TSTP Solution File: LCL357-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL357-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 13:00:37 EDT 2022
% Result : Unsatisfiable 12.58s 12.53s
% Output : Proof 12.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL357-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n021.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 3 04:42:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 12.58/12.53 % SZS status Unsatisfiable
% 12.58/12.53 % SZS output start Proof
% 12.58/12.53 The input problem is unsatisfiable because
% 12.58/12.53
% 12.58/12.53 [1] the following set of Horn clauses is unsatisfiable:
% 12.58/12.53
% 12.58/12.53 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 12.58/12.53 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))
% 12.58/12.53 is_a_theorem(implies(implies(not(X), X), X))
% 12.58/12.53 is_a_theorem(implies(X, implies(not(X), Y)))
% 12.58/12.53 is_a_theorem(implies(implies(x, y), implies(implies(implies(x, z), u), implies(implies(y, z), u)))) ==> \bottom
% 12.58/12.53
% 12.58/12.53 This holds because
% 12.58/12.53
% 12.58/12.53 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 12.58/12.53
% 12.58/12.53 E:
% 12.58/12.53 f1(true__, Y) = is_a_theorem(Y)
% 12.58/12.53 f2(is_a_theorem(X), X, Y) = true__
% 12.58/12.53 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 12.58/12.53 f3(is_a_theorem(implies(implies(x, y), implies(implies(implies(x, z), u), implies(implies(y, z), u))))) = true__
% 12.58/12.53 f3(true__) = false__
% 12.58/12.53 is_a_theorem(implies(X, implies(not(X), Y))) = true__
% 12.58/12.53 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true__
% 12.58/12.53 is_a_theorem(implies(implies(not(X), X), X)) = true__
% 12.58/12.53 G:
% 12.58/12.53 true__ = false__
% 12.58/12.53
% 12.58/12.53 This holds because
% 12.58/12.53
% 12.58/12.53 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 12.58/12.53
% 12.58/12.53
% 12.58/12.53 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(not(X0), X2))), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(X0, implies(not(X0), X1)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(X0, implies(not(implies(not(X0), X1)), X2)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(implies(X0, X2), X3), implies(implies(X1, X2), X3))), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(X0), X0), X1)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(X0, X1), implies(not(implies(implies(X1, X2), implies(X0, X2))), X3)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X2, X1)), X3), implies(implies(X2, X0), X3)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(implies(not(X0), X1), X2), implies(X0, X2)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(not(X0), X0), X0), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(not(X0), X0), implies(not(X0), X1)), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(not(implies(X0, X1)), implies(X0, X1)), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(implies(not(implies(not(X0), X0)), implies(not(X0), X0)), X0), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(not(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2)))), X3), Y1)), Y1) -> true__
% 12.58/12.53 f1(f1(true__, implies(implies(not(implies(implies(not(X0), X0), X0)), X1), Y1)), Y1) -> true__
% 12.58/12.53 f1(true__, implies(X0, implies(implies(Y1, Y2), implies(not(X0), Y2)))) -> true__
% 12.58/12.53 f1(true__, implies(X0, implies(implies(not(not(X0)), not(X0)), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(X0, implies(not(implies(not(X0), X1)), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(Y0, Y0)) -> true__
% 12.58/12.53 f1(true__, implies(Y0, implies(not(Y0), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(Y0, implies(not(Y0), Y1))), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), implies(implies(Y2, Y0), Y3))), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(implies(implies(not(Y0), Y1), Y2), implies(Y0, Y2))), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(implies(not(Y0), Y0), Y0)), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), Y3)), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X1, X2), implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), Y1)), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X2, X0), implies(implies(implies(X2, X1), Y2), implies(implies(X0, X1), Y2)))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X2, X0), implies(implies(not(implies(X0, X1)), implies(X0, X1)), implies(X2, X1)))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X2, X0), implies(not(implies(implies(X0, X1), implies(X2, X1))), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X2, implies(Y0, Y1)), implies(implies(Y2, Y0), implies(X2, implies(Y2, Y1))))) -> true__
% 12.58/12.53 f1(true__, implies(implies(X2, not(Y0)), implies(Y0, implies(X2, Y1)))) -> true__
