%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:37:27 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.30s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:40:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.30 Command-line arguments: --no-flatten-goal
% 0.22/0.30
% 0.22/0.30 % SZS status Unsatisfiable
% 0.22/0.30
% 0.22/0.31 % SZS output start Proof
% 0.22/0.31 Axiom 1 (trans_trancl): trans(trancl(X)) = true.
% 0.22/0.31 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.31 Axiom 3 (diamond_strip_lemmaD_2h4): member(pair(y, z), r) = true.
% 0.22/0.31 Axiom 4 (diamond_strip_lemmaD_2c1): member(pair(x, sk3), r) = true.
% 0.22/0.31 Axiom 5 (r_into_trancl): ifeq(member(pair(X, Y), Z), true, member(pair(X, Y), trancl(Z)), true) = true.
% 0.22/0.31 Axiom 6 (diamond_strip_lemmaD_2h5): ifeq(member(pair(x, X), r), true, member(pair(X, sk2(X)), trancl(r)), true) = true.
% 0.22/0.31 Axiom 7 (diamond_strip_lemmaD_2h6): ifeq(member(pair(x, X), r), true, member(pair(y, sk2(X)), r), true) = true.
% 0.22/0.31 Axiom 8 (diamond_strip_lemmaD_2h2): ifeq(member(pair(X, Y), r), true, ifeq(member(pair(X, Z), r), true, member(pair(Y, sk1(X, Z, Y)), r), true), true) = true.
% 0.22/0.31 Axiom 9 (diamond_strip_lemmaD_2h1): ifeq(member(pair(X, Y), r), true, ifeq(member(pair(X, Z), r), true, member(pair(Z, sk1(X, Z, Y)), r), true), true) = true.
% 0.22/0.31 Axiom 10 (transD): ifeq(trans(X), true, ifeq(member(pair(Y, Z), X), true, ifeq(member(pair(W, Y), X), true, member(pair(W, Z), X), true), true), true) = true.
% 0.22/0.31
% 0.22/0.31 Goal 1 (diamond_strip_lemmaD_2c2): tuple(member(pair(z, X), r), member(pair(sk3, X), trancl(r))) = tuple(true, true).
% 0.22/0.31 The goal is true when:
% 0.22/0.31 X = sk1(y, sk2(sk3), z)
% 0.22/0.31
% 0.22/0.31 Proof:
% 0.22/0.31 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(ifeq(true, true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 7 (diamond_strip_lemmaD_2h6) R->L }
% 0.22/0.31 tuple(ifeq(ifeq(member(pair(x, sk3), r), true, member(pair(y, sk2(sk3)), r), true), true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 4 (diamond_strip_lemmaD_2c1) }
% 0.22/0.31 tuple(ifeq(ifeq(true, true, member(pair(y, sk2(sk3)), r), true), true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.31 tuple(ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(ifeq(true, true, ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 3 (diamond_strip_lemmaD_2h4) R->L }
% 0.22/0.31 tuple(ifeq(member(pair(y, z), r), true, ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(z, sk1(y, sk2(sk3), z)), r), true), true), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 8 (diamond_strip_lemmaD_2h2) }
% 0.22/0.31 tuple(true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(true, ifeq(true, true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 5 (r_into_trancl) R->L }
% 0.22/0.31 tuple(true, ifeq(ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(true, true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 7 (diamond_strip_lemmaD_2h6) R->L }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(ifeq(member(pair(x, sk3), r), true, member(pair(y, sk2(sk3)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 4 (diamond_strip_lemmaD_2c1) }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, member(pair(y, sk2(sk3)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(true, true, ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 3 (diamond_strip_lemmaD_2h4) R->L }
% 0.22/0.31 tuple(true, ifeq(ifeq(ifeq(member(pair(y, z), r), true, ifeq(member(pair(y, sk2(sk3)), r), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true), true), true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 9 (diamond_strip_lemmaD_2h1) }
% 0.22/0.31 tuple(true, ifeq(ifeq(true, true, member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.31 tuple(true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(true, true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.31 tuple(true, ifeq(true, true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(true, true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true), true))
% 0.22/0.31 = { by axiom 1 (trans_trancl) R->L }
% 0.22/0.31 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(true, true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true), true))
% 0.22/0.31 = { by axiom 6 (diamond_strip_lemmaD_2h5) R->L }
% 0.22/0.31 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(ifeq(member(pair(x, sk3), r), true, member(pair(sk3, sk2(sk3)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true), true))
% 0.22/0.31 = { by axiom 4 (diamond_strip_lemmaD_2c1) }
% 0.22/0.31 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(ifeq(true, true, member(pair(sk3, sk2(sk3)), trancl(r)), true), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true), true))
% 0.22/0.31 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.31 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true, ifeq(member(pair(sk3, sk2(sk3)), trancl(r)), true, member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)), true), true), true))
% 0.22/0.31 = { by axiom 10 (transD) }
% 0.22/0.31 tuple(true, true)
% 0.22/0.31 % SZS output end Proof
% 0.22/0.31
% 0.22/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------