TSTP Solution File: LCL098-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL098-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n029.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 12:57:59 EDT 2022
% Result : Unsatisfiable 60.75s 60.54s
% Output : Proof 60.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL098-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : moca.sh %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 21:09:57 EDT 2022
% 0.14/0.37 % CPUTime :
% 60.75/60.54 % SZS status Unsatisfiable
% 60.75/60.54 % SZS output start Proof
% 60.75/60.54 The input problem is unsatisfiable because
% 60.75/60.54
% 60.75/60.54 [1] the following set of Horn clauses is unsatisfiable:
% 60.75/60.54
% 60.75/60.54 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 60.75/60.54 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), U), equivalent(equivalent(Y, Z), U)), V), V))
% 60.75/60.54 is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))) ==> \bottom
% 60.75/60.54
% 60.75/60.54 This holds because
% 60.75/60.54
% 60.75/60.54 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 60.75/60.54
% 60.75/60.54 E:
% 60.75/60.54 f1(true__, Y) = is_a_theorem(Y)
% 60.75/60.54 f2(is_a_theorem(X), X, Y) = true__
% 60.75/60.54 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 60.75/60.54 f3(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))) = true__
% 60.75/60.54 f3(true__) = false__
% 60.75/60.54 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), U), equivalent(equivalent(Y, Z), U)), V), V)) = true__
% 60.75/60.54 G:
% 60.75/60.54 true__ = false__
% 60.75/60.54
% 60.75/60.54 This holds because
% 60.75/60.54
% 60.75/60.54 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 60.75/60.54
% 60.75/60.54
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(X3, X2), equivalent(X3, X1)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, X1))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(X3, X2), equivalent(equivalent(equivalent(X4, X5), X3), equivalent(equivalent(X6, X5), equivalent(equivalent(X4, X6), X1)))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(X3, X2), equivalent(equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X3), equivalent(equivalent(X5, X6), X1))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(equivalent(X3, X4), X2), equivalent(equivalent(X5, X4), equivalent(equivalent(X3, X5), X1))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), X1)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, equivalent(X3, X0)), equivalent(equivalent(equivalent(X4, X5), X2), equivalent(equivalent(X6, X5), equivalent(equivalent(X4, X6), equivalent(X3, X1)))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), X0), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), X1)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), X0), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), X1))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(X4, X0)), equivalent(equivalent(X5, X3), equivalent(equivalent(X2, X5), equivalent(X4, X1))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, equivalent(equivalent(X3, X4), X5)), X0), equivalent(equivalent(X2, equivalent(equivalent(equivalent(X6, X3), equivalent(X6, X4)), X5)), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(X2, X3), X4), X0), equivalent(equivalent(equivalent(equivalent(X5, X2), equivalent(X5, X3)), X4), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X0), equivalent(equivalent(X3, X4), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, X0)), equivalent(equivalent(X3, X4), equivalent(X5, X1)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X4, X2), X5)), X0), equivalent(equivalent(equivalent(X4, X3), X5), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(X2, equivalent(X3, X4)), equivalent(X2, equivalent(X3, X5))), X0), equivalent(equivalent(X4, X5), X1))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), X4), equivalent(equivalent(X5, X3), equivalent(equivalent(X2, X5), X4))), X0), X1)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), X0), X1)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(equivalent(X3, X0), equivalent(X3, equivalent(equivalent(equivalent(X4, X5), X1), equivalent(equivalent(X6, X5), equivalent(equivalent(X4, X6), X2)))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(equivalent(X3, X0), equivalent(X3, equivalent(equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X1), equivalent(equivalent(X5, X6), X2))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(X4, X0), equivalent(X4, equivalent(equivalent(X5, X2), equivalent(equivalent(X1, X5), X3))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), X0), equivalent(equivalent(X2, X3), X4))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4), equivalent(equivalent(X2, X3), X4)), X5)), equivalent(equivalent(X6, X0), equivalent(X6, X5))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), equivalent(equivalent(X0, X3), X2))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