%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:37:24 AM UTC 2026
% Result : Unsatisfiable 0.05s 0.25s
% Output : Proof 0.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.18 % Computer : n013.cluster.edu
% 0.05/0.18 % Model : x86_64 x86_64
% 0.05/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.18 % Memory : 8046.5625MB
% 0.05/0.18 % OS : Linux 6.8.0-71-generic
% 0.05/0.18 % CPULimit : 300
% 0.05/0.18 % WCLimit : 300
% 0.05/0.18 % DateTime : Mon Sep 28 21:34:06 UTC 2026
% 0.05/0.18 % CPUTime :
% 0.05/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.25 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
% 0.05/0.25
% 0.05/0.25 % SZS status Unsatisfiable
% 0.05/0.25
% 0.05/0.25 % SZS output start Proof
% 0.05/0.25 Axiom 1 (k_definition): apply(k(X), Y) = X.
% 0.05/0.25 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.05/0.25 Axiom 3 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, k(Z)), apply(Y, Z)).
% 0.05/0.25 Axiom 4 (extensionality2): ifeq(apply(X, n(X, Y)), apply(Y, n(X, Y)), X, Y) = Y.
% 0.05/0.25
% 0.05/0.25 Goal 1 (prove_TRC2a): apply(abstraction, apply(abstraction, apply(abstraction, b))) = apply(abstraction, b).
% 0.05/0.25 Proof:
% 0.05/0.25 apply(abstraction, apply(abstraction, apply(abstraction, b)))
% 0.05/0.25 = { by axiom 4 (extensionality2) R->L }
% 0.05/0.25 ifeq(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.05/0.25 ifeq(ifeq(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.25 = { by axiom 3 (abstraction) }
% 0.05/0.25 ifeq(ifeq(apply(apply(apply(abstraction, apply(abstraction, b)), k(n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.25 = { by axiom 3 (abstraction) }
% 0.05/0.25 ifeq(ifeq(apply(apply(apply(abstraction, b), k(apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))))), apply(k(n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.25 = { by axiom 1 (k_definition) }
% 0.05/0.25 ifeq(ifeq(apply(apply(apply(abstraction, b), k(apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.26 = { by axiom 3 (abstraction) }
% 0.05/0.26 ifeq(ifeq(apply(apply(b, k(n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(k(apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.26 = { by axiom 1 (k_definition) }
% 0.05/0.26 ifeq(ifeq(apply(apply(b, k(n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.26 = { by axiom 3 (abstraction) R->L }
% 0.05/0.26 ifeq(ifeq(apply(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), n(apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))))), apply(apply(abstraction, b), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.26 = { by axiom 4 (extensionality2) }
% 0.05/0.26 ifeq(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))), apply(abstraction, b), apply(abstraction, apply(abstraction, apply(abstraction, b))))
% 0.05/0.26 = { by axiom 2 (ifeq_axiom) }
% 0.05/0.26 apply(abstraction, b)
% 0.05/0.26 % SZS output end Proof
% 0.05/0.26
% 0.05/0.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------