TSTP Solution File: COL004-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL004-1 : 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 : n025.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 18:31:35 EDT 2023
% Result : Unsatisfiable 20.25s 2.95s
% Output : Proof 20.25s
% 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 : COL004-1 : 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
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 04:10:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.25/2.95 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 20.25/2.95
% 20.25/2.95 % SZS status Unsatisfiable
% 20.25/2.95
% 20.25/2.96 % SZS output start Proof
% 20.25/2.96 Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 20.25/2.96 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 20.25/2.96
% 20.25/2.96 Lemma 3: apply(apply(apply(s, k), X), Y) = Y.
% 20.25/2.96 Proof:
% 20.25/2.96 apply(apply(apply(s, k), X), Y)
% 20.25/2.96 = { by axiom 2 (s_definition) }
% 20.25/2.96 apply(apply(k, Y), apply(X, Y))
% 20.25/2.96 = { by axiom 1 (k_definition) }
% 20.25/2.96 Y
% 20.25/2.96
% 20.25/2.96 Goal 1 (prove_u_combinator): apply(apply(X, f(X)), g(X)) = apply(g(X), apply(apply(f(X), f(X)), g(X))).
% 20.25/2.96 The goal is true when:
% 20.25/2.96 X = apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))
% 20.25/2.96
% 20.25/2.96 Proof:
% 20.25/2.96 apply(apply(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by axiom 2 (s_definition) }
% 20.25/2.96 apply(apply(apply(apply(k, apply(s, apply(apply(s, k), X))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), apply(apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by axiom 1 (k_definition) }
% 20.25/2.96 apply(apply(apply(s, apply(apply(s, k), X)), apply(apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by axiom 2 (s_definition) }
% 20.25/2.96 apply(apply(apply(s, apply(apply(s, k), X)), apply(apply(apply(apply(s, k), Y), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), apply(apply(apply(s, k), Z), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by lemma 3 }
% 20.25/2.96 apply(apply(apply(s, apply(apply(s, k), X)), apply(apply(apply(apply(s, k), Y), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by lemma 3 }
% 20.25/2.96 apply(apply(apply(s, apply(apply(s, k), X)), apply(f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))))
% 20.25/2.96 = { by axiom 2 (s_definition) }
% 20.25/2.96 apply(apply(apply(apply(s, k), X), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), apply(apply(f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))))
% 20.25/2.96 = { by lemma 3 }
% 20.25/2.96 apply(g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))), apply(apply(f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)))), f(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))), g(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z))))))
% 20.25/2.96 % SZS output end Proof
% 20.25/2.96
% 20.25/2.96 RESULT: Unsatisfiable (the axioms are contradictory).
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