TSTP Solution File: COL064-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL064-1 : 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 : n004.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 18:31:56 EDT 2023
% Result : Unsatisfiable 82.62s 10.99s
% Output : Proof 83.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL064-1 : 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
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 05:18:07 EDT 2023
% 0.11/0.33 % CPUTime :
% 82.62/10.99 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 82.62/10.99
% 82.62/10.99 % SZS status Unsatisfiable
% 82.62/10.99
% 82.62/11.00 % SZS output start Proof
% 82.62/11.00 Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
% 82.62/11.00 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 82.62/11.00
% 82.62/11.00 Goal 1 (prove_v_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(apply(h(X), f(X)), g(X)).
% 82.62/11.00 The goal is true when:
% 82.62/11.00 X = apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))
% 82.62/11.00
% 82.62/11.00 Proof:
% 82.62/11.00 apply(apply(apply(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 2 (b_definition) }
% 82.62/11.00 apply(apply(apply(apply(t, apply(apply(b, b), t)), apply(apply(apply(b, b), apply(apply(b, b), t)), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 1 (t_definition) }
% 82.62/11.00 apply(apply(apply(apply(apply(apply(b, b), apply(apply(b, b), t)), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), apply(apply(b, b), t)), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 2 (b_definition) }
% 82.62/11.00 apply(apply(apply(apply(b, apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), apply(apply(b, b), t)), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 2 (b_definition) }
% 82.62/11.00 apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 2 (b_definition) }
% 82.62/11.00 apply(apply(apply(b, apply(t, f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 82.62/11.00 = { by axiom 2 (b_definition) }
% 82.62/11.00 apply(apply(t, f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), apply(apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))))
% 82.62/11.00 = { by axiom 1 (t_definition) }
% 82.62/11.00 apply(apply(apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 83.24/11.00 = { by axiom 2 (b_definition) }
% 83.24/11.01 apply(apply(apply(b, apply(t, g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 83.24/11.01 = { by axiom 2 (b_definition) }
% 83.24/11.01 apply(apply(t, g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), apply(h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))))
% 83.24/11.01 = { by axiom 1 (t_definition) }
% 83.24/11.01 apply(apply(h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), apply(apply(b, b), t)))))
% 83.24/11.01 % SZS output end Proof
% 83.24/11.01
% 83.24/11.01 RESULT: Unsatisfiable (the axioms are contradictory).
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