TSTP Solution File: LCL110-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL110-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 12:58:10 EDT 2022
% Result : Unsatisfiable 9.45s 9.45s
% Output : Proof 9.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL110-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n011.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 : Sun Jul 3 18:24:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.45/9.45 % SZS status Unsatisfiable
% 9.45/9.45 % SZS output start Proof
% 9.45/9.45 The input problem is unsatisfiable because
% 9.45/9.45
% 9.45/9.45 [1] the following set of Horn clauses is unsatisfiable:
% 9.45/9.45
% 9.45/9.45 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 9.45/9.45 is_a_theorem(implies(X, implies(Y, X)))
% 9.45/9.45 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))
% 9.45/9.45 is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X)))
% 9.45/9.45 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X)))
% 9.45/9.45 is_a_theorem(implies(not(not(a)), a)) ==> \bottom
% 9.45/9.45
% 9.45/9.45 This holds because
% 9.45/9.45
% 9.45/9.45 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.45/9.45
% 9.45/9.45 E:
% 9.45/9.45 f1(true__, Y) = is_a_theorem(Y)
% 9.45/9.45 f2(is_a_theorem(X), X, Y) = true__
% 9.45/9.45 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 9.45/9.45 f3(is_a_theorem(implies(not(not(a)), a))) = true__
% 9.45/9.45 f3(true__) = false__
% 9.45/9.45 is_a_theorem(implies(X, implies(Y, X))) = true__
% 9.45/9.45 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true__
% 9.45/9.45 is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true__
% 9.45/9.45 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true__
% 9.45/9.45 G:
% 9.45/9.45 true__ = false__
% 9.45/9.45
% 9.45/9.45 This holds because
% 9.45/9.45
% 9.45/9.45 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.45/9.45
% 9.45/9.45
% 9.45/9.45 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X0)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X1)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X3)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X0))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X1))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X2))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X4))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X2)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X3)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X4)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X5)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(not(X4), implies(X4, X5)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(not(implies(X4, X4)), X5))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, X3), X4), X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(X3), implies(X3, X4))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(X3), implies(X4, implies(X3, X5)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(implies(X3, X3)), X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(implies(X3, X4)), implies(X4, X5))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(not(X3)), implies(X4, X3))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X2), X3), X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X2), X3), implies(X4, X3)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), X4), implies(X3, X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), X4), implies(not(X2), X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, X2)), X4), X4))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, X3)), X4), X4))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(not(X2), implies(X2, X3)), X4), X4))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(not(X2), not(X3)), implies(X3, X2)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X2), implies(X2, X3)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X2), implies(X3, implies(X2, X4))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X2), implies(X3, implies(X4, implies(X2, X5)))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(implies(X2, X2)), X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(implies(X2, X3)), implies(X3, X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(not(X2)), implies(X3, X2)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(not(X2)), implies(X3, implies(X4, X2))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(X2, X3), implies(X1, X3)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), X2)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), implies(X3, X2))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), not(X2)), implies(X2, X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X2), implies(implies(X2, X1), X1))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X3), implies(X2, X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X3), implies(not(X1), X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X1)), X3), X3)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X2)), X3), X3)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(implies(not(X1), implies(X1, X2)), X3), X3)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(implies(not(X1), not(X2)), implies(X2, X1))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(X1), implies(X1, X2))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(X1), implies(X2, implies(X1, X3)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(X1), implies(X2, implies(X3, implies(X1, X4))))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X1)), X2)), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X2)), implies(X2, X3))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X2)), implies(X3, implies(X2, X4)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(not(X1)), implies(X2, X1))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(X0, implies(not(not(X1)), implies(X2, implies(X3, X1)))), Y1)), Y1) -> true__
