TSTP Solution File: COL027-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL027-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n029.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 : Wed Aug 30 18:31:41 EDT 2023
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL027-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 05:37:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.40
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 Axiom 1 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.18/0.40 Axiom 2 (h_definition): apply(apply(apply(h, X), Y), Z) = apply(apply(apply(X, Y), Z), Y).
% 0.18/0.40
% 0.18/0.40 Goal 1 (prove_fixed_point): X = apply(combinator, X).
% 0.18/0.40 The goal is true when:
% 0.18/0.40 X = apply(apply(apply(h, apply(b, apply(b, combinator))), apply(h, apply(b, apply(b, combinator)))), apply(h, apply(b, apply(b, combinator))))
% 0.18/0.40
% 0.18/0.40 Proof:
% 0.18/0.40 apply(apply(apply(h, apply(b, apply(b, combinator))), apply(h, apply(b, apply(b, combinator)))), apply(h, apply(b, apply(b, combinator))))
% 0.18/0.40 = { by axiom 2 (h_definition) }
% 0.18/0.40 apply(apply(apply(apply(b, apply(b, combinator)), apply(h, apply(b, apply(b, combinator)))), apply(h, apply(b, apply(b, combinator)))), apply(h, apply(b, apply(b, combinator))))
% 0.18/0.40 = { by axiom 1 (b_definition) }
% 0.18/0.40 apply(apply(apply(b, combinator), apply(apply(h, apply(b, apply(b, combinator))), apply(h, apply(b, apply(b, combinator))))), apply(h, apply(b, apply(b, combinator))))
% 0.18/0.40 = { by axiom 1 (b_definition) }
% 0.18/0.40 apply(combinator, apply(apply(apply(h, apply(b, apply(b, combinator))), apply(h, apply(b, apply(b, combinator)))), apply(h, apply(b, apply(b, combinator)))))
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40
% 0.18/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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