%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% 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 09:37:27 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.32s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n009.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:37:00 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 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
% 0.19/0.32
% 0.19/0.32 % SZS status Unsatisfiable
% 0.19/0.32
% 0.19/0.33 % SZS output start Proof
% 0.19/0.33 Axiom 1 (diamond_trancl_2h1): diamond(r) = true.
% 0.19/0.33 Axiom 2 (trans_trancl): trans(trancl(X)) = true.
% 0.19/0.34 Axiom 3 (diamond_trancl_2c1): member(pair(y, yp), trancl(r)) = true.
% 0.19/0.34 Axiom 4 (diamond_trancl_2h3): member(pair(ya, z), r) = true.
% 0.19/0.34 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.34 Axiom 6 (r_into_trancl): ifeq(member(pair(X, Y), Z), true, member(pair(X, Y), trancl(Z)), true) = true.
% 0.19/0.34 Axiom 7 (diamond_trancl_2h5): ifeq(member(pair(y, X), trancl(r)), true, member(pair(X, sk1(X)), trancl(r)), true) = true.
% 0.19/0.34 Axiom 8 (diamond_trancl_2h4): ifeq(member(pair(y, X), trancl(r)), true, member(pair(ya, sk1(X)), trancl(r)), true) = true.
% 0.19/0.34 Axiom 9 (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.
% 0.19/0.34 Axiom 10 (diamond_strip_lemmaD1): ifeq(diamond(X), true, ifeq(member(pair(Y, Z), X), true, ifeq(member(pair(Y, W), trancl(X)), true, member(pair(Z, diamond_strip_lemmaD_sk1(Y, W, Z, X)), trancl(X)), true), true), true) = true.
% 0.19/0.34 Axiom 11 (diamond_strip_lemmaD2): ifeq(diamond(X), true, ifeq(member(pair(Y, Z), X), true, ifeq(member(pair(Y, W), trancl(X)), true, member(pair(W, diamond_strip_lemmaD_sk1(Y, W, Z, X)), X), true), true), true) = true.
% 0.19/0.34
% 0.19/0.34 Goal 1 (diamond_trancl_2c2): tuple(member(pair(z, X), trancl(r)), member(pair(yp, X), trancl(r))) = tuple(true, true).
% 0.19/0.34 The goal is true when:
% 0.19/0.34 X = diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)
% 0.19/0.34
% 0.19/0.34 Proof:
% 0.19/0.34 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(ifeq(true, true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 8 (diamond_trancl_2h4) R->L }
% 0.19/0.34 tuple(ifeq(ifeq(member(pair(y, yp), trancl(r)), true, member(pair(ya, sk1(yp)), trancl(r)), true), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 3 (diamond_trancl_2c1) }
% 0.19/0.34 tuple(ifeq(ifeq(true, true, member(pair(ya, sk1(yp)), trancl(r)), true), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.34 tuple(ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(ifeq(true, true, ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 1 (diamond_trancl_2h1) R->L }
% 0.19/0.34 tuple(ifeq(diamond(r), true, ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 4 (diamond_trancl_2h3) R->L }
% 0.19/0.34 tuple(ifeq(diamond(r), true, ifeq(member(pair(ya, z), r), true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 10 (diamond_strip_lemmaD1) }
% 0.19/0.34 tuple(true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(true, true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 6 (r_into_trancl) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(true, true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 8 (diamond_trancl_2h4) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(ifeq(member(pair(y, yp), trancl(r)), true, member(pair(ya, sk1(yp)), trancl(r)), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 3 (diamond_trancl_2c1) }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, member(pair(ya, sk1(yp)), trancl(r)), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(true, true, ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 1 (diamond_trancl_2h1) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(diamond(r), true, ifeq(true, true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 4 (diamond_trancl_2h3) R->L }
% 0.19/0.34 tuple(true, ifeq(ifeq(ifeq(diamond(r), true, ifeq(member(pair(ya, z), r), true, ifeq(member(pair(ya, sk1(yp)), trancl(r)), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true), true), true), true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 11 (diamond_strip_lemmaD2) }
% 0.19/0.34 tuple(true, ifeq(ifeq(true, true, member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.34 tuple(true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(true, true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(true, ifeq(true, true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(true, true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true))
% 0.19/0.34 = { by axiom 2 (trans_trancl) R->L }
% 0.19/0.34 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(true, true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true))
% 0.19/0.34 = { by axiom 7 (diamond_trancl_2h5) R->L }
% 0.19/0.34 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(ifeq(member(pair(y, yp), trancl(r)), true, member(pair(yp, sk1(yp)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true))
% 0.19/0.34 = { by axiom 3 (diamond_trancl_2c1) }
% 0.19/0.34 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(ifeq(true, true, member(pair(yp, sk1(yp)), trancl(r)), true), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true))
% 0.19/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.35 tuple(true, ifeq(trans(trancl(r)), true, ifeq(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true, ifeq(member(pair(yp, sk1(yp)), trancl(r)), true, member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true), true), true))
% 0.19/0.35 = { by axiom 9 (transD) }
% 0.19/0.35 tuple(true, true)
% 0.19/0.35 % SZS output end Proof
% 0.19/0.35
% 0.19/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------