TSTP Solution File: LCL033-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL033-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n013.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 : 600s
% DateTime : Sun Jul 17 12:57:27 EDT 2022
% Result : Unsatisfiable 3.27s 3.34s
% Output : Proof 3.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL033-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.13/0.35 % Computer : n013.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 : 600
% 0.13/0.35 % DateTime : Sun Jul 3 10:30:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.27/3.34 % SZS status Unsatisfiable
% 3.27/3.34 % SZS output start Proof
% 3.27/3.34 The input problem is unsatisfiable because
% 3.27/3.34
% 3.27/3.34 [1] the following set of Horn clauses is unsatisfiable:
% 3.27/3.34
% 3.27/3.34 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 3.27/3.34 is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X))))
% 3.27/3.34 is_a_theorem(implies(a, implies(b, a))) ==> \bottom
% 3.27/3.34
% 3.27/3.34 This holds because
% 3.27/3.34
% 3.27/3.34 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.27/3.34
% 3.27/3.34 E:
% 3.27/3.34 f1(true__, Y) = is_a_theorem(Y)
% 3.27/3.34 f2(is_a_theorem(X), X, Y) = true__
% 3.27/3.34 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 3.27/3.34 f3(is_a_theorem(implies(a, implies(b, a)))) = true__
% 3.27/3.34 f3(true__) = false__
% 3.27/3.34 is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X)))) = true__
% 3.27/3.34 G:
% 3.27/3.34 true__ = false__
% 3.27/3.34
% 3.27/3.34 This holds because
% 3.27/3.34
% 3.27/3.34 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.27/3.34
% 3.27/3.34
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(falsehood, X3)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(X1, implies(falsehood, X2))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(falsehood, X1)), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X2, implies(X1, X2)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(implies(falsehood, X1), implies(X2, implies(falsehood, X1)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(falsehood, X2)), implies(falsehood, X3)), implies(X4, implies(falsehood, X3)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(X0, implies(implies(implies(falsehood, X1), X2), implies(X3, X2))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(falsehood, X0), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(implies(X2, implies(falsehood, X3)), X1), implies(X0, X1))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(implies(implies(implies(X3, X1), implies(X4, X1)), implies(X1, X2)), implies(X0, implies(X1, X2)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(X0, implies(falsehood, X1)), implies(X2, implies(X0, implies(falsehood, X1)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), implies(X2, implies(implies(X0, X1), implies(X1, implies(X0, X1))))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(X2, X1)), implies(implies(implies(implies(implies(X1, X3), implies(X2, falsehood)), X4), X0), implies(implies(X0, X1), implies(X2, X1)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(X0, implies(falsehood, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, X2), implies(X3, falsehood)), X0)), X1), implies(X3, X1)), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(falsehood, X0), X1), implies(X2, X1)), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(falsehood, X0), implies(X1, implies(falsehood, X0))), implies(X2, implies(implies(falsehood, X0), implies(X1, implies(falsehood, X0))))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X2, X1)), implies(X1, X3)), implies(X4, implies(X1, X3))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(implies(falsehood, X0), X1), implies(X2, X1)), implies(X3, implies(implies(implies(falsehood, X0), X1), implies(X2, X1)))), Y1)), Y1) -> true__
