%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN178-1 : TPTP v9.3.1. Released v1.1.0.
% 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 01:47:15 PM UTC 2026
% Result : Unsatisfiable 7.30s 1.17s
% Output : Proof 7.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN178-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 15:33:06 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.30/1.17 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 7.30/1.17
% 7.30/1.17 % SZS status Unsatisfiable
% 7.30/1.17
% 7.30/1.18 % SZS output start Proof
% 7.30/1.18 Axiom 1 (axiom_1): s0(d) = true.
% 7.30/1.18 Axiom 2 (axiom_32): k0(b) = true.
% 7.30/1.18 Axiom 3 (axiom_14): p0(b, X) = true.
% 7.30/1.18 Axiom 4 (axiom_17): q0(X, d) = true.
% 7.30/1.18 Axiom 5 (axiom_7): n0(d, b) = true.
% 7.30/1.18 Axiom 6 (axiom_19): m0(X, d, Y) = true.
% 7.30/1.18 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.30/1.18 Axiom 8 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 7.30/1.18 Axiom 9 (rule_122): ifeq(m0(X, Y, X), true, q1(X, X, X), true) = true.
% 7.30/1.18 Axiom 10 (rule_177): ifeq(p1(X, X, X), true, ifeq(k0(Y), true, q2(X, Y, Y), true), true) = true.
% 7.30/1.18 Axiom 11 (rule_255): ifeq(q2(X, Y, Z), true, ifeq(n0(X, Y), true, q3(Y, Z), true), true) = true.
% 7.30/1.18 Axiom 12 (rule_124): ifeq(q1(d, X, d), true, ifeq(q0(Y, X), true, ifeq(s0(d), true, r1(Y), true), true), true) = true.
% 7.30/1.18 Axiom 13 (rule_187): ifeq(q2(X, X, X), true, ifeq(r1(X), true, ifeq(k0(X), true, ifeq(m0(Y, Z, W), true, q2(W, X, W), true), true), true), true) = true.
% 7.30/1.18
% 7.30/1.18 Goal 1 (prove_this): q3(b, d) = true.
% 7.30/1.18 Proof:
% 7.30/1.18 q3(b, d)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(true, true, q3(b, d), true)
% 7.30/1.18 = { by axiom 13 (rule_187) R->L }
% 7.30/1.18 ifeq(ifeq(q2(b, b, b), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(true, true, q2(b, b, b), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(true, true, ifeq(true, true, q2(b, b, b), true), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 8 (rule_085) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(ifeq(p0(b, b), true, p1(b, b, b), true), true, ifeq(true, true, q2(b, b, b), true), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 3 (axiom_14) }
% 7.30/1.18 ifeq(ifeq(ifeq(ifeq(true, true, p1(b, b, b), true), true, ifeq(true, true, q2(b, b, b), true), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(ifeq(ifeq(p1(b, b, b), true, ifeq(true, true, q2(b, b, b), true), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 2 (axiom_32) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(p1(b, b, b), true, ifeq(k0(b), true, q2(b, b, b), true), true), true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 10 (rule_177) }
% 7.30/1.18 ifeq(ifeq(true, true, ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(ifeq(r1(b), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(true, true, r1(b), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 4 (axiom_17) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(q0(b, d), true, r1(b), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(true, true, ifeq(q0(b, d), true, r1(b), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 9 (rule_122) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, q1(d, d, d), true), true, ifeq(q0(b, d), true, r1(b), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 6 (axiom_19) }
% 7.30/1.18 ifeq(ifeq(ifeq(ifeq(true, true, q1(d, d, d), true), true, ifeq(q0(b, d), true, r1(b), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(b, d), true, r1(b), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(b, d), true, ifeq(true, true, r1(b), true), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 1 (axiom_1) R->L }
% 7.30/1.18 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(b, d), true, ifeq(s0(d), true, r1(b), true), true), true), true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 12 (rule_124) }
% 7.30/1.18 ifeq(ifeq(true, true, ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(ifeq(k0(b), true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 2 (axiom_32) }
% 7.30/1.18 ifeq(ifeq(true, true, ifeq(m0(X, d, d), true, q2(d, b, d), true), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(ifeq(m0(X, d, d), true, q2(d, b, d), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 6 (axiom_19) }
% 7.30/1.18 ifeq(ifeq(true, true, q2(d, b, d), true), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) }
% 7.30/1.18 ifeq(q2(d, b, d), true, q3(b, d), true)
% 7.30/1.18 = { by axiom 7 (ifeq_axiom) R->L }
% 7.30/1.18 ifeq(q2(d, b, d), true, ifeq(true, true, q3(b, d), true), true)
% 7.30/1.18 = { by axiom 5 (axiom_7) R->L }
% 7.30/1.18 ifeq(q2(d, b, d), true, ifeq(n0(d, b), true, q3(b, d), true), true)
% 7.30/1.18 = { by axiom 11 (rule_255) }
% 7.30/1.18 true
% 7.30/1.18 % SZS output end Proof
% 7.30/1.18
% 7.30/1.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------