%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN175-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 01:47:14 PM UTC 2026
% Result : Unsatisfiable 5.16s 0.92s
% Output : Proof 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN175-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n005.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 15:37:46 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/0.92 Command-line arguments: --flatten --complete-subsets
% 5.16/0.92
% 5.16/0.92 % SZS status Unsatisfiable
% 5.16/0.92
% 5.16/0.92 % SZS output start Proof
% 5.16/0.92 Axiom 1 (axiom_13): r0(e) = true.
% 5.16/0.92 Axiom 2 (axiom_1): s0(d) = true.
% 5.16/0.92 Axiom 3 (axiom_17): q0(X, d) = true.
% 5.16/0.92 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.16/0.92 Axiom 5 (rule_045): ifeq(q0(d, d), true, n1(d, d, d), true) = true.
% 5.16/0.92 Axiom 6 (rule_178): ifeq(n1(X, Y, Z), true, ifeq(q0(X, Y), true, q2(Y, Y, Y), true), true) = true.
% 5.16/0.92
% 5.16/0.92 Lemma 7: s0(d) = r0(e).
% 5.16/0.92 Proof:
% 5.16/0.92 s0(d)
% 5.16/0.92 = { by axiom 2 (axiom_1) }
% 5.16/0.92 true
% 5.16/0.92 = { by axiom 1 (axiom_13) R->L }
% 5.16/0.92 r0(e)
% 5.16/0.92
% 5.16/0.92 Lemma 8: q0(X, d) = s0(d).
% 5.16/0.92 Proof:
% 5.16/0.92 q0(X, d)
% 5.16/0.92 = { by axiom 3 (axiom_17) }
% 5.16/0.92 true
% 5.16/0.92 = { by axiom 1 (axiom_13) R->L }
% 5.16/0.92 r0(e)
% 5.16/0.92 = { by lemma 7 R->L }
% 5.16/0.92 s0(d)
% 5.16/0.92
% 5.16/0.92 Goal 1 (prove_this): q2(X, d, Y) = true.
% 5.16/0.92 The goal is true when:
% 5.16/0.92 X = d
% 5.16/0.92 Y = d
% 5.16/0.92
% 5.16/0.92 Proof:
% 5.16/0.92 q2(d, d, d)
% 5.16/0.92 = { by axiom 4 (ifeq_axiom) R->L }
% 5.16/0.92 ifeq(s0(d), s0(d), q2(d, d, d), s0(d))
% 5.16/0.92 = { by lemma 8 R->L }
% 5.16/0.92 ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d))
% 5.16/0.92 = { by axiom 4 (ifeq_axiom) R->L }
% 5.16/0.92 ifeq(s0(d), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 ifeq(r0(e), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 ifeq(true, s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by axiom 5 (rule_045) R->L }
% 5.16/0.92 ifeq(ifeq(q0(d, d), true, n1(d, d, d), true), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 8 }
% 5.16/0.92 ifeq(ifeq(s0(d), true, n1(d, d, d), true), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by axiom 1 (axiom_13) R->L }
% 5.16/0.92 ifeq(ifeq(s0(d), true, n1(d, d, d), r0(e)), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by axiom 1 (axiom_13) R->L }
% 5.16/0.92 ifeq(ifeq(s0(d), r0(e), n1(d, d, d), r0(e)), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 R->L }
% 5.16/0.92 ifeq(ifeq(s0(d), r0(e), n1(d, d, d), s0(d)), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 R->L }
% 5.16/0.92 ifeq(ifeq(s0(d), s0(d), n1(d, d, d), s0(d)), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by axiom 4 (ifeq_axiom) }
% 5.16/0.92 ifeq(n1(d, d, d), s0(d), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 ifeq(n1(d, d, d), r0(e), ifeq(q0(d, d), s0(d), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 ifeq(n1(d, d, d), r0(e), ifeq(q0(d, d), r0(e), q2(d, d, d), s0(d)), s0(d))
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 ifeq(n1(d, d, d), r0(e), ifeq(q0(d, d), r0(e), q2(d, d, d), r0(e)), s0(d))
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 ifeq(n1(d, d, d), r0(e), ifeq(q0(d, d), r0(e), q2(d, d, d), r0(e)), r0(e))
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 ifeq(n1(d, d, d), true, ifeq(q0(d, d), r0(e), q2(d, d, d), r0(e)), r0(e))
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 ifeq(n1(d, d, d), true, ifeq(q0(d, d), true, q2(d, d, d), r0(e)), r0(e))
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 ifeq(n1(d, d, d), true, ifeq(q0(d, d), true, q2(d, d, d), true), r0(e))
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 ifeq(n1(d, d, d), true, ifeq(q0(d, d), true, q2(d, d, d), true), true)
% 5.16/0.92 = { by axiom 6 (rule_178) }
% 5.16/0.92 true
% 5.16/0.92 = { by axiom 1 (axiom_13) R->L }
% 5.16/0.92 r0(e)
% 5.16/0.92 = { by lemma 7 R->L }
% 5.16/0.92 s0(d)
% 5.16/0.92 = { by lemma 7 }
% 5.16/0.92 r0(e)
% 5.16/0.92 = { by axiom 1 (axiom_13) }
% 5.16/0.92 true
% 5.16/0.92 % SZS output end Proof
% 5.16/0.92
% 5.16/0.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------