TSTP Solution File: LCL083-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL083-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n024.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 12:57:52 EDT 2022
% Result : Unsatisfiable 16.61s 16.63s
% Output : Proof 16.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL083-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n024.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 22:14:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 16.61/16.63 % SZS status Unsatisfiable
% 16.61/16.63 % SZS output start Proof
% 16.61/16.63 The input problem is unsatisfiable because
% 16.61/16.63
% 16.61/16.63 [1] the following set of Horn clauses is unsatisfiable:
% 16.61/16.63
% 16.61/16.63 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 16.61/16.63 is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(U, X))))
% 16.61/16.63 is_a_theorem(implies(X, X))
% 16.61/16.63 is_a_theorem(implies(implies(implies(a, b), a), a)) ==> \bottom
% 16.61/16.63
% 16.61/16.63 This holds because
% 16.61/16.63
% 16.61/16.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 16.61/16.63
% 16.61/16.63 E:
% 16.61/16.63 f1(true__, Y) = is_a_theorem(Y)
% 16.61/16.63 f2(is_a_theorem(X), X, Y) = true__
% 16.61/16.63 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 16.61/16.63 f3(is_a_theorem(implies(implies(implies(a, b), a), a))) = true__
% 16.61/16.63 f3(true__) = false__
% 16.61/16.63 is_a_theorem(implies(X, X)) = true__
% 16.61/16.63 is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(U, X)))) = true__
% 16.61/16.63 G:
% 16.61/16.63 true__ = false__
% 16.61/16.63
% 16.61/16.63 This holds because
% 16.61/16.63
% 16.61/16.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 16.61/16.63
% 16.61/16.63
% 16.61/16.63 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X4)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X5)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, implies(X6, X5))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, implies(X6, X6))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, implies(X6, implies(X7, X6)))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, implies(X6, implies(X7, X7)))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, implies(X6, implies(X7, implies(X8, X7))))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(implies(X5, X4), implies(X6, X4))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(implies(implies(X5, X6), X5), implies(X7, X5))))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(implies(X4, X3), implies(X5, X3)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(implies(X4, X5), implies(X5, X5)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(implies(implies(X4, X4), X5), implies(X6, X5)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(implies(implies(X4, X5), X4), implies(X6, X4)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(implies(implies(X4, implies(X5, X6)), X5), implies(X7, X5)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(X3, X2), implies(X4, X2))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(X3, X4), implies(X4, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, X3), X4), implies(X5, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, X4), X3), implies(X5, X3))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, X4), X5), implies(implies(X5, X3), implies(X6, X3)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, X4), implies(X4, X5)), implies(X6, implies(X4, X5)))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, implies(X4, X3)), X5), implies(X6, X5))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, implies(X4, X4)), X5), implies(X6, X5))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(X3, implies(X4, X5)), X4), implies(X6, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(implies(implies(X3, X4), X5), X4), implies(X3, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, X1), implies(X3, X1)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, X3), implies(X3, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, X3), implies(X3, implies(X2, X3))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X2), X3), implies(X4, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), X2), implies(X4, X2)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), X4), implies(implies(X4, X2), implies(X5, X2))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), implies(X3, X4)), implies(X5, implies(X3, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, X2)), X4), implies(X5, X4)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, X3)), X4), implies(X5, X4)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, X4)), X3), implies(X5, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, implies(X4, X3))), X5), implies(X6, X5)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X2, implies(X3, implies(X4, X4))), X5), implies(X6, X5)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(implies(X2, X3), X4), X3), implies(X2, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(X1, X0), implies(X2, X0))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X2, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X2, implies(X1, X2)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), X2)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), implies(X3, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X1), X1)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X1), implies(X3, X1))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X3), implies(implies(X3, X1), implies(X4, X1)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), implies(X2, X3)), implies(X4, implies(X2, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), implies(X3, implies(X2, X4))), implies(X5, implies(X3, implies(X2, X4))))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X1)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X2)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X3)), X2), implies(X4, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X3)), implies(X4, X2)), implies(X5, implies(X4, X2)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, implies(X3, X2))), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, implies(X3, X3))), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, implies(X3, implies(X4, X3)))), X5), implies(X6, X5))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, implies(X3, implies(X4, X4)))), X5), implies(X6, X5))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(implies(X2, X1), implies(X3, X1))), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, X2), X3), X2), implies(X1, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, X2), implies(X3, X2)), implies(X2, X4)), implies(X5, implies(X2, X4)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, implies(X2, X3)), implies(X4, implies(X2, X3))), X2), implies(X5, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(implies(X1, X1), X2), implies(X3, X2)), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(implies(X1, X2), X1), implies(X3, X1)), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), X1), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), implies(X2, X1)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), X0), X0), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), X0), implies(X2, X0)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(implies(X2, X0), implies(X3, X0))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(X1, X2)), implies(X3, implies(X1, X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(X2, implies(X1, X3))), implies(X4, implies(X2, implies(X1, X3)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(implies(X0, X1), X2)), implies(X3, implies(implies(X0, X1), X2))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X0)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), X1), implies(X3, X1)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), implies(X3, X1)), implies(X4, implies(X3, X1))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), implies(implies(X3, X1), implies(X4, X1))), implies(X5, implies(implies(X3, X1), implies(X4, X1)))), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, X1))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, X2))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, X3)))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X3))))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, X4))))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X4)))))), X6), implies(X7, X6)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X4, implies(X5, X5)))))), X6), implies(X7, X6)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(implies(X3, X2), implies(X4, X2))))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(implies(X2, X1), implies(X3, X1)))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(implies(implies(X2, X2), X3), implies(X4, X3)))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(implies(implies(X2, X3), X2), implies(X4, X2)))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X1, X0), implies(X2, X0))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, X1), X2), implies(X3, X2))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, X2), X1), implies(X3, X1))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, implies(X2, X1)), X3), implies(X4, X3))), X5), implies(X6, X5)), Y1)), Y1) -> true__
% 16.61/16.63 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, implies(X2, X2)), X3), implies(X4, X3))), X5), implies(X6, X5)), Y1)), Y1) -> true__
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% 16.61/16.63 f1(true__, implies(X3, implies(implies(implies(Y0, Y0), Y1), Y1))) -> true__
% 16.61/16.63 f1(true__, implies(X3, implies(implies(implies(Y0, Y1), Y0), Y0))) -> true__
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% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, Y1), Y2), implies(implies(Y2, Y0), implies(Y3, Y0)))), implies(X2, implies(implies(implies(Y0, Y1), Y2), implies(implies(Y2, Y0), implies(Y3, Y0)))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, Y1), implies(Y1, Y2)), implies(Y3, implies(Y1, Y2)))), implies(X2, implies(implies(implies(Y0, Y1), implies(Y1, Y2)), implies(Y3, implies(Y1, Y2)))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(Y1, Y2)), implies(Y3, Y1)), implies(Y4, implies(Y3, Y1)))), implies(X2, implies(implies(implies(Y0, implies(Y1, Y2)), implies(Y3, Y1)), implies(Y4, implies(Y3, Y1)))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y1))), Y3), implies(Y4, Y3))), implies(X2, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y1))), Y3), implies(Y4, Y3))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y2))), Y3), implies(Y4, Y3))), implies(X2, implies(implies(implies(Y0, implies(Y1, implies(Y2, Y2))), Y3), implies(Y4, Y3))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y2)))), Y4), implies(Y5, Y4))), implies(X2, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y2)))), Y4), implies(Y5, Y4))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y3)))), Y4), implies(Y5, Y4))), implies(X2, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, Y3)))), Y4), implies(Y5, Y4))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(Y0, implies(implies(Y1, Y0), implies(Y2, Y0))), Y3), implies(Y4, Y3))), implies(X2, implies(implies(implies(Y0, implies(implies(Y1, Y0), implies(Y2, Y0))), Y3), implies(Y4, Y3))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(implies(implies(Y0, Y0), Y1), implies(Y2, Y1)), Y3), implies(Y4, Y3))), implies(X2, implies(implies(implies(implies(implies(Y0, Y0), Y1), implies(Y2, Y1)), Y3), implies(Y4, Y3))))) -> true__
% 16.61/16.63 f1(true__, implies(implies(X1, implies(implies(implies(implies(implies(Y0, Y1), Y0), implies(Y2, Y0)), Y3), implies(Y4, Y3))), implies(X2, implies(implies(implies(implies(implies(Y0, Y1), Y0), implies(Y2, Y0)), Y3), implies(Y4, Y3))))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(X0, X1), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(X1, X1), X2), X2)) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(X1, X2), X1), X1)) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y0, Y1), Y2), implies(implies(Y2, Y0), implies(Y3, Y0)))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y0, Y1), implies(implies(Y0, Y1), Y2)), implies(X3, implies(implies(Y0, Y1), Y2)))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, Y1), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(X0, X1)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, Y1)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, Y2)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, Y2))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, Y3))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, Y3)))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, Y4)))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, implies(Y5, Y4))))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, implies(Y5, Y5))))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, implies(Y5, implies(Y6, Y5)))))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(Y4, implies(Y5, implies(Y6, Y6)))))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(Y3, implies(implies(Y4, Y3), implies(Y5, Y3))))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(implies(Y3, Y2), implies(Y4, Y2)))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(implies(implies(Y3, Y3), Y4), implies(Y5, Y4)))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(Y2, implies(implies(implies(Y3, Y4), Y3), implies(Y5, Y3)))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(Y2, Y1), implies(Y3, Y1))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(implies(Y2, Y2), Y3), implies(Y4, Y3))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(implies(Y2, Y3), Y2), implies(Y4, Y2))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(implies(Y2, implies(Y3, Y2)), Y4), implies(Y5, Y4))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(implies(Y2, implies(Y3, Y3)), Y4), implies(Y5, Y4))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y1, implies(implies(implies(Y2, implies(Y3, Y4)), Y3), implies(Y5, Y3))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y2, Y0), implies(Y0, Y1)), implies(X3, implies(Y0, Y1)))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y3, Y1), implies(Y0, implies(Y1, Y2))), implies(X3, implies(Y0, implies(Y1, Y2))))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y3, implies(Y1, Y2)), implies(Y0, Y1)), implies(X3, implies(Y0, Y1)))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(Y4, implies(Y1, Y3)), implies(implies(Y0, Y1), implies(Y2, Y1))), implies(X3, implies(implies(Y0, Y1), implies(Y2, Y1))))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(X1, X2), X3), X2), implies(X1, X2))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(Y1, implies(X0, X1)), implies(Y2, implies(X0, X1))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(Y2, Y0), implies(Y3, Y0)), implies(Y0, Y1)), implies(X3, implies(Y0, Y1)))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, Y1), Y2), implies(Y3, Y2)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, Y2), Y1), implies(Y3, Y1)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, Y2), Y3), implies(implies(Y3, Y1), implies(Y4, Y1))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, Y2), implies(Y2, Y3)), implies(Y4, implies(Y2, Y3))), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, implies(Y2, Y1)), Y3), implies(Y4, Y3)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, implies(Y2, Y2)), Y3), implies(Y4, Y3)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, implies(Y2, Y3)), Y2), implies(Y4, Y2)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, implies(Y2, implies(Y3, Y2))), Y4), implies(Y5, Y4)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(Y1, implies(Y2, implies(Y3, Y3))), Y4), implies(Y5, Y4)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f1(true__, implies(implies(implies(implies(implies(implies(Y1, Y2), Y3), Y2), implies(Y1, Y2)), X0), implies(X3, X0))) -> true__
% 16.61/16.64 f2(f1(true__, Y0), Y0, Y1) -> true__
% 16.61/16.64 f2(is_a_theorem(X), X, Y) -> true__
% 16.61/16.64 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 16.61/16.64 f3(f1(true__, implies(implies(implies(a, b), a), a))) -> true__
% 16.61/16.64 f3(is_a_theorem(implies(implies(implies(a, b), a), a))) -> true__
% 16.61/16.64 f3(true__) -> false__
% 16.61/16.64 false__ -> true__
% 16.61/16.64 is_a_theorem(Y) -> f1(true__, Y)
% 16.61/16.64 is_a_theorem(implies(X, X)) -> true__
% 16.61/16.64 is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(U, X)))) -> true__
% 16.61/16.64 with the LPO induced by
% 16.61/16.64 b > a > f3 > f2 > implies > is_a_theorem > f1 > false__ > true__
% 16.61/16.64
% 16.61/16.64 % SZS output end Proof
% 16.61/16.64
%------------------------------------------------------------------------------