TSTP Solution File: LCL086-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL086-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 12:57:54 EDT 2022
% Result : Unsatisfiable 6.56s 6.59s
% Output : Proof 6.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL086-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n025.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 : Sat Jul 2 20:34:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.56/6.59 % SZS status Unsatisfiable
% 6.56/6.59 % SZS output start Proof
% 6.56/6.59 The input problem is unsatisfiable because
% 6.56/6.59
% 6.56/6.59 [1] the following set of Horn clauses is unsatisfiable:
% 6.56/6.59
% 6.56/6.59 is_a_theorem(implies(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 6.56/6.59 is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(T, implies(implies(S, P), implies(R, P)))))
% 6.56/6.59 is_a_theorem(implies(a, a)) ==> \bottom
% 6.56/6.59
% 6.56/6.59 This holds because
% 6.56/6.59
% 6.56/6.59 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 6.56/6.59
% 6.56/6.59 E:
% 6.56/6.59 f1(true__, Y) = is_a_theorem(Y)
% 6.56/6.59 f2(is_a_theorem(X), X, Y) = true__
% 6.56/6.59 f2(true__, X, Y) = f1(is_a_theorem(implies(X, Y)), Y)
% 6.56/6.59 f3(is_a_theorem(implies(a, a))) = true__
% 6.56/6.59 f3(true__) = false__
% 6.56/6.59 is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(T, implies(implies(S, P), implies(R, P))))) = true__
% 6.56/6.59 G:
% 6.56/6.59 true__ = false__
% 6.56/6.59
% 6.56/6.59 This holds because
% 6.56/6.59
% 6.56/6.59 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 6.56/6.59
% 6.56/6.59
% 6.56/6.59 f1(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X0, X0)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X0, implies(X1, X0))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X1, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X0, X0)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X2, X2)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X1, X1))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, implies(X3, X3))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(X0, X0), implies(X0, X0))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(implies(X2, X3), implies(X4, X3))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X1, X2), implies(X3, X2)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, X3), implies(X2, X3)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, implies(X2, X2)), implies(X2, implies(X2, X2))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(X1, implies(implies(implies(X1, X2), X1), X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X1, X2))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X2, X2))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(X2, implies(X1, X2)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(X0, X2), implies(X1, X2)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, X2), implies(implies(implies(X2, X1), X2), implies(X1, X2)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, implies(X1, X1)), implies(X1, implies(X1, X1)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(X1, implies(X1, X1)), implies(X2, implies(X1, implies(X1, X1))))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X0, X0), X1), implies(X2, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X0, X1), X0), X0)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X0, X1), implies(X2, X1)), implies(implies(X0, X1), implies(X2, X1)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X1), X2), implies(X1, X2))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X1), implies(X2, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X1), implies(implies(X1, X2), X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, X2), X3), implies(implies(implies(X3, X4), X2), X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X1, X1)), X2), implies(X3, X2))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, X3)), X4), implies(implies(implies(implies(X5, X2), implies(X6, X2)), implies(X2, X3)), X4))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(X2, implies(X2, X2))), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(implies(X1, X2), implies(X3, X2))), X4), implies(X5, X4))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(X1, implies(implies(implies(X1, X2), X1), X1)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X0, X0), X1), implies(X0, X0)), implies(X0, X0))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X0, X1), implies(X2, X1)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, X2), implies(X1, X2)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, X2), implies(X2, implies(X1, X2))), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(X1, X2), implies(X3, X2)), X4), implies(X1, X4))), Y1)), Y1) -> true__
% 6.56/6.59 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__
