%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN629-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:48:12 PM UTC 2026
% Result : Unsatisfiable 31.26s 4.21s
% Output : Proof 31.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN629-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n009.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 16:37:45 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.26/4.21 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
% 31.26/4.21
% 31.26/4.21 % SZS status Unsatisfiable
% 31.26/4.21
% 31.26/4.23 % SZS output start Proof
% 31.26/4.23 Axiom 1 (p9_2): p9(X, X) = true.
% 31.26/4.23 Axiom 2 (p9_6): p9(c28, c26) = true.
% 31.26/4.23 Axiom 3 (p2_1): p2(X, X) = true.
% 31.26/4.23 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 31.26/4.23 Axiom 5 (p9_13): ifeq(p9(X, Y), true, p9(f16(X), f16(Y)), true) = true.
% 31.26/4.23 Axiom 6 (p20_34): p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))) = true.
% 31.26/4.23 Axiom 7 (p9_29): ifeq(p9(X, Y), true, ifeq(p9(Z, W), true, p9(f17(Z, X), f17(W, Y)), true), true) = true.
% 31.26/4.23 Axiom 8 (p9_31): ifeq(p9(X, Y), true, ifeq(p9(Z, W), true, p9(f10(Z, X), f10(W, Y)), true), true) = true.
% 31.26/4.23 Axiom 9 (p9_30): ifeq(p9(X, Y), true, ifeq(p2(Z, W), true, p9(f15(Z, X), f15(W, Y)), true), true) = true.
% 31.26/4.23 Axiom 10 (p20_26): ifeq(p20(X, Y), true, ifeq(p9(Y, Z), true, ifeq(p9(X, W), true, p20(W, Z), true), true), true) = true.
% 31.26/4.23
% 31.26/4.23 Goal 1 (not_p20_35): p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))) = true.
% 31.26/4.23 Proof:
% 31.26/4.23 p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29))))))
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.23 ifeq(true, true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 8 (p9_31) R->L }
% 31.26/4.23 ifeq(ifeq(p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29))))), true, ifeq(p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 1 (p9_2) }
% 31.26/4.23 ifeq(ifeq(true, true, ifeq(p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.23 ifeq(ifeq(p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.23 ifeq(ifeq(ifeq(true, true, p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 2 (p9_6) R->L }
% 31.26/4.23 ifeq(ifeq(ifeq(p9(c28, c26), true, p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.23 ifeq(ifeq(ifeq(p9(c28, c26), true, ifeq(true, true, p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true), true), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 3 (p2_1) R->L }
% 31.26/4.23 ifeq(ifeq(ifeq(p9(c28, c26), true, ifeq(p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25))), true, p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c26)), true), true), true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 9 (p9_30) }
% 31.26/4.23 ifeq(ifeq(true, true, p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.23 ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.23 ifeq(true, true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 10 (p20_26) R->L }
% 31.26/4.23 ifeq(ifeq(p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 1 (p9_2) }
% 31.26/4.23 ifeq(ifeq(p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(true, true, ifeq(p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.23 ifeq(ifeq(p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 6 (p20_34) }
% 31.26/4.23 ifeq(ifeq(true, true, ifeq(p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.23 ifeq(ifeq(p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.23 ifeq(ifeq(ifeq(true, true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.23 = { by axiom 7 (p9_29) R->L }
% 31.26/4.24 ifeq(ifeq(ifeq(ifeq(p9(c27, c27), true, ifeq(p9(c28, c26), true, p9(f17(c28, c27), f17(c26, c27)), true), true), true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 1 (p9_2) }
% 31.26/4.24 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p9(c28, c26), true, p9(f17(c28, c27), f17(c26, c27)), true), true), true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.24 ifeq(ifeq(ifeq(ifeq(p9(c28, c26), true, p9(f17(c28, c27), f17(c26, c27)), true), true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 2 (p9_6) }
% 31.26/4.24 ifeq(ifeq(ifeq(ifeq(true, true, p9(f17(c28, c27), f17(c26, c27)), true), true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.24 ifeq(ifeq(ifeq(p9(f17(c28, c27), f17(c26, c27)), true, p9(f16(f17(c28, c27)), f16(f17(c26, c27))), true), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 5 (p9_13) }
% 31.26/4.24 ifeq(ifeq(true, true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 4 (ifeq_axiom) }
% 31.26/4.24 ifeq(p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true)
% 31.26/4.24 = { by axiom 4 (ifeq_axiom) R->L }
% 31.26/4.24 ifeq(p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, ifeq(true, true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true), true)
% 31.26/4.24 = { by axiom 1 (p9_2) R->L }
% 31.26/4.24 ifeq(p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true, ifeq(p9(f16(f17(c26, c27)), f16(f17(c26, c27))), true, p20(f16(f17(c26, c27)), f10(f15(f7(c23, f8(c24, c25)), c26), f11(f12(f13(f14(c29)))))), true), true), true)
% 31.26/4.24 = { by axiom 10 (p20_26) }
% 31.26/4.24 true
% 31.26/4.24 % SZS output end Proof
% 31.26/4.24
% 31.26/4.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------