TSTP Solution File: COL039-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL039-1 : 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 : n015.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 18:31:44 EDT 2023
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 05:06:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.39 Command-line arguments: --ground-connectedness --complete-subsets
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39
% 0.13/0.39 % SZS output start Proof
% 0.13/0.40 Axiom 1 (m_definition): apply(m, X) = apply(X, X).
% 0.13/0.40 Axiom 2 (o_definition): apply(apply(o, X), Y) = apply(Y, apply(X, Y)).
% 0.13/0.40 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.13/0.40
% 0.13/0.40 Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
% 0.13/0.40 The goal is true when:
% 0.13/0.40 X = apply(m, apply(apply(b, o), m))
% 0.13/0.40
% 0.13/0.40 Proof:
% 0.13/0.40 apply(apply(m, apply(apply(b, o), m)), f(apply(m, apply(apply(b, o), m))))
% 0.13/0.40 = { by axiom 1 (m_definition) }
% 0.13/0.40 apply(apply(apply(apply(b, o), m), apply(apply(b, o), m)), f(apply(m, apply(apply(b, o), m))))
% 0.13/0.40 = { by axiom 3 (b_definition) }
% 0.13/0.40 apply(apply(o, apply(m, apply(apply(b, o), m))), f(apply(m, apply(apply(b, o), m))))
% 0.13/0.40 = { by axiom 2 (o_definition) }
% 0.13/0.40 apply(f(apply(m, apply(apply(b, o), m))), apply(apply(m, apply(apply(b, o), m)), f(apply(m, apply(apply(b, o), m)))))
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40
% 0.13/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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