% 6.56/6.59 f1(f1(true__, implies(implies(X0, implies(implies(implies(implies(implies(X1, X2), X1), implies(X2, X1)), X3), implies(X4, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, X1), implies(X0, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, X1), implies(X1, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, X1), implies(implies(implies(implies(X0, X1), X2), X1), implies(X0, X1))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, implies(X0, X0)), implies(X0, implies(X0, X0))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(X0, implies(X0, X0)), implies(X1, implies(X0, implies(X0, X0)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, X0), X1), implies(X0, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, X1), X2), implies(implies(implies(X2, X3), X1), X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, X1), implies(X2, X3)), implies(X4, implies(implies(X3, X0), implies(X2, X0)))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X0, X0)), X1), implies(X2, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, X2)), X3), implies(implies(implies(implies(X4, X1), implies(X5, X1)), implies(X1, X2)), X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X1, X1))), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X0, X0)))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(X2, implies(X2, X2)))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(X1, implies(implies(X1, X2), implies(X3, X2)))), X4), implies(X5, X4)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X1, X2), implies(X1, X2))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X1, X2), implies(X2, X2))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(X1, X2), implies(X2, implies(X1, X2)))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X0, X1), X0), X0)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(X0, implies(implies(implies(X1, X2), X1), implies(X2, X1))), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), X2), X1), implies(X0, X1)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X0, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X1, X1)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X2, X1)), X3), implies(X0, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X2, X1)), implies(X1, X3)), implies(X4, implies(X1, X3))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(X0, implies(X1, X0)), X2), X0), implies(X0, implies(X1, X0))), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), X2), implies(X3, X2)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(implies(X0, implies(X0, X0)), X1), implies(X2, X1)), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(f1(true__, implies(implies(implies(implies(implies(implies(implies(X0, X1), X2), X1), implies(X0, X1)), X3), implies(X4, X3)), Y1)), Y1) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(Y1, Y1))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(Y1, implies(Y2, implies(implies(X0, X0), implies(X0, X0)))))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(Y1, implies(Y2, implies(implies(implies(X0, X1), implies(X2, X1)), implies(implies(X0, X1), implies(X2, X1))))))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(X2, X1), implies(implies(X0, X1), implies(X2, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(implies(X0, X0), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(implies(X0, X1), implies(X2, X1)), implies(implies(X0, X1), implies(X2, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(implies(implies(X0, X0), Y1), implies(X0, X0)), implies(X0, X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(implies(implies(X0, X1), implies(X2, X1)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X0, implies(implies(implies(implies(implies(X0, X1), implies(X2, X1)), Y1), implies(implies(X0, X1), implies(X2, X1))), implies(implies(X0, X1), implies(X2, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X1, X1)) -> true__
% 6.56/6.59 f1(true__, implies(X1, implies(implies(X1, X2), implies(X3, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(Y0, implies(Y0, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(Y1, implies(Y2, implies(implies(X0, implies(X0, X0)), implies(X0, implies(X0, X0))))))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(Y2, implies(implies(Y0, implies(Y0, Y0)), implies(Y0, implies(Y0, Y0)))))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(implies(X0, implies(X0, X0)), implies(X0, implies(X0, X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(implies(implies(X0, implies(X0, X0)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X2, implies(implies(implies(implies(X0, implies(X0, X0)), Y1), implies(X0, implies(X0, X0))), implies(X0, implies(X0, X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y0, implies(X1, implies(X1, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y0, implies(implies(implies(Y0, X1), Y0), Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y1, implies(Y2, implies(implies(X0, implies(X1, implies(X1, X1))), implies(X0, implies(X1, implies(X1, X1)))))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y1, implies(Y2, implies(implies(implies(X0, X1), implies(X0, X1)), implies(implies(X0, X1), implies(X0, X1))))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y1, implies(Y2, implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), implies(implies(X0, X1), implies(X1, implies(X0, X1)))))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(Y1, implies(Y2, implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), implies(implies(implies(X0, X1), X0), implies(X1, X0))))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(X0, X1), implies(X0, X1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(X0, implies(implies(implies(X0, X1), X0), X0)), implies(X0, implies(implies(implies(X0, X1), X0), X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(X1, X0), implies(implies(implies(X0, X1), X0), implies(X1, X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(X1, implies(X1, X1)), implies(Y0, implies(X1, implies(X1, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(X0, X1), implies(X0, X1)), implies(implies(X0, X1), implies(X0, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), implies(implies(X0, X1), implies(X1, implies(X0, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(X0, implies(X1, implies(X1, X1))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(X0, implies(implies(implies(X0, X1), X0), X0)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), implies(implies(implies(X0, X1), X0), implies(X1, X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, X1), implies(X0, X1)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, X1), implies(X1, X1)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, implies(X1, implies(X1, X1))), Y1), implies(X0, implies(X1, implies(X1, X1)))), implies(X0, implies(X1, implies(X1, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(X0, implies(implies(implies(X0, X1), X0), X0)), Y1), implies(X0, implies(implies(implies(X0, X1), X0), X0))), implies(X0, implies(implies(implies(X0, X1), X0), X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(implies(X0, X1), implies(X0, X1)), Y1), implies(implies(X0, X1), implies(X0, X1))), implies(implies(X0, X1), implies(X0, X1))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(implies(X0, X1), implies(X1, implies(X0, X1))), Y1), implies(implies(X0, X1), implies(X1, implies(X0, X1)))), implies(implies(X0, X1), implies(X1, implies(X0, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X3, implies(implies(implies(implies(implies(implies(X0, X1), X0), implies(X1, X0)), Y1), implies(implies(implies(X0, X1), X0), implies(X1, X0))), implies(implies(implies(X0, X1), X0), implies(X1, X0))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(Y0, implies(X1, implies(X2, implies(X2, X2)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(Y0, implies(X1, implies(X2, implies(Y0, Y0)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(Y0, implies(implies(X1, X2), implies(X1, X2))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(Y1, implies(Y2, implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), implies(X0, implies(implies(X0, X1), implies(X2, X1)))))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(Y4, implies(implies(Y4, Y0), implies(Y2, Y0))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), implies(X0, implies(implies(X0, X1), implies(X2, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(X1, implies(X2, implies(X2, X2))), implies(Y0, implies(X1, implies(X2, implies(X2, X2))))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(Y1, Y0), implies(Y0, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(Y2, Y1), implies(Y1, implies(Y2, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X0, X1), X0), implies(implies(X0, X1), X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X0, implies(X1, implies(X2, implies(X2, X2)))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X0, implies(implies(X1, X2), implies(X1, X2))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X0, implies(implies(X1, X2), implies(X2, implies(X1, X2)))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(X1, X2), implies(X1, X2)), implies(Y0, implies(implies(X1, X2), implies(X1, X2)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y0, X1), implies(X2, X1)), implies(Y0, implies(implies(Y0, X1), implies(X2, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y0, Y1), Y0), implies(Y1, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y1, Y1), X0), implies(Y1, X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y1, Y3), implies(implies(Y0, Y1), implies(Y2, Y1))), implies(Y4, implies(implies(Y0, Y1), implies(Y2, Y1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y2, Y1), X0), implies(implies(implies(X0, X1), Y1), X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(Y5, implies(Y2, Y4)), X0), implies(implies(implies(implies(Y1, Y2), implies(Y3, Y2)), implies(Y2, Y4)), X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(implies(X0, implies(implies(X0, X1), implies(X2, X1))), Y1), implies(X0, implies(implies(X0, X1), implies(X2, X1)))), implies(X0, implies(implies(X0, X1), implies(X2, X1)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(implies(X0, implies(implies(X1, X2), implies(X1, X2))), Y1), implies(X0, implies(implies(X1, X2), implies(X1, X2)))), implies(X0, implies(implies(X1, X2), implies(X1, X2)))))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(implies(Y1, Y2), implies(Y3, Y2)), X0), implies(Y1, X0)))) -> true__
% 6.56/6.59 f1(true__, implies(X4, implies(implies(implies(implies(Y3, Y0), implies(Y2, Y0)), implies(Y0, Y1)), implies(Y4, implies(Y0, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(X5, implies(Y0, implies(X1, implies(implies(X1, X2), implies(X3, X2)))))) -> true__
% 6.56/6.59 f1(true__, implies(X5, implies(implies(X1, implies(implies(X1, X2), implies(X3, X2))), implies(Y0, implies(X1, implies(implies(X1, X2), implies(X3, X2))))))) -> true__
% 6.56/6.59 f1(true__, implies(X5, implies(implies(implies(X0, implies(X1, implies(implies(X1, X2), implies(X3, X2)))), Y1), implies(Y2, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(Y0, implies(Y0, implies(X2, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(Y0, implies(Y2, implies(X2, implies(Y0, Y0))))) -> true__
% 6.56/6.59 f1(true__, implies(Y1, implies(Y1, Y1))) -> true__
