ifeq(p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), true, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), true), true), p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 8 (p2_10) }
% 0.20/0.38 tuple(true, p8(c14, c12), p8(c11, c14))
% 0.20/0.38 = { by axiom 3 (p8_3) }
% 0.20/0.38 tuple(true, true, p8(c11, c14))
% 0.20/0.38 = { by axiom 2 (p8_5) }
% 0.20/0.38 tuple(true, true, true)
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38
% 0.20/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------