TSTP Solution File: LCL041-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL041-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n018.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 12:57:32 EDT 2022
% Result : Unsatisfiable 14.05s 13.97s
% Output : Proof 14.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL041-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 19:03:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 14.05/13.97 % SZS status Unsatisfiable
% 14.05/13.97 % SZS output start Proof
% 14.05/13.97 The input problem is unsatisfiable because
% 14.05/13.97
% 14.05/13.97 [1] the following set of Horn clauses is unsatisfiable:
% 14.05/13.97
% 14.05/13.97 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 14.05/13.97 is_a_theorem(implies(X, implies(not(X), Y)))
% 14.05/13.97 is_a_theorem(implies(X, implies(Y, X)))
% 14.05/13.97 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z))))
% 14.05/13.97 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z))))
% 14.05/13.97 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y)))
% 14.05/13.97 is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))) ==> \bottom
% 14.05/13.97
% 14.05/13.97 This holds because
% 14.05/13.97
% 14.05/13.97 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 14.05/13.97
% 14.05/13.97 E:
% 14.05/13.97 f1(true__, Y) = is_a_theorem(Y)
% 14.05/13.97 f2(is_a_theorem(X), X, Y) = true__
% 14.05/13.97 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 14.05/13.97 f3(is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b)))) = true__
% 14.05/13.97 f3(true__) = false__
% 14.05/13.97 is_a_theorem(implies(X, implies(Y, X))) = true__
% 14.05/13.97 is_a_theorem(implies(X, implies(not(X), Y))) = true__
% 14.05/13.97 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) = true__
% 14.05/13.97 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) = true__
% 14.05/13.97 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z)))) = true__
% 14.05/13.97 G:
% 14.05/13.97 true__ = false__
% 14.05/13.97
% 14.05/13.97 This holds because
% 14.05/13.97
% 14.05/13.97 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 14.05/13.97
% 14.05/13.97
% 14.05/13.97 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(not(X2), X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X0), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X1), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(X1, implies(not(X2), implies(X2, X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X0, X1), implies(X2, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X0, X1), implies(not(X1), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X1, X0))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X1, implies(X3, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(X3, X1), implies(X3, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(not(X1), X2), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, implies(X0, X2)), implies(X1, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, implies(X2, X3)), implies(X2, implies(X1, X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(X1, not(X0)), implies(X1, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(implies(not(not(X0)), X1), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(X0), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(X1), implies(X1, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X0)), X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, X1)), X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(X2, X1))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(X2, X2))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(X2, implies(X3, X2)))), X4)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(X1, implies(not(X1), X2))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(not(X0), X1)), X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(X0, implies(not(implies(not(X1), implies(X1, X2))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, implies(X3, X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, implies(not(X2), X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(not(X1), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X2, implies(implies(X2, X0), X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X2, implies(implies(X3, X0), implies(X3, X1)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(X2, implies(implies(not(X0), X1), X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(X2, X0), implies(X2, X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(X0), X1), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(not(implies(not(X0), X1)), X1), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(not(implies(implies(X2, X0), implies(X2, X1))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, X1), implies(not(implies(implies(not(X0), X1), X1)), X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X0, X1)), implies(X0, X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X0, implies(X1, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X0, implies(implies(X3, X1), implies(X3, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X0, implies(implies(not(X1), X2), X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X3, implies(X1, implies(X0, X2)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(not(implies(X1, implies(X0, X2))), X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, implies(X2, X3))), implies(X0, implies(X2, implies(X1, X3)))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(X1, not(X0))), implies(X1, not(X0))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(implies(X1, implies(X2, X1)), X3)), implies(X0, X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(implies(X1, implies(not(X1), X2)), X3)), implies(X0, X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, implies(not(not(X0)), X1)), implies(not(not(X0)), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, not(X1)), implies(X0, implies(X1, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, not(implies(X1, implies(X2, X1)))), implies(X0, X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(X0, not(implies(X1, implies(X2, X2)))), implies(X0, X3)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), implies(X2, X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(X1, X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(implies(not(X0), X1), X2), implies(X0, X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(X0), X1), implies(implies(X0, X1), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(X0), implies(X1, X0)), implies(X1, X0)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(X0), implies(not(X0), X1)), implies(not(X0), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(implies(X0, X1)), implies(implies(X2, X0), implies(X2, X1))), implies(implies(X2, X0), implies(X2, X1))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(implies(X0, X1)), implies(implies(not(X0), X1), X1)), implies(implies(not(X0), X1), X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(implies(X0, implies(X1, X2))), implies(X1, implies(X0, X2))), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(not(X0)), implies(X0, X1)), implies(X0, X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(not(implies(X0, implies(X1, X0)))), X2), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(not(implies(X0, implies(X1, X1)))), X2), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(implies(not(not(implies(X0, implies(not(X0), X1)))), X2), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(X0), implies(X0, X1)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(X0), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(X0), implies(not(implies(X0, X1)), X2)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(X0), not(X0)), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, X0))), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, X1))), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, X1)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, X2)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(X2, implies(X3, X2))))), X4), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(X1, implies(not(X1), X2)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X0), X1))), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(X0, implies(not(X1), implies(X1, X2)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(implies(X0, X1), implies(implies(X2, X0), implies(X2, X1)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(implies(X0, X1), implies(implies(not(X0), X1), X1))), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(implies(X0, implies(X1, X2)), implies(X1, implies(X0, X2)))), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(not(X0), implies(X0, X1))), X2), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(X1, X0))), X2)), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(X1, X1))), X2)), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(not(implies(X0, implies(not(X0), X1))), X2)), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(implies(not(implies(not(X0), implies(X0, X1))), X2)), X3), Y1)), Y1) -> true__
% 14.05/13.97 f1(f1(true__, implies(implies(not(not(X0)), X0), Y1)), Y1) -> true__
% 14.05/13.97 f1(true__, implies(X1, X1)) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, Y0))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, Y1))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y0)))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(Y2, Y1)))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(not(Y0), Y2)))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(Y1, implies(not(Y1), Y2)))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(Y0, implies(not(Y0), Y1))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(implies(Y0, Y1), implies(Y0, implies(Y2, Y1)))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(implies(Y0, Y1), implies(implies(not(Y0), Y1), Y1))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(not(Y0), implies(Y0, Y1))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(not(implies(Y0, implies(Y1, Y0))), Y2)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(not(implies(Y0, implies(not(Y0), Y1))), Y2)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(X2, implies(not(not(Y0)), Y0)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(Y1, Y0)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(Y1, Y1)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(Y2, Y0))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(Y1, implies(not(Y0), Y2))))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(not(Y0), Y1)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(Y0, implies(not(implies(Y1, Y0)), Y2)))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(implies(X1, X2), X2))) -> true__
% 14.05/13.97 f1(true__, implies(X1, implies(implies(Y0, Y1), implies(Y0, implies(Y2, Y1))))) -> true__
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% 14.05/13.97 f1(true__, implies(not(implies(not(implies(Y0, implies(Y1, implies(not(Y1), Y2)))), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(implies(Y0, implies(not(Y0), Y1))), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(implies(not(Y0), implies(Y0, Y1))), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(implies(not(Y0), not(Y0))), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(implies(not(implies(Y0, implies(Y1, Y0))), Y2)), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(implies(not(not(Y0)), Y0)), X1)), X2)) -> true__
% 14.05/13.97 f1(true__, implies(not(implies(not(not(Y0)), Y0)), X1)) -> true__
% 14.05/13.97 f1(true__, implies(not(not(Y0)), implies(X2, Y0))) -> true__
% 14.05/13.97 f1(true__, implies(not(not(Y1)), Y1)) -> true__
% 14.05/13.97 f1(true__, implies(not(not(not(X1))), implies(X1, X2))) -> true__
% 14.05/13.97 f1(true__, not(not(implies(X0, implies(X1, X0))))) -> true__
% 14.05/13.97 f1(true__, not(not(implies(X0, implies(X1, X1))))) -> true__
% 14.05/13.97 f2(f1(true__, Y0), Y0, Y1) -> true__
% 14.05/13.97 f2(is_a_theorem(X), X, Y) -> true__
% 14.05/13.97 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 14.05/13.97 f3(f1(true__, implies(implies(a, implies(a, b)), implies(a, b)))) -> true__
% 14.05/13.97 f3(is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b)))) -> true__
% 14.05/13.97 f3(true__) -> false__
% 14.05/13.97 false__ -> true__
% 14.05/13.97 is_a_theorem(Y) -> f1(true__, Y)
% 14.05/13.97 is_a_theorem(implies(X, implies(Y, X))) -> true__
% 14.05/13.97 is_a_theorem(implies(X, implies(not(X), Y))) -> true__
% 14.05/13.97 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) -> true__
% 14.05/13.97 is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) -> true__
% 14.05/13.97 is_a_theorem(implies(implies(Y, Z), implies(implies(X, Y), implies(X, Z)))) -> true__
% 14.05/13.97 with the LPO induced by
% 14.05/13.97 f2 > implies > is_a_theorem > f1 > b > a > f3 > not > false__ > true__
% 14.05/13.97
% 14.05/13.97 % SZS output end Proof
% 14.05/13.97
%------------------------------------------------------------------------------