%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN572-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 4.40s 0.83s
% Output : Proof 4.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN572-1 : 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 : n020.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 16:29:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.40/0.83 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
% 4.40/0.83
% 4.40/0.83 % SZS status Unsatisfiable
% 4.40/0.83
% 4.40/0.85 % SZS output start Proof
% 4.40/0.85 Axiom 1 (p2_1): p2(X, X) = true.
% 4.40/0.85 Axiom 2 (p4_3): p4(X, X) = true.
% 4.40/0.85 Axiom 3 (p4_4): p4(f10(f9(X)), f10(X)) = true.
% 4.40/0.85 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.40/0.85 Axiom 5 (p12_15): p12(f10(f3(X, Y)), f11(f10(X), f10(Y))) = true.
% 4.40/0.85 Axiom 6 (p2_5): p2(f3(X, f5(f7(f8(c13)))), X) = true.
% 4.40/0.85 Axiom 7 (p4_9): ifeq(p2(X, Y), true, p4(f10(X), f10(Y)), true) = true.
% 4.40/0.85 Axiom 8 (p2_11): p2(f3(X, f9(X)), f5(f7(f8(c13)))) = true.
% 4.40/0.85 Axiom 9 (p2_17): p2(f3(X, f3(Y, Z)), f3(f3(X, Y), Z)) = true.
% 4.40/0.85 Axiom 10 (p2_12): ifeq(p2(X, Y), true, ifeq(p2(X, Z), true, p2(Z, Y), true), true) = true.
% 4.40/0.85 Axiom 11 (p2_20): ifeq(p2(X, Y), true, ifeq(p2(Z, W), true, p2(f3(Z, X), f3(W, Y)), true), true) = true.
% 4.40/0.85 Axiom 12 (p4_19): ifeq(p4(X, Y), true, ifeq(p4(Z, W), true, p4(f11(Z, X), f11(W, Y)), true), true) = true.
% 4.40/0.86 Axiom 13 (p12_18): ifeq(p12(X, Y), true, ifeq(p4(Y, Z), true, ifeq(p4(X, W), true, p12(W, Z), true), true), true) = true.
% 4.40/0.86
% 4.40/0.86 Goal 1 (not_p12_16): p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))) = true.
% 4.40/0.86 Proof:
% 4.40/0.86 p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15)))
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(true, true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 7 (p4_9) R->L }
% 4.40/0.86 ifeq(ifeq(p2(f3(f3(c14, c15), f9(c15)), c14), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(true, true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 10 (p2_12) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(p2(f3(c14, f3(c15, f9(c15))), f3(f3(c14, c15), f9(c15))), true, ifeq(p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 9 (p2_17) }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 8 (p2_11) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c15, f9(c15)), f5(f7(f8(c13)))), true, p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c15, f9(c15)), f5(f7(f8(c13)))), true, ifeq(true, true, p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true), true), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 1 (p2_1) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(ifeq(p2(f3(c15, f9(c15)), f5(f7(f8(c13)))), true, ifeq(p2(c14, c14), true, p2(f3(c14, f3(c15, f9(c15))), f3(c14, f5(f7(f8(c13))))), true), true), true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 11 (p2_20) }
% 4.40/0.86 ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(ifeq(ifeq(p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 6 (p2_5) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(p2(f3(c14, f5(f7(f8(c13)))), c14), true, ifeq(p2(f3(c14, f5(f7(f8(c13)))), f3(f3(c14, c15), f9(c15))), true, p2(f3(f3(c14, c15), f9(c15)), c14), true), true), true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 10 (p2_12) }
% 4.40/0.86 ifeq(ifeq(true, true, p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(true, true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 13 (p12_18) R->L }
% 4.40/0.86 ifeq(ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(f9(c15)))), true, ifeq(p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(f3(f3(c14, c15), f9(c15)))), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 2 (p4_3) }
% 4.40/0.86 ifeq(ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(f9(c15)))), true, ifeq(p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(true, true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(f9(c15)))), true, ifeq(p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 5 (p12_15) }
% 4.40/0.86 ifeq(ifeq(true, true, ifeq(p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(ifeq(p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(true, true, p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 3 (p4_4) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(p4(f10(f9(c15)), f10(c15)), true, p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(p4(f10(f9(c15)), f10(c15)), true, ifeq(true, true, p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 2 (p4_3) R->L }
% 4.40/0.86 ifeq(ifeq(ifeq(p4(f10(f9(c15)), f10(c15)), true, ifeq(p4(f10(f3(c14, c15)), f10(f3(c14, c15))), true, p4(f11(f10(f3(c14, c15)), f10(f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true), true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 12 (p4_19) }
% 4.40/0.86 ifeq(ifeq(true, true, p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) }
% 4.40/0.86 ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true)
% 4.40/0.86 = { by axiom 4 (ifeq_axiom) R->L }
% 4.40/0.86 ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(true, true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true), true)
% 4.40/0.86 = { by axiom 2 (p4_3) R->L }
% 4.40/0.86 ifeq(p12(f10(f3(f3(c14, c15), f9(c15))), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(p4(f11(f10(f3(c14, c15)), f10(c15)), f11(f10(f3(c14, c15)), f10(c15))), true, ifeq(p4(f10(f3(f3(c14, c15), f9(c15))), f10(c14)), true, p12(f10(c14), f11(f10(f3(c14, c15)), f10(c15))), true), true), true)
% 4.40/0.86 = { by axiom 13 (p12_18) }
% 4.40/0.86 true
% 4.40/0.86 % SZS output end Proof
% 4.40/0.86
% 4.40/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------