%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.08s 0.26s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:36:55 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 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
% 0.08/0.26
% 0.08/0.26 % SZS status Unsatisfiable
% 0.08/0.26
% 0.08/0.26 % SZS output start Proof
% 0.08/0.26 Axiom 1 (k_definition): apply(k(X), Y) = X.
% 0.08/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.26 Axiom 3 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, k(Z)), apply(Y, Z)).
% 0.19/0.26 Axiom 4 (extensionality2): ifeq(apply(X, n(X, Y)), apply(Y, n(X, Y)), X, Y) = Y.
% 0.19/0.26
% 0.19/0.26 Lemma 5: ifeq(X, apply(Y, n(k(X), Y)), k(X), Y) = Y.
% 0.19/0.26 Proof:
% 0.19/0.26 ifeq(X, apply(Y, n(k(X), Y)), k(X), Y)
% 0.19/0.26 = { by axiom 1 (k_definition) R->L }
% 0.19/0.26 ifeq(apply(k(X), n(k(X), Y)), apply(Y, n(k(X), Y)), k(X), Y)
% 0.19/0.26 = { by axiom 4 (extensionality2) }
% 0.19/0.26 Y
% 0.19/0.26
% 0.19/0.26 Goal 1 (prove_TRC2c): k(k(b)) = apply(abstraction, k(k(b))).
% 0.19/0.26 Proof:
% 0.19/0.26 k(k(b))
% 0.19/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.26 ifeq(k(b), k(b), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.27 ifeq(k(b), ifeq(b, b, k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.27 = { by axiom 1 (k_definition) R->L }
% 0.19/0.27 ifeq(k(b), ifeq(b, apply(k(b), apply(n(k(k(b)), apply(abstraction, k(k(b)))), n(k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))))), k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.27 = { by axiom 1 (k_definition) R->L }
% 0.19/0.27 ifeq(k(b), ifeq(b, apply(apply(k(k(b)), k(n(k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))))), apply(n(k(k(b)), apply(abstraction, k(k(b)))), n(k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))))), k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.27 = { by axiom 3 (abstraction) R->L }
% 0.19/0.27 ifeq(k(b), ifeq(b, apply(apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b))))), n(k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b))))))), k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b)))))), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.27 = { by lemma 5 }
% 0.19/0.27 ifeq(k(b), apply(apply(abstraction, k(k(b))), n(k(k(b)), apply(abstraction, k(k(b))))), k(k(b)), apply(abstraction, k(k(b))))
% 0.19/0.27 = { by lemma 5 }
% 0.19/0.27 apply(abstraction, k(k(b)))
% 0.19/0.27 % SZS output end Proof
% 0.19/0.27
% 0.19/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
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