TSTP Solution File: LCL076-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL076-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 12:57:47 EDT 2022
% Result : Unsatisfiable 0.85s 1.06s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL076-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : moca.sh %s
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Mon Jul 4 06:46:21 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.85/1.06 % SZS status Unsatisfiable
% 0.85/1.06 % SZS output start Proof
% 0.85/1.06 The input problem is unsatisfiable because
% 0.85/1.06
% 0.85/1.06 [1] the following set of Horn clauses is unsatisfiable:
% 0.85/1.06
% 0.85/1.06 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 0.85/1.06 is_a_theorem(implies(X, implies(Y, X)))
% 0.85/1.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z))))
% 0.85/1.06 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X)))
% 0.85/1.06 is_a_theorem(implies(not(not(X1)), X1))
% 0.85/1.06 is_a_theorem(implies(a, not(not(a)))) ==> \bottom
% 0.85/1.06
% 0.85/1.06 This holds because
% 0.85/1.06
% 0.85/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.85/1.06
% 0.85/1.06 E:
% 0.85/1.06 f1(true__, Y) = is_a_theorem(Y)
% 0.85/1.06 f2(is_a_theorem(X), X, Y) = true__
% 0.85/1.06 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 0.85/1.06 f3(is_a_theorem(implies(a, not(not(a))))) = true__
% 0.85/1.06 f3(true__) = false__
% 0.85/1.06 is_a_theorem(implies(X, implies(Y, X))) = true__
% 0.85/1.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true__
% 0.85/1.06 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true__
% 0.85/1.06 is_a_theorem(implies(not(not(X1)), X1)) = true__
% 0.85/1.06 G:
% 0.85/1.06 true__ = false__
% 0.85/1.06
% 0.85/1.06 This holds because
% 0.85/1.06
% 0.85/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.85/1.06
% 0.85/1.06
% 0.85/1.06 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(X0, implies(not(not(X1)), X1)), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(X0, not(not(X0))), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(implies(X0, X1), implies(X0, X2))), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(implies(not(X0), not(X1)), implies(X1, X0)), Y1)), Y1) -> true__
% 0.85/1.06 f1(f1(true__, implies(implies(not(not(X0)), X0), Y1)), Y1) -> true__
% 0.85/1.06 f1(true__, implies(X1, implies(Y0, implies(Y1, Y0)))) -> true__
% 0.85/1.06 f1(true__, implies(X1, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0)))) -> true__
% 0.85/1.06 f1(true__, implies(X1, implies(not(not(Y0)), Y0))) -> true__
% 0.85/1.06 f1(true__, implies(X1, not(not(X1)))) -> true__
% 0.85/1.06 f1(true__, implies(Y0, implies(Y1, Y0))) -> true__
% 0.85/1.06 f1(true__, implies(implies(Y0, implies(Y1, Y2)), implies(implies(Y0, Y1), implies(Y0, Y2)))) -> true__
% 0.85/1.06 f1(true__, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0))) -> true__
% 0.85/1.06 f1(true__, implies(not(not(Y0)), Y0)) -> true__
% 0.85/1.06 f1(true__, not(not(implies(Y0, implies(Y1, Y0))))) -> true__
% 0.85/1.06 f1(true__, not(not(implies(not(not(Y0)), Y0)))) -> true__
% 0.85/1.06 f2(f1(true__, Y0), Y0, Y1) -> true__
% 0.85/1.06 f2(is_a_theorem(X), X, Y) -> true__
% 0.85/1.06 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 0.85/1.06 f3(f1(true__, implies(a, not(not(a))))) -> true__
% 0.85/1.06 f3(is_a_theorem(implies(a, not(not(a))))) -> true__
% 0.85/1.06 f3(true__) -> false__
% 0.85/1.06 false__ -> true__
% 0.85/1.06 is_a_theorem(Y) -> f1(true__, Y)
% 0.85/1.06 is_a_theorem(implies(X, implies(Y, X))) -> true__
% 0.85/1.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) -> true__
% 0.85/1.06 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) -> true__
% 0.85/1.06 is_a_theorem(implies(not(not(X1)), X1)) -> true__
% 0.85/1.06 with the LPO induced by
% 0.85/1.06 a > f3 > not > f2 > implies > is_a_theorem > f1 > false__ > true__
% 0.85/1.06
% 0.85/1.06 % SZS output end Proof
% 0.85/1.06
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