% 12.58/12.53 f1(true__, implies(implies(Y0, X2), implies(implies(not(Y0), Y0), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(Y0, Y2), X2), implies(implies(implies(not(Y0), Y1), Y2), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(Y0, Y1), X2), X3), implies(implies(implies(implies(not(Y0), Y0), Y1), X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(Y1, Y2), implies(Y0, Y2)), X2), implies(implies(Y0, Y1), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(Y2, Y0), Y3), X2), implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), X2), X3), implies(implies(implies(implies(Y2, Y0), Y3), X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(implies(not(Y0), Y1), Y2), X2), X3), implies(implies(implies(Y0, Y2), X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(implies(not(Y0), Y0), Y1), X2), implies(implies(Y0, Y1), X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(not(Y0), Y1), X2), implies(Y0, X2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(not(implies(Y0, implies(not(Y0), Y1))), X2), X3), implies(implies(Y2, X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X2), X3), implies(implies(Y3, X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(implies(not(implies(implies(not(Y0), Y0), Y0)), X2), X3), implies(implies(Y1, X2), X3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(Y0), Y0), Y0)) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(Y0), Y0), implies(not(Y0), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(implies(Y0, Y1)), implies(Y0, Y1)), implies(implies(Y1, Y2), implies(Y0, Y2)))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(implies(Y0, Y1)), implies(Y0, Y1)), implies(implies(not(Y0), Y0), Y1))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3)), implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3)), implies(implies(Y2, Y0), Y3))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(implies(implies(not(Y0), Y1), Y2)), implies(implies(not(Y0), Y1), Y2)), implies(Y0, Y2))) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(implies(not(Y0), Y0)), implies(not(Y0), Y0)), Y0)) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(not(implies(Y0, implies(not(Y0), Y1)))), not(implies(Y0, implies(not(Y0), Y1)))), Y2)) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2))))), not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2))))), Y3)) -> true__
% 12.58/12.53 f1(true__, implies(implies(not(not(implies(implies(not(Y0), Y0), Y0))), not(implies(implies(not(Y0), Y0), Y0))), Y1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(Y0, implies(not(Y0), Y1))), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(Y1, X2), implies(not(implies(implies(not(Y0), Y0), Y0)), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(Y2, X2), implies(not(implies(Y0, implies(not(Y0), Y1))), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(Y3, X2), implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(implies(Y0, Y2), X2), implies(implies(implies(not(Y0), Y1), Y2), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), implies(implies(Y2, Y0), Y3))), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(implies(implies(Y2, Y0), Y3), X2), implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(implies(implies(not(Y0), Y0), Y1), X2), implies(implies(Y0, Y1), X2))), X3)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(implies(not(Y0), Y1), Y2), implies(Y0, Y2))), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(implies(not(Y0), Y0), Y0)), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), Y3)), X1)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y0), Y1))), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), implies(implies(Y2, Y0), Y3))), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(implies(implies(not(Y0), Y1), Y2), implies(Y0, Y2))), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(not(implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))), Y3)), X1)), X2)) -> true__
% 12.58/12.53 f1(true__, implies(not(implies(not(implies(not(implies(implies(not(Y0), Y0), Y0)), Y1)), X1)), X2)) -> true__
% 12.58/12.53 f2(f1(true__, Y0), Y0, Y1) -> true__
% 12.58/12.53 f2(is_a_theorem(X), X, Y) -> true__
% 12.58/12.53 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 12.58/12.53 f3(f1(true__, implies(implies(x, y), implies(implies(implies(x, z), u), implies(implies(y, z), u))))) -> true__
% 12.58/12.53 f3(is_a_theorem(implies(implies(x, y), implies(implies(implies(x, z), u), implies(implies(y, z), u))))) -> true__
% 12.58/12.53 f3(true__) -> false__
% 12.58/12.53 false__ -> true__
% 12.58/12.53 is_a_theorem(Y) -> f1(true__, Y)
% 12.58/12.53 is_a_theorem(implies(X, implies(not(X), Y))) -> true__
% 12.58/12.53 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) -> true__
% 12.58/12.53 is_a_theorem(implies(implies(not(X), X), X)) -> true__
% 12.58/12.53 with the LPO induced by
% 12.58/12.53 u > z > y > x > f3 > not > f2 > implies > is_a_theorem > f1 > false__ > true__
% 12.58/12.53
% 12.58/12.53 % SZS output end Proof
% 12.58/12.53
%------------------------------------------------------------------------------