TSTP Solution File: LCL043-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL043-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n013.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 12:57:33 EDT 2022
% Result : Unsatisfiable 8.09s 8.06s
% Output : Proof 8.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL043-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 23:54:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 8.09/8.06 % SZS status Unsatisfiable
% 8.09/8.06 % SZS output start Proof
% 8.09/8.06 The input problem is unsatisfiable because
% 8.09/8.06
% 8.09/8.06 [1] the following set of Horn clauses is unsatisfiable:
% 8.09/8.06
% 8.09/8.06 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 8.09/8.06 is_a_theorem(implies(X, implies(not(X), Y)))
% 8.09/8.06 is_a_theorem(implies(X, implies(Y, X)))
% 8.09/8.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 8.09/8.06 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z))))
% 8.09/8.06 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y)))
% 8.09/8.06 is_a_theorem(implies(not(not(a)), a)) ==> \bottom
% 8.09/8.06
% 8.09/8.06 This holds because
% 8.09/8.06
% 8.09/8.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.09/8.06
% 8.09/8.06 E:
% 8.09/8.06 f1(true__, Y) = is_a_theorem(Y)
% 8.09/8.06 f2(is_a_theorem(X), X, Y) = true__
% 8.09/8.06 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 8.09/8.06 f3(is_a_theorem(implies(not(not(a)), a))) = true__
% 8.09/8.06 f3(true__) = false__
% 8.09/8.06 is_a_theorem(implies(X, implies(Y, X))) = true__
% 8.09/8.06 is_a_theorem(implies(X, implies(not(X), Y))) = true__
% 8.09/8.06 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) = true__
% 8.09/8.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) = true__
% 8.09/8.06 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z)))) = true__
% 8.09/8.06 G:
% 8.09/8.06 true__ = false__
% 8.09/8.06
% 8.09/8.06 This holds because
% 8.09/8.06
% 8.09/8.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.09/8.06
% 8.09/8.06
% 8.09/8.06 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X1)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X3)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X2))))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X4))))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(X2, X3), X3)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(X2), X3)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X1, X2), X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X2), X3), X3))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(not(X2), X2), X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X0), X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X1), X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(implies(X2, X2)), X3))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(implies(X0, X1), X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(not(X1), X2), X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(implies(X1, implies(X2, X3)), implies(X2, implies(X1, X3)))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), X2)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(implies(not(X1), X1), X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(X0), X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X1)), X2)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(X2, X1))), X3)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(X2, X2))), X3)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(not(X1), X2))), X3)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(implies(not(X1), X1), X1)), X2)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(X0, implies(not(implies(not(implies(X1, X1)), X2)), X3)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, X1))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X2, X0), implies(X2, X1))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(X0), X1), X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), X1), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X0)), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X1)), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, X0))), X3), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, X1))), X3), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, X2))), X3), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X0, X1), X1)), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(X0, implies(not(X0), X1)), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(implies(implies(X0, X0), X1), X1), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(implies(not(X0), X0), X0), X1), X1), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(implies(not(implies(X0, X0)), X1), X2), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(not(X0), X0), X0), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(not(X0), X0), implies(X1, X0)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(not(X0), implies(X1, X0)), implies(X1, X0)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(implies(not(X0), implies(not(X0), X1)), implies(not(X0), X1)), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, X0)), X1), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, X0))), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, X1))), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, X0)))), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, X1)))), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, X2)))), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(not(X1), X2)))), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(implies(X0, X1), X1))), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(implies(X0, X1), implies(implies(not(X0), X1), X1))), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(implies(implies(X0, X0), X1), X1)), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(implies(not(X0), X0), X0)), X1), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(not(implies(X0, X0)), X1)), X2), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(X1, X0))), X2)), X3), Y1)), Y1) -> true__
% 8.09/8.06 f1(f1(true__, implies(implies(not(not(X0)), X0), Y1)), Y1) -> true__
% 8.09/8.06 f1(true__, implies(X1, X1)) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, Y1))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y0)))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y2)))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(Y0, implies(implies(Y0, Y1), Y1))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(implies(implies(Y0, Y0), Y1), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(implies(not(Y0), Y0), Y0)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(X2, implies(not(implies(Y0, Y0)), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, Y0)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, Y0))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, Y1))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y2)))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(not(Y1), Y2))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(implies(Y0, Y1), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(Y0, implies(not(Y0), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(implies(X1, X2), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(implies(Y0, Y1), implies(implies(not(Y0), Y1), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(implies(Y0, implies(Y1, Y2)), implies(Y1, implies(Y0, Y2))))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(implies(implies(Y0, Y0), Y1), Y1))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(implies(not(Y0), Y0), Y0))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, Y0)), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(Y1, Y0))), Y2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(Y1, Y1))), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(Y1, implies(Y2, Y0)))), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(Y1, implies(Y2, Y1)))), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(Y1, implies(Y2, Y2)))), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(implies(Y0, Y1), Y1))), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(Y0, implies(not(Y0), Y1))), Y2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(implies(not(Y0), Y0), Y0)), X2))) -> true__
% 8.09/8.06 f1(true__, implies(X1, implies(not(implies(not(implies(Y0, Y0)), Y1)), X2))) -> true__
% 8.09/8.06 f1(true__, implies(Y0, implies(X2, implies(Y1, Y0)))) -> true__
% 8.09/8.06 f1(true__, implies(Y0, implies(X2, implies(not(Y0), Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(Y0, implies(Y1, Y0))) -> true__
% 8.09/8.06 f1(true__, implies(Y0, implies(not(Y0), Y1))) -> true__
% 8.09/8.06 f1(true__, implies(Y1, implies(Y0, Y0))) -> true__
% 8.09/8.06 f1(true__, implies(implies(X2, Y0), implies(X2, implies(Y1, Y0)))) -> true__
% 8.09/8.06 f1(true__, implies(implies(Y0, Y1), implies(implies(Y2, Y0), implies(Y2, Y1)))) -> true__
% 8.09/8.06 f1(true__, implies(implies(Y0, Y1), implies(implies(not(Y0), Y1), Y1))) -> true__
% 8.09/8.06 f1(true__, implies(implies(Y0, implies(Y1, Y2)), implies(Y1, implies(Y0, Y2)))) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, Y0), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(Y1, Y0)), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(Y1, Y1)), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y0))), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y1))), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y2))), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(implies(Y0, Y1), Y1)), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(Y0, implies(not(Y0), Y1)), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(implies(implies(Y0, Y0), Y1), Y1), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(implies(not(Y0), Y0), Y0), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(implies(not(implies(Y0, Y0)), Y1), X1), X1)) -> true__
% 8.09/8.06 f1(true__, implies(implies(not(Y0), Y0), Y0)) -> true__
% 8.09/8.06 f1(true__, implies(implies(not(Y0), Y0), implies(X2, Y0))) -> true__
% 8.09/8.06 f1(true__, implies(implies(not(Y0), implies(Y1, Y0)), implies(Y1, Y0))) -> true__
% 8.09/8.06 f1(true__, implies(implies(not(Y0), implies(not(Y0), Y1)), implies(not(Y0), Y1))) -> true__
% 8.09/8.06 f1(true__, implies(implies(not(not(implies(Y0, Y0))), Y1), Y1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, Y0)), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, Y0))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, Y1))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, implies(Y2, Y0)))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, implies(Y2, Y1)))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, implies(Y2, Y2)))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(Y1, implies(not(Y1), Y2)))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(implies(Y0, Y1), Y1))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(Y0, implies(not(Y0), Y1))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(implies(Y0, Y1), implies(implies(not(Y0), Y1), Y1))), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(implies(implies(Y0, Y0), Y1), Y1)), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(implies(not(Y0), Y0), Y0)), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(not(implies(Y0, Y0)), Y1)), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(implies(not(implies(Y0, implies(Y1, Y0))), Y2)), X1)) -> true__
% 8.09/8.06 f1(true__, implies(not(not(Y1)), Y1)) -> true__
% 8.09/8.06 f2(f1(true__, Y0), Y0, Y1) -> true__
% 8.09/8.06 f2(is_a_theorem(X), X, Y) -> true__
% 8.09/8.06 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 8.09/8.06 f3(f1(true__, implies(not(not(a)), a))) -> true__
% 8.09/8.06 f3(is_a_theorem(implies(not(not(a)), a))) -> true__
% 8.09/8.06 f3(true__) -> false__
% 8.09/8.06 false__ -> true__
% 8.09/8.06 is_a_theorem(Y) -> f1(true__, Y)
% 8.09/8.06 is_a_theorem(implies(X, implies(Y, X))) -> true__
% 8.09/8.06 is_a_theorem(implies(X, implies(not(X), Y))) -> true__
% 8.09/8.06 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) -> true__
% 8.09/8.06 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) -> true__
% 8.09/8.06 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z)))) -> true__
% 8.09/8.06 with the LPO induced by
% 8.09/8.06 a > f3 > not > f2 > implies > is_a_theorem > f1 > false__ > true__
% 8.09/8.06
% 8.09/8.06 % SZS output end Proof
% 8.09/8.06
%------------------------------------------------------------------------------