% 6.56/6.59 f1(true__, implies(Y2, implies(implies(implies(Y2, Y3), Y2), Y2))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(X2, X2))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(X2, implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y0, Y0)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y1, implies(Y1, Y1))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(implies(Y0, Y1), implies(Y0, Y1)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(implies(Y0, Y1), implies(Y1, Y1)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(implies(implies(Y0, Y1), Y0), implies(Y1, Y0)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(implies(implies(Y0, implies(Y0, Y0)), Y1), implies(Y2, Y1)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(X1, X2), implies(implies(implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1)), X2), implies(X1, X2)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, Y1), implies(Y0, Y1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, Y1), implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(Y0, Y0)), implies(Y0, implies(Y0, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(Y1, Y1)), implies(X1, implies(Y0, implies(Y1, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))), implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))), implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)), implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))), implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, Y1), implies(Y0, implies(Y1, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(Y1, Y1)), implies(Y0, implies(Y1, implies(Y1, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(Y2, implies(Y0, Y0))), implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(Y2, implies(Y2, Y2))), implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(Y2, implies(Y3, implies(Y1, Y1)))), implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y1, Y1))))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3)))), implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3))))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2))), implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3))), implies(Y0, implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1)), implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(X1, X1), X2), implies(X1, X2))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(X1, X2), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(X1, X2), X3), implies(implies(implies(X3, X4), X2), X3))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(X1, implies(X2, X3)), X4), implies(implies(implies(implies(X5, X2), implies(X6, X2)), implies(X2, X3)), X4))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, Y1), implies(Y2, Y3)), implies(Y4, implies(implies(Y3, Y0), implies(Y2, Y0))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y0, Y0)), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, Y1)), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y1, Y1))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y1, Y1))))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3))))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(Y0, Y1), implies(Y2, Y1))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, Y2))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2)))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y0, implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y1, Y2), implies(Y1, Y2)), implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y1, Y2), implies(Y2, Y2)), implies(Y0, implies(implies(Y1, Y2), implies(Y2, Y2))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2))), implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2))), implies(Y0, implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(X1, X2), implies(X3, X2)), X4), implies(X1, X4))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(X1, X2), implies(X3, X2)), implies(X2, X4)), implies(X5, implies(X2, X4)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, Y1), implies(Y0, Y1)), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, Y1), implies(Y1, Y1)), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, Y1), implies(Y1, implies(Y0, Y1))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y0, Y0)), X1), implies(Y0, implies(Y0, Y0))), implies(Y0, implies(Y0, Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y0, Y0)), implies(Y0, implies(Y0, Y0))), X1), implies(X2, X1))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, Y1)), X1), implies(Y0, implies(Y1, Y1))), implies(Y0, implies(Y1, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(Y1, Y1))), X1), implies(Y0, implies(Y1, implies(Y1, Y1)))), implies(Y0, implies(Y1, implies(Y1, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))), X1), implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0))))), implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))), X1), implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2))))), implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3))))), X1), implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3)))))), implies(Y0, implies(Y1, implies(Y2, implies(Y3, implies(Y3, Y3))))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))), X1), implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2))))), implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3)))), X1), implies(Y0, implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3))))), implies(Y0, implies(Y1, implies(implies(Y2, Y3), implies(Y2, Y3)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1))), X1), implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1)))), implies(Y0, implies(Y1, implies(implies(implies(Y1, Y2), Y1), Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))), X1), implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2)))), implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, Y2))), X1), implies(Y0, implies(implies(Y1, Y2), implies(Y2, Y2)))), implies(Y0, implies(implies(Y1, Y2), implies(Y2, Y2))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))), X1), implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2))))), implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2)))), X1), implies(Y0, implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2))))), implies(Y0, implies(implies(Y1, Y2), implies(implies(Y0, Y2), implies(Y1, Y2)))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)), X1), implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0))), implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))), X1), implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1)))), implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y0, implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2))), X1), implies(Y0, implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2)))), implies(Y0, implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y1, Y0), X3), Y0), implies(Y1, Y0))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1)), implies(Y0, implies(implies(implies(Y1, Y2), Y1), implies(Y2, Y1))))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y1, implies(Y0, Y1)), X3), Y1), implies(Y1, implies(Y0, Y1)))) -> true__
% 6.56/6.59 f1(true__, implies(implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2)), implies(Y0, implies(implies(implies(Y1, implies(Y1, Y1)), Y2), implies(Y3, Y2))))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(Y1, implies(Y2, implies(implies(X0, X1), implies(X0, X1)))), X3), X1), implies(Y1, implies(Y2, implies(implies(X0, X1), implies(X0, X1)))))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(X0, X1), implies(X0, X1)), X3), X1), implies(implies(X0, X1), implies(X0, X1)))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, Y0), Y1), implies(Y0, Y1)), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, Y1), Y0), implies(Y1, Y0)), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, Y1), Y2), implies(implies(implies(Y2, Y3), Y1), Y2)), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, Y1), implies(Y0, Y1)), X1), implies(implies(Y0, Y1), implies(Y0, Y1))), implies(implies(Y0, Y1), implies(Y0, Y1)))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y3)), implies(Y4, implies(implies(Y3, Y0), implies(Y2, Y0)))), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(Y0, Y0)), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(Y1, implies(Y1, Y1))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y0, Y0)))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(Y1, implies(Y2, implies(Y2, Y2)))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(Y1, implies(implies(Y1, Y2), implies(Y3, Y2)))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(implies(Y0, Y1), implies(Y2, Y1))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y1, Y2))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(implies(Y1, Y2), implies(Y2, implies(Y1, Y2)))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(Y0, implies(implies(implies(Y0, Y1), Y0), Y0)), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(X0, X1), Y1), implies(Y2, Y1)), X3), X1), implies(implies(implies(X0, X1), Y1), implies(Y2, Y1)))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1)), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(Y0, Y1), implies(Y0, Y1)), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(Y0, Y1), implies(Y1, implies(Y0, Y1))), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(Y0, Y1), implies(Y2, Y1)), Y3), implies(Y0, Y3)), X1), implies(X2, X1))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(implies(X0, X1), Y1), implies(X0, X1)), implies(X0, X1)), X3), X1), implies(implies(implies(implies(X0, X1), Y1), implies(X0, X1)), implies(X0, X1)))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(implies(Y0, Y1), Y0), implies(Y1, Y0)), X1), implies(X2, X1)), X3), implies(X4, X3))) -> true__
% 6.60/6.60 f1(true__, implies(implies(implies(implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1)), X1), implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1))), implies(implies(implies(implies(Y0, Y1), Y2), Y1), implies(Y0, Y1)))) -> true__
% 6.60/6.60 f2(f1(true__, Y0), Y0, Y1) -> true__
% 6.60/6.60 f2(is_a_theorem(X), X, Y) -> true__
% 6.60/6.60 f2(true__, X, Y) -> f1(is_a_theorem(implies(X, Y)), Y)
% 6.60/6.60 f3(f1(true__, implies(a, a))) -> true__
% 6.60/6.60 f3(is_a_theorem(implies(a, a))) -> true__
% 6.60/6.60 f3(true__) -> false__
% 6.60/6.60 false__ -> true__
% 6.60/6.60 is_a_theorem(Y) -> f1(true__, Y)
% 6.60/6.60 is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(T, implies(implies(S, P), implies(R, P))))) -> true__
% 6.60/6.60 with the LPO induced by
% 6.60/6.60 a > f3 > f2 > implies > is_a_theorem > f1 > false__ > true__
% 6.60/6.60
% 6.60/6.60 % SZS output end Proof
% 6.60/6.60
%------------------------------------------------------------------------------