% 9.45/9.45 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(implies(X2, X2), X0), X1)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(X0, X1), implies(not(implies(X2, X2)), X1)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), X1), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), implies(X2, X1)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), implies(X2, implies(X3, X1))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), not(X1)), implies(X1, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), not(implies(X1, X1))), X2), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X0), not(not(X1))), implies(X2, X1)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X1), implies(implies(X1, X0), X0)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(X1, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(implies(not(X1), not(X0)), X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(not(X0), X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(not(implies(X3, X0)), X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(not(not(X1)), X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X0)), X2), X2), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X0)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X1)), X2), X2), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), X3), implies(X2, X3)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), X3), implies(not(X1), X3)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(not(X0), implies(X0, X1)), X2), X2), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(implies(not(X0), implies(X0, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(not(X0), not(X1)), implies(X1, X0)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(implies(not(X0), not(X1)), implies(X2, implies(X1, X0))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(X0), implies(X0, X1)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(X0), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(X0), implies(X1, implies(X2, implies(X0, X3)))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(X0), implies(X1, implies(X2, implies(X3, implies(X0, X4))))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(implies(X0, X0)), X1), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(implies(X0, X1)), implies(X1, X2)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(implies(X0, X1)), implies(X2, implies(X1, X3))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(not(X0)), X0), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(not(X0)), implies(X1, X0)), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(not(X0)), implies(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 9.54/9.45 f1(f1(true__, implies(implies(not(not(X0)), implies(X1, implies(X2, implies(X3, X0)))), Y1)), Y1) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(Y0, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(Y0, implies(Y1, Y1))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(Y0, implies(Y1, implies(Y2, Y0)))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(Y0, implies(Y1, implies(Y2, Y2)))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(implies(implies(Y0, Y0), Y1), Y1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(not(implies(Y0, Y0)), Y1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(X4, implies(not(not(Y0)), implies(Y1, Y0))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, implies(Y1, implies(Y2, Y0))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, implies(Y1, implies(Y2, Y1))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y0)))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y2)))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(Y0, implies(not(Y1), implies(Y1, Y2))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(implies(implies(Y0, Y0), Y1), Y1))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(implies(implies(Y0, Y0), Y1), implies(Y2, Y1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(implies(implies(Y0, Y1), Y2), implies(Y1, Y2)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(implies(implies(Y0, implies(Y1, Y0)), Y2), Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(Y0), implies(Y0, Y1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(Y0), implies(Y1, implies(Y0, Y2))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(implies(Y0, Y0)), Y1))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(implies(Y0, Y1)), implies(Y1, Y2)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(not(Y0)), implies(Y1, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(X3, implies(not(not(Y0)), implies(Y1, implies(Y2, Y0))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(Y0, Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y0))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, Y0), Y1), Y1)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, Y0), Y1), implies(Y2, Y1))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, Y1), Y2), implies(Y1, Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, Y1), Y2), implies(not(Y0), Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, implies(Y1, Y0)), Y2), Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, implies(Y1, Y1)), Y2), Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(implies(not(Y0), implies(Y0, Y1)), Y2), Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(Y0), implies(Y0, Y1))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(Y0), implies(Y1, implies(Y0, Y2)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(Y0), implies(Y1, implies(Y2, implies(Y0, Y3))))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(implies(Y0, Y0)), Y1)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(implies(Y0, Y1)), implies(Y1, Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(not(Y0)), implies(Y1, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(X2, implies(not(not(Y0)), implies(Y1, implies(Y2, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y0, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y0, implies(Y1, Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