TSTP Solution File: LCL104-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 12:58:01 EDT 2022
% Result : Unsatisfiable 7.19s 7.15s
% Output : Proof 7.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL104-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 03:52:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 7.19/7.15 % SZS status Unsatisfiable
% 7.19/7.15 % SZS output start Proof
% 7.19/7.15 The input problem is unsatisfiable because
% 7.19/7.15
% 7.19/7.15 [1] the following set of Horn clauses is unsatisfiable:
% 7.19/7.15
% 7.19/7.15 is_a_theorem(equivalent(X, Y)) & is_a_theorem(X) ==> is_a_theorem(Y)
% 7.19/7.15 is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, U)), equivalent(Z, U)), X)))
% 7.19/7.15 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z))
% 7.19/7.15 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) ==> \bottom
% 7.19/7.15
% 7.19/7.15 This holds because
% 7.19/7.15
% 7.19/7.15 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 7.19/7.15
% 7.19/7.15 E:
% 7.19/7.15 f1(true__, Y) = is_a_theorem(Y)
% 7.19/7.15 f2(is_a_theorem(X), X, Y) = true__
% 7.19/7.15 f2(true__, X, Y) = f1(is_a_theorem(equivalent(X, Y)), Y)
% 7.19/7.15 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) = true__
% 7.19/7.15 f3(true__) = false__
% 7.19/7.15 is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, U)), equivalent(Z, U)), X))) = true__
% 7.19/7.15 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z)) = true__
% 7.19/7.15 G:
% 7.19/7.15 true__ = false__
% 7.19/7.15
% 7.19/7.15 This holds because
% 7.19/7.15
% 7.19/7.15 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 7.19/7.15
% 7.19/7.15
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(X0, X0), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(X0, equivalent(X1, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), X0))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, X0))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(X0, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), X0)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(X0, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), X1))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X1))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(equivalent(X3, X2), equivalent(X3, X1)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, equivalent(X3, X0)), equivalent(X2, equivalent(X3, X1)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, equivalent(X3, equivalent(X4, X0))), equivalent(X2, equivalent(X3, equivalent(X4, X1))))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X0)), X1)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(equivalent(X3, X1), equivalent(X3, X2)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(equivalent(X3, X1), equivalent(equivalent(X4, X3), equivalent(X4, X2))))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(equivalent(X3, equivalent(X4, X1)), equivalent(X3, equivalent(X4, X2))))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(equivalent(X3, X0), equivalent(X3, equivalent(equivalent(X4, X1), equivalent(X4, X2))))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(equivalent(equivalent(X1, X3), X0), equivalent(X3, X2))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, equivalent(X2, X3))), equivalent(X0, equivalent(X1, equivalent(equivalent(X4, X2), equivalent(X4, X3))))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, equivalent(equivalent(X2, X3), X4))), equivalent(X0, equivalent(equivalent(equivalent(X3, X2), X1), X4))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, equivalent(equivalent(X2, X3), equivalent(X2, X4)))), equivalent(X0, equivalent(X1, equivalent(X3, X4)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(X1, equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X4)))), equivalent(X0, equivalent(X1, X4))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(X4, equivalent(equivalent(X2, X1), X0)), equivalent(X4, X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), X3)), equivalent(equivalent(equivalent(X2, X1), X0), X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X0, equivalent(X2, X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X0, equivalent(equivalent(X4, X2), equivalent(X4, X3)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(equivalent(X4, X0), equivalent(X4, equivalent(X2, X3)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X0, equivalent(X2, X1)), X3))), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))), equivalent(X0, X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))), equivalent(equivalent(X4, X0), equivalent(X4, X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(equivalent(X3, equivalent(X2, X1)), equivalent(X3, X4)))), equivalent(X0, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(X2, X3)), equivalent(X1, equivalent(X2, X4)))), equivalent(X0, equivalent(X3, X4))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, equivalent(X2, X3)), equivalent(X1, equivalent(equivalent(X3, X2), X4)))), equivalent(X0, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), X4)), equivalent(X0, equivalent(equivalent(X2, X3), X4))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3))), equivalent(X0, equivalent(X4, X4))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(X0, equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(X3, X1), equivalent(X3, X2))), X4)), equivalent(X0, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(equivalent(X3, X1), equivalent(equivalent(X0, X3), X2))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(X3, X1), equivalent(X3, X2))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(X3, equivalent(X4, X1)), equivalent(X3, equivalent(X4, X2)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, equivalent(X2, X3))), equivalent(X1, equivalent(equivalent(X4, X2), equivalent(X4, X3)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X4)))), equivalent(X1, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), X2)), X2), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), equivalent(X2, X3))), equivalent(equivalent(X4, X2), equivalent(X4, X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), equivalent(equivalent(X2, X3), equivalent(X2, X4)))), equivalent(X3, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X1, X0), equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X4)))), X4), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