% 3.27/3.34 f1(f1(true__, implies(implies(implies(implies(implies(implies(X0, X1), implies(X2, falsehood)), X3), X4), implies(implies(X4, X0), implies(X2, X0))), Y1)), Y1) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(X2, X1))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, Y1))))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, implies(falsehood, Y3)))))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(Y0, implies(implies(implies(falsehood, Y1), Y2), implies(Y3, Y2))))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(falsehood, X2))) -> true__
% 3.27/3.34 f1(true__, implies(X1, implies(implies(implies(Y0, implies(falsehood, Y1)), Y2), implies(Y3, Y2)))) -> true__
% 3.27/3.34 f1(true__, implies(X3, implies(Y2, implies(Y0, implies(falsehood, Y1))))) -> true__
% 3.27/3.34 f1(true__, implies(X3, implies(Y4, implies(falsehood, Y3)))) -> true__
% 3.27/3.34 f1(true__, implies(X3, implies(implies(falsehood, X1), implies(Y0, implies(falsehood, X1))))) -> true__
% 3.27/3.34 f1(true__, implies(X3, implies(implies(implies(Y2, implies(falsehood, Y3)), implies(falsehood, X1)), implies(Y0, implies(falsehood, X1))))) -> true__
% 3.27/3.34 f1(true__, implies(X3, implies(implies(implies(falsehood, X1), Y0), implies(Y2, Y0)))) -> true__
% 3.27/3.34 f1(true__, implies(X4, implies(Y2, implies(X2, Y2)))) -> true__
% 3.27/3.34 f1(true__, implies(X4, implies(implies(Y2, Y1), implies(Y1, implies(Y2, Y1))))) -> true__
% 3.27/3.34 f1(true__, implies(falsehood, X1)) -> true__
% 3.27/3.34 f1(true__, implies(implies(X1, X2), implies(X2, implies(X1, X2)))) -> true__
% 3.27/3.34 f1(true__, implies(implies(Y1, implies(falsehood, Y2)), implies(Y0, implies(Y1, implies(falsehood, Y2))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(Y3, Y2), implies(implies(implies(Y0, implies(falsehood, Y1)), Y2), implies(Y3, Y2)))) -> true__
% 3.27/3.34 f1(true__, implies(implies(Y4, implies(Y1, Y3)), implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), implies(Y1, Y3)), implies(Y4, implies(Y1, Y3))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2))), implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(Y1, implies(implies(implies(X0, X1), implies(X2, falsehood)), Y1)), X0), implies(X2, X0))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(Y4, Y0), implies(Y2, Y0)), implies(implies(implies(implies(implies(Y0, Y1), implies(Y2, falsehood)), Y3), Y4), implies(implies(Y4, Y0), implies(Y2, Y0))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(Y4, implies(falsehood, Y3)), Y0), implies(Y2, Y0))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(falsehood, X1), X2), implies(X3, X2))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(falsehood, Y1), implies(Y2, implies(falsehood, Y1))), implies(Y0, implies(implies(falsehood, Y1), implies(Y2, implies(falsehood, Y1)))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2))), X0), implies(X2, X0))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(implies(Y4, Y0), implies(Y2, Y0)), implies(Y0, Y1)), implies(X2, implies(Y0, Y1)))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(implies(falsehood, Y1), Y2), implies(Y3, Y2)), implies(Y0, implies(implies(implies(falsehood, Y1), Y2), implies(Y3, Y2))))) -> true__
% 3.27/3.34 f1(true__, implies(implies(implies(implies(implies(Y0, Y1), implies(Y2, falsehood)), Y3), Y4), implies(implies(Y4, Y0), implies(Y2, Y0)))) -> true__
% 3.27/3.34 f2(f1(true__, Y0), Y0, Y1) -> true__
% 3.27/3.34 f2(is_a_theorem(X), X, Y) -> true__
% 3.27/3.34 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 3.27/3.34 f3(f1(true__, implies(a, implies(b, a)))) -> true__
% 3.27/3.34 f3(is_a_theorem(implies(a, implies(b, a)))) -> true__
% 3.27/3.34 f3(true__) -> false__
% 3.27/3.34 false__ -> true__
% 3.27/3.34 is_a_theorem(Y) -> f1(true__, Y)
% 3.27/3.34 is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X)))) -> true__
% 3.27/3.34 with the LPO induced by
% 3.27/3.34 f2 > implies > is_a_theorem > f1 > b > a > f3 > falsehood > false__ > true__
% 3.27/3.34
% 3.27/3.34 % SZS output end Proof
% 3.27/3.34
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