), equivalent(equivalent(X4, equivalent(X0, X3)), equivalent(X4, X2)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X2, X3)), equivalent(equivalent(X4, X1), equivalent(equivalent(X0, X4), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), X2), X3)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X3), X4)), equivalent(equivalent(X5, X1), equivalent(equivalent(X0, X5), equivalent(equivalent(X6, X3), equivalent(equivalent(X2, X6), X4))))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5)), equivalent(equivalent(X6, X1), equivalent(equivalent(X0, X6), equivalent(equivalent(X3, X4), X5)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), X6)), equivalent(equivalent(X7, X1), equivalent(equivalent(X0, X7), X6))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), X3), equivalent(equivalent(X4, X2), equivalent(equivalent(X0, equivalent(X1, X4)), X3))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), X3), equivalent(equivalent(X4, X2), equivalent(equivalent(equivalent(equivalent(X5, X0), equivalent(X5, X1)), X4), X3))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), X3), equivalent(equivalent(X4, equivalent(equivalent(equivalent(X5, X0), equivalent(X5, X1)), X2)), equivalent(X4, X3))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), X3), equivalent(equivalent(equivalent(X0, X4), X2), equivalent(equivalent(X1, X4), X3))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X3, X4)), equivalent(equivalent(X1, X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), X3), X4))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(X1, X2), equivalent(equivalent(X6, X4), equivalent(equivalent(X3, X6), X5)))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6)), equivalent(equivalent(X1, X2), equivalent(equivalent(X4, X5), X6))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X7)), equivalent(equivalent(X1, X2), X7)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), X3)), X4), equivalent(equivalent(equivalent(X2, X1), X3), X4)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), equivalent(equivalent(X0, X3), X2))), X4), X4), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), X4), X4), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), equivalent(X4, X5)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6, X7), equivalent(X6, X8)), X9), equivalent(equivalent(X7, X8), X9)), X4), X5)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(X4, X5), X6)), equivalent(equivalent(X7, X5), equivalent(equivalent(X4, X7), X6))), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X7)), equivalent(equivalent(X5, X6), X7)), Y1)), Y1) -> true__
% 60.75/60.54 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X7), equivalent(equivalent(X5, X6), X7)), X8)), X8), Y1)), Y1) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X6, equivalent(X0, X1)), equivalent(equivalent(equivalent(Y2, Y3), X6), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), equivalent(X0, X2))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X6, equivalent(X0, X1)), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), X6), equivalent(equivalent(Y3, Y4), equivalent(X0, X2)))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(X6, equivalent(X0, X1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), X6), equivalent(X0, X2))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(Y3, X1), equivalent(equivalent(X0, Y3), equivalent(X0, X2))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(equivalent(equivalent(Y3, Y4), Y5), X1), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), X2)))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(Y2, Y3), equivalent(X0, X1))), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), equivalent(X0, X2)))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), equivalent(X0, X1))), equivalent(equivalent(Y3, Y4), equivalent(X0, X2))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X1, X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), equivalent(X0, X1))), equivalent(X0, X2)))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(Y2, Y0), equivalent(equivalent(equivalent(equivalent(Y3, Y4), equivalent(Y3, Y5)), Y2), equivalent(equivalent(Y4, Y5), Y1))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))))) -> true__
% 60.75/60.54 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(X3, X4), X2), equivalent(equivalent(X5, X4), equivalent(equivalent(X3, X5), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(X3, X4), X2), equivalent(equivalent(X5, X4), equivalent(equivalent(X3, X5), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(X3, X4), X2), equivalent(equivalent(X5, X4), equivalent(equivalent(X3, X5), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X3, X2), equivalent(equivalent(X4, X3), equivalent(X4, equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(equivalent(X3, X4), X2), equivalent(equivalent(X5, X4), equivalent(equivalent(X3, X5), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(X3, X2), equivalent(X3, Y4)))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), Y4)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X2), Y4))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y4, Y5), Y6))), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(Y7, Y5), equivalent(equivalent(Y4, Y7), Y6)))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6)), Y7), equivalent(equivalent(Y5, Y6), Y7)), Y8))), equivalent(equivalent(X3, X2), equivalent(X3, Y8)))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X3, Y1), equivalent(equivalent(X4, equivalent(Y0, X3)), equivalent(X4, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X3, Y1), equivalent(equivalent(Y0, X3), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X3, Y1), equivalent(equivalent(Y0, X3), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X3, Y2), equivalent(equivalent(X4, equivalent(equivalent(Y0, Y1), X3)), equivalent(X4, equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X3, Y2), equivalent(equivalent(equivalent(Y0, Y1), X3), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X4, Y1), equivalent(equivalent(equivalent(equivalent(X5, X0), equivalent(X5, X1)), X4), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), equivalent(X0, X1)), equivalent(equivalent(Y3, Y4), Y1))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X4, Y2), equivalent(equivalent(equivalent(equivalent(X5, Y0), equivalent(X5, Y1)), X4), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X4, equivalent(Y0, Y1)), equivalent(X4, equivalent(equivalent(X5, Y0), equivalent(equivalent(Y2, X5), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X4, equivalent(Y0, Y1)), equivalent(X4, equivalent(equivalent(X5, Y0), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), X5), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X4, equivalent(equivalent(Y0, Y1), Y2)), equivalent(X4, equivalent(equivalent(X5, Y1), equivalent(equivalent(Y3, X5), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X4, equivalent(equivalent(equivalent(X5, Y0), equivalent(X5, Y1)), Y2)), equivalent(X4, equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X5, X6), equivalent(equivalent(equivalent(Y0, Y2), equivalent(X4, X5)), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), equivalent(X4, X6)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X5, X6), equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X4, X5)), equivalent(equivalent(X1, X2), equivalent(X4, X6))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X5, Y1), equivalent(equivalent(Y0, X5), equivalent(equivalent(X6, Y0), equivalent(equivalent(Y2, X6), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X5, Y1), equivalent(equivalent(Y0, X5), equivalent(equivalent(X6, Y0), equivalent(equivalent(equivalent(Y2, Y3), X6), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X5, Y1), equivalent(equivalent(Y0, X5), equivalent(equivalent(X6, Y0), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), X6), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X5, Y2), equivalent(equivalent(equivalent(Y0, Y1), X5), equivalent(equivalent(X6, Y1), equivalent(equivalent(Y3, X6), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X6, equivalent(equivalent(Y0, equivalent(equivalent(X2, X3), X4)), Y2)), equivalent(X6, equivalent(equivalent(Y0, equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4)), Y2)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X7, Y1), equivalent(equivalent(Y3, X7), equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), Y3), equivalent(equivalent(X1, X2), Y1))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(X7, Y1), equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(equivalent(X2, X3), Y4)), X7), equivalent(equivalent(equivalent(X2, X4), Y4), Y1)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(X7, Y1), equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y4), X4), equivalent(equivalent(Y3, Y4), equivalent(equivalent(Y2, Y3), X4))), X7), Y1))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(Y2, equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3)), equivalent(equivalent(Y3, Y2), equivalent(Y3, equivalent(equivalent(X1, X2), X3))))) -> true__
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% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(Y0, Y1)), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), Y4)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(X4, X3), equivalent(equivalent(X5, X4), equivalent(equivalent(X2, X5), Y4))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y4, Y5), Y6))), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), equivalent(equivalent(Y7, Y5), equivalent(equivalent(Y4, Y7), Y6)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6)), Y7), equivalent(equivalent(Y5, Y6), Y7)), Y8))), equivalent(equivalent(X4, X3), equivalent(equivalent(X2, X4), Y8)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, Y1), X3), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), equivalent(equivalent(X2, Y0), X3))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X2, equivalent(equivalent(Y1, Y2), Y3)), X3), equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3)), X3))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X3, X5), X2), equivalent(equivalent(X4, X5), equivalent(equivalent(Y0, equivalent(X3, X4)), equivalent(Y0, X2))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(X4, equivalent(X0, X2)), Y4), equivalent(equivalent(X1, X2), equivalent(equivalent(X4, equivalent(X0, X1)), Y4)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(Y0, Y2), X2), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), X2)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(Y2, Y3), equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3)), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), equivalent(equivalent(X1, X2), X3))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), Y4), X3), equivalent(equivalent(equivalent(X0, X2), Y4), equivalent(equivalent(X1, X2), X3)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), X7)), equivalent(equivalent(X1, X2), equivalent(equivalent(X5, X6), X7)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), X4), equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(X5, X2), equivalent(X5, X3)), X4), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), X4), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(equivalent(equivalent(X5, X2), equivalent(X5, X3)), X4), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), X4), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(equivalent(equivalent(X5, X2), equivalent(X5, X3)), X4), Y4))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, equivalent(Y0, Y1))), equivalent(equivalent(X3, X4), equivalent(X5, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, equivalent(Y0, Y1))), equivalent(equivalent(X3, X4), equivalent(X5, equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, equivalent(Y0, Y1))), equivalent(equivalent(X3, X4), equivalent(X5, equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, equivalent(equivalent(Y0, Y1), Y2))), equivalent(equivalent(X3, X4), equivalent(X5, equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X5, equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4))), equivalent(equivalent(X3, X4), equivalent(X5, Y4)))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(Y0, Y1)), equivalent(equivalent(X3, X4), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(Y0, Y1)), equivalent(equivalent(X3, X4), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1)))))) -> true__
% 60.75/60.55 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(Y0, Y1)), equivalent(equivalent(X3, X4), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(Y0, Y1)), equivalent(equivalent(X3, X4), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X3, X4), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), equivalent(equivalent(X3, X4), Y4))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y4, Y5), Y6))), equivalent(equivalent(X3, X4), equivalent(equivalent(Y7, Y5), equivalent(equivalent(Y4, Y7), Y6))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6)), Y7), equivalent(equivalent(Y5, Y6), Y7)), Y8))), equivalent(equivalent(X3, X4), Y8))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X4, X2), X5)), equivalent(Y0, Y1)), equivalent(equivalent(equivalent(X4, X3), X5), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X4, X2), X5)), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(equivalent(X4, X3), X5), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, equivalent(X3, X4)), equivalent(X2, equivalent(X3, X5))), equivalent(Y0, Y1)), equivalent(equivalent(X4, X5), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X2, equivalent(X3, X4)), equivalent(X2, equivalent(X3, X5))), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(X4, X5), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(X4, X5), X6), X2), equivalent(equivalent(Y0, equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6)), equivalent(Y0, X2)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), Y3), X2), equivalent(equivalent(X6, Y3), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), X6), X2)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), Y3), X2), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3)), X2))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), Y5), Y6), equivalent(equivalent(X6, Y5), equivalent(equivalent(Y7, X6), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y7), Y6))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), Y5), Y6), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(Y7, Y5)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y7), Y6)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(X3, X5)), Y6), equivalent(equivalent(X4, X5), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(X3, X4)), Y6)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(X4, X5), X6)), Y6), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6)), Y6))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), X5)), X2), equivalent(equivalent(equivalent(Y0, Y2), X5), X2))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), X4), equivalent(equivalent(X5, X3), equivalent(equivalent(X2, X5), X4))), equivalent(Y0, Y1)), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X3, X5), Y2), equivalent(equivalent(X4, X5), equivalent(equivalent(X3, X4), Y2))), X2), X2)) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y6), Y2), equivalent(equivalent(Y5, Y6), equivalent(equivalent(Y4, Y5), Y2))), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(X6, X4), equivalent(equivalent(X3, X6), X5)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y6), Y2), equivalent(equivalent(Y5, Y6), equivalent(equivalent(Y4, Y5), Y2))), equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6)), equivalent(equivalent(X4, X5), X6))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y6), Y2), equivalent(equivalent(Y5, Y6), equivalent(equivalent(Y4, Y5), Y2))), equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X7)), X7)) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(Y0, Y1)), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(Y0, Y1)), equivalent(equivalent(equivalent(Y2, Y3), Y0), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y0), equivalent(equivalent(Y3, Y4), Y1)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(Y0, Y1)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), Y0), Y1))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(Y0, Y1), Y2)), equivalent(equivalent(Y3, Y1), equivalent(equivalent(Y0, Y3), Y2)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4)), Y4)) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y4, Y5), Y6))), equivalent(equivalent(Y7, Y5), equivalent(equivalent(Y4, Y7), Y6)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), X5), equivalent(equivalent(X3, X4), X5)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(equivalent(equivalent(Y4, Y5), equivalent(Y4, Y6)), Y7), equivalent(equivalent(Y5, Y6), Y7)), Y8))), Y8)) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(Y0, equivalent(X1, X3)), Y2)), equivalent(equivalent(X2, X3), equivalent(equivalent(Y0, equivalent(X1, X2)), Y2)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(Y2, X3), Y1)), equivalent(equivalent(Y3, X3), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), Y1))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(Y2, Y3), X3), Y1)), equivalent(equivalent(equivalent(Y2, Y4), X3), equivalent(equivalent(Y3, Y4), Y1)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y4, equivalent(X1, X3)), Y6))), equivalent(equivalent(X2, X3), equivalent(equivalent(Y4, equivalent(X1, X2)), Y6)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4))), equivalent(equivalent(X2, X3), X4))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5, X6), equivalent(X5, X7)), X8), equivalent(equivalent(X6, X7), X8)), equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), X3), Y1)), equivalent(equivalent(equivalent(equivalent(Y3, Y4), Y5), X3), Y1))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6, X7), equivalent(X6, X8)), X9), equivalent(equivalent(X7, X8), X9)), equivalent(equivalent(Y2, Y3), equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3))), equivalent(equivalent(Y4, Y3), equivalent(equivalent(Y2, Y4), equivalent(equivalent(X1, X2), X3))))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6, X7), equivalent(X6, X8)), X9), equivalent(equivalent(X7, X8), X9)), equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3))), equivalent(equivalent(Y3, Y4), equivalent(equivalent(X1, X2), X3)))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), X4), Y4), equivalent(equivalent(equivalent(equivalent(Y1, Y2), Y3), X4), Y4))) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)), Y4), Y4)) -> true__
% 60.75/60.56 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(Y2, Y4)), Y5), equivalent(equivalent(Y3, Y4), Y5)), equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3)), equivalent(equivalent(X1, X2), X3))) -> true__
% 60.75/60.56 f2(f1(true__, Y0), Y0, Y1) -> true__
% 60.75/60.56 f2(is_a_theorem(X), X, Y) -> true__
% 60.75/60.56 f2(true__, X, Y) -> f1(is_a_theorem(equivalent(X, Y)), Y)
% 60.75/60.56 f3(f1(true__, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))) -> true__
% 60.75/60.56 f3(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))) -> true__
% 60.75/60.56 f3(true__) -> false__
% 60.75/60.56 false__ -> true__
% 60.75/60.56 is_a_theorem(Y) -> f1(true__, Y)
% 60.75/60.56 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), U), equivalent(equivalent(Y, Z), U)), V), V)) -> true__
% 60.75/60.56 with the LPO induced by
% 60.75/60.56 falsehood > e > c > b > a > f3 > f2 > equivalent > is_a_theorem > f1 > false__ > true__
% 60.75/60.56
% 60.75/60.56 % SZS output end Proof
% 60.75/60.56
%------------------------------------------------------------------------------