TSTP Solution File: COL046-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL046-1 : 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 : n009.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 18:31:48 EDT 2023
% Result : Unsatisfiable 183.88s 24.93s
% Output : Proof 183.88s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : COL046-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 05:00:50 EDT 2023
% 0.10/0.31 % CPUTime :
% 183.88/24.93 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 183.88/24.93
% 183.88/24.93 % SZS status Unsatisfiable
% 183.88/24.93
% 183.88/24.94 % SZS output start Proof
% 183.88/24.94 Axiom 1 (m_definition): apply(m, X) = apply(X, X).
% 183.88/24.94 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 183.88/24.94 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 183.88/24.94
% 183.88/24.94 Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
% 183.88/24.94 The goal is true when:
% 183.88/24.94 X = apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)
% 183.88/24.94
% 183.88/24.94 Proof:
% 183.88/24.94 apply(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)))
% 183.88/24.94 = { by axiom 1 (m_definition) }
% 183.88/24.94 apply(apply(apply(s, apply(apply(apply(b, apply(s, b)), m), apply(apply(b, apply(s, b)), m))), X), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)))
% 183.88/24.94 = { by axiom 3 (b_definition) }
% 183.88/24.94 apply(apply(apply(s, apply(apply(s, b), apply(m, apply(apply(b, apply(s, b)), m)))), X), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)))
% 183.88/24.94 = { by axiom 2 (s_definition) }
% 183.88/24.94 apply(apply(apply(apply(s, b), apply(m, apply(apply(b, apply(s, b)), m))), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))), apply(X, f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))))
% 183.88/24.94 = { by axiom 2 (s_definition) }
% 183.88/24.94 apply(apply(apply(b, f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))), apply(apply(m, apply(apply(b, apply(s, b)), m)), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)))), apply(X, f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))))
% 183.88/24.94 = { by axiom 3 (b_definition) }
% 183.88/24.94 apply(f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)), apply(apply(apply(m, apply(apply(b, apply(s, b)), m)), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))), apply(X, f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)))))
% 183.88/24.94 = { by axiom 2 (s_definition) R->L }
% 183.88/24.94 apply(f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X)), apply(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X), f(apply(apply(s, apply(m, apply(apply(b, apply(s, b)), m))), X))))
% 183.88/24.94 % SZS output end Proof
% 183.88/24.94
% 183.88/24.94 RESULT: Unsatisfiable (the axioms are contradictory).
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