X3))), equivalent(X1, X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), equivalent(X0, X4)))), equivalent(X1, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), equivalent(equivalent(X1, X0), X4)))), X4), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, equivalent(X1, X0)), equivalent(X2, X3))), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X1), equivalent(X2, X0)), X3)), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, X0)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(X1, X3))), equivalent(X2, X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), equivalent(X0, equivalent(equivalent(X2, X1), X3))), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(X0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X0, equivalent(X2, X3))), equivalent(X4, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(X1, X3)), equivalent(X2, equivalent(X0, X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), X3), equivalent(equivalent(X1, X2), X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), equivalent(X3, X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), equivalent(X3, equivalent(equivalent(equivalent(equivalent(X4, X5), equivalent(X4, X6)), equivalent(X5, X6)), X3))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), equivalent(equivalent(X3, X4), equivalent(equivalent(X5, X3), equivalent(X5, X4)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), equivalent(equivalent(equivalent(X3, X4), equivalent(equivalent(X4, X3), X5)), X5)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X3)), equivalent(X2, X3)), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(equivalent(X2, X1), X3)), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(equivalent(X2, X0), equivalent(X2, X1))), X3), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X0, equivalent(X1, X2)), X3), equivalent(X2, X4)), equivalent(X3, equivalent(X0, equivalent(X1, X4)))), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), X2), equivalent(X1, X0)), equivalent(X2, X3)), X3), Y1)), Y1) -> true__
% 7.19/7.15 f1(f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0, X1), equivalent(X0, X2)), equivalent(X1, X2)), X3), X4), equivalent(X3, X4)), Y1)), Y1) -> true__
% 7.19/7.15 f1(true__, equivalent(X1, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(Y0, Y0)))) -> true__
% 7.19/7.15 f1(true__, equivalent(X1, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1)))))) -> true__
% 7.19/7.15 f1(true__, equivalent(X1, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), Y2)), Y2)))) -> true__
% 7.19/7.15 f1(true__, equivalent(X2, equivalent(X0, equivalent(equivalent(X0, equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3))), X2)))) -> true__
% 7.19/7.15 f1(true__, equivalent(Y0, equivalent(equivalent(X3, equivalent(X4, equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)))), equivalent(X3, equivalent(X4, Y0))))) -> true__
% 7.19/7.15 f1(true__, equivalent(Y0, equivalent(equivalent(X3, equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3))), equivalent(X3, Y0)))) -> true__
% 7.19/7.15 f1(true__, equivalent(Y0, equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0)))) -> true__
% 7.19/7.15 f1(true__, equivalent(Y0, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0))) -> true__
% 7.19/7.15 f1(true__, equivalent(Y2, Y2)) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, Y3), equivalent(equivalent(equivalent(Y2, Y1), equivalent(equivalent(Y1, Y2), X1)), Y3))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, equivalent(Y0, Y0)))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, equivalent(Y0, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0))))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1)))))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))), equivalent(Y0, Y3))))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X1, equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4))), equivalent(X1, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X2, Y0), equivalent(X2, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0)))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X2, Y0), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0))))) -> true__
% 7.19/7.15 f1(true__, equivalent(equivalent(X2, equivalent(X3, Y0)), equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, Y1))), equivalent(X2, equivalent(X3, equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, Y1))), equivalent(X2, equivalent(X3, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, Y1))), equivalent(X2, equivalent(X3, equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(Y1, Y2)))), equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3)))), equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(Y2, Y1), Y0), Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3))))), equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(Y2, Y3)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))))), equivalent(X2, equivalent(X3, equivalent(Y0, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)))), equivalent(X2, equivalent(X3, equivalent(Y1, Y2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)))), equivalent(X2, equivalent(X3, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, Y3))))), equivalent(X2, equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(Y1, Y3))))), equivalent(X2, equivalent(X3, equivalent(Y2, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), Y3))))), equivalent(X2, equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(Y1, Y3)))), equivalent(X2, equivalent(X3, equivalent(Y2, equivalent(Y0, Y3)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3))), equivalent(X2, equivalent(X3, equivalent(equivalent(Y1, Y2), Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2)))), equivalent(X2, equivalent(X3, equivalent(Y3, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(X3, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), Y3))), equivalent(X2, equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(X2, equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(X2, equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(X2, equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, Y1)), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(Y1, Y2))), equivalent(X2, equivalent(equivalent(equivalent(Y1, Y3), Y0), equivalent(Y3, Y2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(Y1, