TSTP Solution File: COL036-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL036-1 : 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 : n031.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 18:31:43 EDT 2023
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL036-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 04:27:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
% 0.19/0.49 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 0.19/0.49 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.19/0.49
% 0.19/0.49 Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
% 0.19/0.49 The goal is true when:
% 0.19/0.49 X = apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))
% 0.19/0.49
% 0.19/0.49 Proof:
% 0.19/0.49 apply(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))))
% 0.19/0.49 = { by axiom 3 (b_definition) }
% 0.19/0.49 apply(apply(t, X), apply(apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))))
% 0.19/0.49 = { by axiom 1 (t_definition) }
% 0.19/0.49 apply(apply(apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), X)
% 0.19/0.49 = { by axiom 2 (s_definition) }
% 0.19/0.49 apply(apply(apply(apply(t, apply(apply(s, t), apply(b, apply(s, b)))), apply(apply(b, apply(s, b)), apply(apply(s, t), apply(b, apply(s, b))))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), X)
% 0.19/0.49 = { by axiom 1 (t_definition) }
% 0.19/0.49 apply(apply(apply(apply(apply(b, apply(s, b)), apply(apply(s, t), apply(b, apply(s, b)))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), X)
% 0.19/0.50 = { by axiom 3 (b_definition) }
% 0.19/0.50 apply(apply(apply(apply(s, b), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), X)
% 0.19/0.50 = { by axiom 2 (s_definition) }
% 0.19/0.50 apply(apply(apply(b, f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), apply(apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))))), X)
% 0.19/0.50 = { by axiom 3 (b_definition) }
% 0.19/0.50 apply(f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))), apply(apply(apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))), X))
% 0.19/0.50 = { by axiom 1 (t_definition) R->L }
% 0.19/0.50 apply(f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))), apply(apply(t, X), apply(apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))))))
% 0.19/0.50 = { by axiom 3 (b_definition) R->L }
% 0.19/0.50 apply(f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b)))))), apply(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))), f(apply(apply(b, apply(t, X)), apply(apply(apply(s, t), apply(b, apply(s, b))), apply(apply(s, t), apply(b, apply(s, b))))))))
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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