TSTP Solution File: COL060-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL060-1 : 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 : n021.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 18:31:52 EDT 2023
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% 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 : COL060-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % 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 : n021.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 04:33:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
% 0.20/0.45 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.20/0.45
% 0.20/0.45 Goal 1 (prove_q_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(g(X), apply(f(X), h(X))).
% 0.20/0.45 The goal is true when:
% 0.20/0.45 X = apply(apply(b, apply(t, b)), apply(apply(b, b), t))
% 0.20/0.45
% 0.20/0.45 Proof:
% 0.20/0.45 apply(apply(apply(apply(apply(b, apply(t, b)), apply(apply(b, b), t)), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 2 (b_definition) }
% 0.20/0.45 apply(apply(apply(apply(t, b), apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 1 (t_definition) }
% 0.20/0.45 apply(apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), b), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 2 (b_definition) }
% 0.20/0.45 apply(apply(apply(apply(b, apply(t, f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), b), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 2 (b_definition) }
% 0.20/0.45 apply(apply(apply(t, f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), apply(b, g(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 1 (t_definition) }
% 0.20/0.45 apply(apply(apply(b, g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
% 0.20/0.45 = { by axiom 2 (b_definition) }
% 0.20/0.45 apply(g(apply(apply(b, apply(t, b)), apply(apply(b, b), t))), apply(f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))))
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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