y0)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y1, implies(X0, X1)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y1, implies(Y2, implies(X0, X1))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(Y1, implies(Y2, implies(Y3, implies(X0, X1)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y0), Y1), Y1))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y0), Y1), implies(Y2, Y1)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y0), not(Y1)), implies(Y1, Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y0), not(implies(Y1, Y1))), Y2))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y1), Y1), implies(implies(Y1, Y0), Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y1), Y2), implies(Y1, Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, Y1), Y2), implies(not(Y0), Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, implies(Y1, Y0)), Y2), Y2))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(Y0, implies(Y1, Y1)), Y2), Y2))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(implies(not(Y0), implies(Y0, Y1)), Y2), Y2))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(Y0), implies(Y0, Y1)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(Y0), implies(Y1, implies(Y0, Y2))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(Y0), implies(Y1, implies(Y2, implies(Y0, Y3)))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(implies(Y0, Y0)), Y1))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(implies(Y0, Y1)), implies(Y1, Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(implies(Y0, Y1)), implies(Y2, implies(Y1, Y3))))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(not(Y0)), implies(Y1, Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(X1, implies(not(not(Y0)), implies(Y1, implies(Y2, Y0))))) -> true__
% 9.54/9.45 f1(true__, implies(Y0, implies(Y1, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(Y2, Y2)) -> true__
% 9.54/9.45 f1(true__, implies(implies(Y0, Y1), implies(implies(Y1, Y2), implies(Y0, Y2)))) -> true__
% 9.54/9.45 f1(true__, implies(implies(Y1, X2), implies(implies(implies(Y0, Y0), Y1), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(Y1, X2), implies(not(implies(Y0, Y0)), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(X2, X2), Y0), implies(Y1, implies(Y2, Y0)))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(X2, X2), not(Y0)), implies(Y0, Y1))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(X2, X2), not(implies(Y0, Y0))), Y1)) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(X2, X2), not(not(Y0))), implies(Y1, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y0, Y1), X2), implies(not(Y0), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y0, Y1), Y1), implies(implies(Y1, Y0), Y0))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y0), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y0), X2), implies(implies(not(Y0), not(Y1)), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y0), X2), implies(not(not(Y0)), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y1), X0), X0)) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y1), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, Y2), X2), implies(not(implies(Y0, Y1)), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y0, Y2)), X2), implies(not(Y0), X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y2, Y0)), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y2, Y1)), X0), X0)) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y2, Y1)), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y2, Y2)), X0), X0)) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(Y1, implies(Y2, Y2)), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(not(Y1), implies(Y1, Y2)), X0), X0)) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(not(Y1), implies(Y1, Y2)), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(implies(not(implies(Y1, Y1)), Y2), X2), implies(Y0, X2))) -> true__
% 9.54/9.45 f1(true__, implies(implies(not(X1), not(X0)), implies(Y1, implies(X0, X1)))) -> true__
% 9.54/9.45 f1(true__, implies(implies(not(Y0), not(Y1)), implies(Y1, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(not(X0), implies(Y1, implies(X0, X1)))) -> true__
% 9.54/9.45 f1(true__, implies(not(X0), implies(Y1, implies(Y2, implies(X0, X1))))) -> true__
% 9.54/9.45 f1(true__, implies(not(X1), implies(Y1, implies(Y2, implies(X0, implies(X1, X2)))))) -> true__
% 9.54/9.45 f1(true__, implies(not(Y1), implies(Y1, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(not(implies(X3, X0)), implies(Y1, implies(X0, X1)))) -> true__
% 9.54/9.45 f1(true__, implies(not(implies(Y0, Y0)), Y1)) -> true__
% 9.54/9.45 f1(true__, implies(not(implies(Y0, Y1)), implies(Y1, Y2))) -> true__
% 9.54/9.45 f1(true__, implies(not(not(X1)), implies(Y1, implies(X0, X1)))) -> true__
% 9.54/9.45 f1(true__, implies(not(not(X1)), implies(Y1, implies(Y2, implies(X0, X1))))) -> true__
% 9.54/9.45 f1(true__, implies(not(not(Y0)), implies(Y1, Y0))) -> true__
% 9.54/9.45 f1(true__, implies(not(not(Y1)), Y1)) -> true__
% 9.54/9.45 f2(f1(true__, Y0), Y0, Y1) -> true__
% 9.54/9.45 f2(is_a_theorem(X), X, Y) -> true__
% 9.54/9.45 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 9.54/9.45 f3(f1(true__, implies(not(not(a)), a))) -> true__
% 9.54/9.45 f3(is_a_theorem(implies(not(not(a)), a))) -> true__
% 9.54/9.45 f3(true__) -> false__
% 9.54/9.45 false__ -> true__
% 9.54/9.45 is_a_theorem(Y) -> f1(true__, Y)
% 9.54/9.45 is_a_theorem(implies(X, implies(Y, X))) -> true__
% 9.54/9.45 is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) -> true__
% 9.54/9.45 is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) -> true__
% 9.54/9.45 is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) -> true__
% 9.54/9.45 with the LPO induced by
% 9.54/9.45 a > f3 > not > f2 > implies > is_a_theorem > f1 > false__ > true__
% 9.54/9.45
% 9.54/9.45 % SZS output end Proof
% 9.54/9.45
%------------------------------------------------------------------------------