TSTP Solution File: LCL046-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL046-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n010.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 12:57:35 EDT 2022
% Result : Unsatisfiable 2.56s 2.69s
% Output : Proof 2.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL046-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 14:08:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.56/2.69 % SZS status Unsatisfiable
% 2.56/2.69 % SZS output start Proof
% 2.56/2.69 The input problem is unsatisfiable because
% 2.56/2.69
% 2.56/2.69 [1] the following set of Horn clauses is unsatisfiable:
% 2.56/2.69
% 2.56/2.69 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 2.56/2.69 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))
% 2.56/2.69 is_a_theorem(implies(implies(not(X), X), X))
% 2.56/2.69 is_a_theorem(implies(X, implies(not(X), Y)))
% 2.56/2.69 is_a_theorem(implies(a, a)) ==> \bottom
% 2.56/2.69
% 2.56/2.69 This holds because
% 2.56/2.69
% 2.56/2.69 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.56/2.69
% 2.56/2.69 E:
% 2.56/2.69 f1(true__, Y) = is_a_theorem(Y)
% 2.56/2.69 f2(is_a_theorem(X), X, Y) = true__
% 2.56/2.69 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 2.56/2.69 f3(is_a_theorem(implies(a, a))) = true__
% 2.56/2.69 f3(true__) = false__
% 2.56/2.69 is_a_theorem(implies(X, implies(not(X), Y))) = true__
% 2.56/2.69 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true__
% 2.56/2.69 is_a_theorem(implies(implies(not(X), X), X)) = true__
% 2.56/2.69 G:
% 2.56/2.69 true__ = false__
% 2.56/2.69
% 2.56/2.69 This holds because
% 2.56/2.69
% 2.56/2.69 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.56/2.69
% 2.56/2.69
% 2.56/2.69 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(X0, implies(not(X0), X1)), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(X0), X0), X1)), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(implies(not(X0), X1), X2), implies(X0, X2)), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(not(X0), X0), X0), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(not(X0), X0), implies(not(X0), X1)), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(implies(not(implies(not(X0), X0)), implies(not(X0), X0)), X0), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(not(implies(implies(not(X0), X0), X0)), X1), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(not(X0), X1))), X2)), X3), Y1)), Y1) -> true__
% 2.56/2.69 f1(f1(true__, implies(implies(not(implies(not(implies(implies(not(X0), X0), X0)), X1)), X2), Y1)), Y1) -> true__
% 2.56/2.69 f1(true__, implies(X0, implies(not(implies(not(X0), X1)), Y1))) -> true__
% 2.56/2.69 f1(true__, implies(Y0, Y0)) -> true__
% 2.56/2.69 f1(true__, implies(Y0, implies(not(Y0), Y1))) -> true__
% 2.56/2.69 f1(true__, implies(implies(Y0, X2), implies(implies(not(Y0), Y0), X2))) -> true__
% 2.56/2.69 f1(true__, implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))) -> true__
% 2.56/2.69 f1(true__, implies(implies(implies(not(Y0), Y1), X2), implies(Y0, X2))) -> true__
% 2.56/2.69 f1(true__, implies(implies(not(Y0), Y0), Y0)) -> true__
% 2.56/2.69 f1(true__, implies(implies(not(Y0), Y0), implies(not(Y0), Y1))) -> true__
% 2.56/2.69 f1(true__, implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), Y0)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(Y0, implies(not(Y0), Y1))), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(implies(not(Y0), Y1), Y2), implies(Y0, Y2))), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(not(Y0), Y0), Y0)), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(not(Y0), Y0), implies(not(Y0), Y1))), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), Y0)), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)), X1)) -> true__
% 2.56/2.69 f1(true__, implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), Y1)), X1)) -> true__
% 2.56/2.69 f2(f1(true__, Y0), Y0, Y1) -> true__
% 2.56/2.69 f2(true__, X, Y) -> f1(f1(true__, implies(X, Y)), Y)
% 2.56/2.69 f3(f1(true__, implies(a, a))) -> true__
% 2.56/2.69 f3(true__) -> false__
% 2.56/2.69 false__ -> true__
% 2.56/2.69 is_a_theorem(Y) -> f1(true__, Y)
% 2.56/2.69 with the LPO induced by
% 2.56/2.69 not > a > f2 > implies > f3 > is_a_theorem > f1 > false__ > true__
% 2.56/2.69
% 2.56/2.69 % SZS output end Proof
% 2.56/2.69
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