TSTP Solution File: COL006-1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : COL006-1 : 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 : n023.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 18:31:36 EDT 2023
% Result : Unsatisfiable 6.79s 1.28s
% Output : Proof 7.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % 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 : n023.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 05:14:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 6.79/1.28 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.79/1.28
% 6.79/1.28 % SZS status Unsatisfiable
% 6.79/1.28
% 7.43/1.28 % SZS output start Proof
% 7.43/1.28 Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 7.43/1.28 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 7.43/1.28
% 7.43/1.28 Lemma 3: apply(apply(apply(s, k), X), Y) = Y.
% 7.43/1.28 Proof:
% 7.43/1.28 apply(apply(apply(s, k), X), Y)
% 7.43/1.28 = { by axiom 2 (s_definition) }
% 7.43/1.28 apply(apply(k, Y), apply(X, Y))
% 7.43/1.28 = { by axiom 1 (k_definition) }
% 7.43/1.28 Y
% 7.43/1.28
% 7.43/1.28 Lemma 4: apply(apply(apply(s, apply(s, k)), X), Y) = apply(X, Y).
% 7.43/1.28 Proof:
% 7.43/1.28 apply(apply(apply(s, apply(s, k)), X), Y)
% 7.43/1.28 = { by axiom 2 (s_definition) }
% 7.43/1.28 apply(apply(apply(s, k), Y), apply(X, Y))
% 7.43/1.28 = { by lemma 3 }
% 7.43/1.28 apply(X, Y)
% 7.43/1.28
% 7.43/1.28 Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
% 7.43/1.28 The goal is true when:
% 7.43/1.28 X = apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))
% 7.43/1.28
% 7.43/1.28 Proof:
% 7.43/1.28 apply(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.28 = { by lemma 4 }
% 7.43/1.28 apply(apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.28 = { by axiom 2 (s_definition) }
% 7.43/1.28 apply(apply(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), apply(apply(apply(s, k), Y), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.28 = { by lemma 3 }
% 7.43/1.28 apply(apply(apply(apply(s, apply(k, apply(s, apply(apply(s, k), X)))), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.29 = { by axiom 2 (s_definition) }
% 7.43/1.29 apply(apply(apply(apply(k, apply(s, apply(apply(s, k), X))), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.29 = { by axiom 1 (k_definition) }
% 7.43/1.29 apply(apply(apply(s, apply(apply(s, k), X)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))))
% 7.43/1.29 = { by axiom 2 (s_definition) }
% 7.43/1.29 apply(apply(apply(apply(s, k), X), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))))), apply(apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))))))
% 7.43/1.29 = { by lemma 3 }
% 7.43/1.29 apply(f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))), apply(apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))))))
% 7.43/1.29 = { by lemma 4 R->L }
% 7.43/1.29 apply(f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y))))), apply(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))), f(apply(apply(s, apply(s, k)), apply(apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)), apply(apply(s, apply(s, apply(k, apply(s, apply(apply(s, k), X))))), apply(apply(s, k), Y)))))))
% 7.43/1.29 % SZS output end Proof
% 7.43/1.29
% 7.43/1.29 RESULT: Unsatisfiable (the axioms are contradictory).
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