TSTP Solution File: LCL398-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL398-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% 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 : 600s
% DateTime : Sun Jul 17 13:00:57 EDT 2022
% Result : Unsatisfiable 4.28s 4.34s
% Output : Proof 4.28s
% 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 : LCL398-1 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n025.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 2 23:18:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.28/4.34 % SZS status Unsatisfiable
% 4.28/4.34 % SZS output start Proof
% 4.28/4.34 The input problem is unsatisfiable because
% 4.28/4.34
% 4.28/4.34 [1] the following set of Horn clauses is unsatisfiable:
% 4.28/4.34
% 4.28/4.34 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 4.28/4.34 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))
% 4.28/4.34 is_a_theorem(implies(implies(not(X), X), X))
% 4.28/4.34 is_a_theorem(implies(X, implies(not(X), Y)))
% 4.28/4.34 is_a_theorem(implies(not(implies(x, x)), y)) ==> \bottom
% 4.28/4.34
% 4.28/4.34 This holds because
% 4.28/4.34
% 4.28/4.34 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 4.28/4.34
% 4.28/4.34 E:
% 4.28/4.34 f1(true__, Y) = is_a_theorem(Y)
% 4.28/4.34 f2(is_a_theorem(X), X, Y) = true__
% 4.28/4.34 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 4.28/4.34 f3(is_a_theorem(implies(not(implies(x, x)), y))) = true__
% 4.28/4.34 f3(true__) = false__
% 4.28/4.34 is_a_theorem(implies(X, implies(not(X), Y))) = true__
% 4.28/4.34 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true__
% 4.28/4.34 is_a_theorem(implies(implies(not(X), X), X)) = true__
% 4.28/4.34 G:
% 4.28/4.34 true__ = false__
% 4.28/4.34
% 4.28/4.34 This holds because
% 4.28/4.34
% 4.28/4.34 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 4.28/4.34
% 4.28/4.34
% 4.28/4.34 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(X0, implies(not(X0), X1)), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(X0, implies(not(implies(not(X0), X1)), X2)), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(X0), X0), X1)), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(implies(not(X0), X1), X2), implies(X0, X2)), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(not(X0), X0), X0), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(not(X0), X0), implies(not(X0), X1)), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(implies(not(implies(not(X0), X0)), implies(not(X0), X0)), X0), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(X0, X0)), X1), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(implies(not(X0), X0), X0)), X1), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(implies(not(X0), X0), implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(not(implies(X0, X0)), X1)), X2), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(not(X0), X1))), X2)), X3), Y1)), Y1) -> true__
% 4.28/4.34 f1(f1(true__, implies(implies(not(implies(not(implies(implies(not(X0), X0), X0)), X1)), X2), Y1)), Y1) -> true__
% 4.28/4.34 f1(true__, implies(X0, implies(not(implies(not(X0), X1)), Y1))) -> true__
% 4.28/4.34 f1(true__, implies(Y0, Y0)) -> true__
% 4.28/4.34 f1(true__, implies(Y0, implies(not(Y0), Y1))) -> true__
% 4.28/4.34 f1(true__, implies(implies(Y0, X2), implies(implies(not(Y0), Y0), X2))) -> true__
% 4.28/4.34 f1(true__, implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))) -> true__
% 4.28/4.34 f1(true__, implies(implies(Y1, X2), implies(not(implies(implies(not(Y0), Y0), Y0)), X2))) -> true__
% 4.28/4.34 f1(true__, implies(implies(implies(not(Y0), Y1), X2), implies(Y0, X2))) -> true__
% 4.28/4.34 f1(true__, implies(implies(not(Y0), Y0), Y0)) -> true__
% 4.28/4.34 f1(true__, implies(implies(not(Y0), Y0), implies(not(Y0), Y1))) -> true__
% 4.28/4.34 f1(true__, implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), Y0)) -> true__
% 4.28/4.34 f1(true__, implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), implies(not(Y0), Y1))) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(Y0, Y0)), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(Y0, implies(not(Y0), Y1))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(Y0, implies(not(implies(not(Y0), Y1)), Y2))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(implies(not(Y0), Y1), Y2), implies(Y0, Y2))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(not(Y0), Y0), Y0)), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(not(Y0), Y0), implies(not(Y0), Y1))), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), Y0)), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(Y0, Y0)), X1)), X2)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(Y0, implies(not(implies(not(Y0), Y1)), Y2))), X1)), X2)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X1)), X2)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), Y1)), X1)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(implies(not(Y0), Y0), implies(not(Y0), Y1))), X1)), X2)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)), X1)), X2)) -> true__
% 4.28/4.34 f1(true__, implies(not(implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), Y1)), X1)), X2)) -> true__
% 4.28/4.34 f2(f1(true__, Y0), Y0, Y1) -> true__
% 4.28/4.34 f2(true__, X, Y) -> f1(f1(true__, implies(X, Y)), Y)
% 4.28/4.34 f3(f1(true__, implies(not(implies(x, x)), y))) -> true__
% 4.28/4.34 f3(true__) -> false__
% 4.28/4.34 false__ -> true__
% 4.28/4.34 is_a_theorem(Y) -> f1(true__, Y)
% 4.28/4.34 with the LPO induced by
% 4.28/4.34 y > x > not > f2 > implies > f3 > is_a_theorem > f1 > false__ > true__
% 4.28/4.34
% 4.28/4.34 % SZS output end Proof
% 4.28/4.34
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