TSTP Solution File: COL001-1 by Twee---2.5.0
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% File : Twee---2.5.0
% Problem : COL001-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 04:50:03 EDT 2024
% Result : Unsatisfiable 2.43s 0.71s
% Output : Proof 2.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL001-1 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Jun 18 16:30:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 2.43/0.71 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.43/0.71
% 2.43/0.71 % SZS status Unsatisfiable
% 2.43/0.71
% 2.43/0.71 % SZS output start Proof
% 2.43/0.71 Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 2.43/0.71 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 2.43/0.71
% 2.43/0.71 Goal 1 (prove_fixed_point): X = apply(combinator, X).
% 2.43/0.71 The goal is true when:
% 2.43/0.71 X = apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
% 2.43/0.71
% 2.43/0.71 Proof:
% 2.43/0.71 apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
% 2.43/0.71 = { by axiom 2 (s_definition) }
% 2.43/0.71 apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(k, apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))), apply(X, apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
% 2.43/0.71 = { by axiom 1 (k_definition) }
% 2.43/0.71 apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))
% 2.43/0.71 = { by axiom 2 (s_definition) }
% 2.43/0.71 apply(apply(apply(s, apply(k, combinator)), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
% 2.43/0.71 = { by axiom 2 (s_definition) }
% 2.43/0.71 apply(apply(apply(k, combinator), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))), apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
% 2.43/0.71 = { by axiom 1 (k_definition) }
% 2.43/0.71 apply(combinator, apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
% 2.43/0.71 % SZS output end Proof
% 2.43/0.71
% 2.43/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
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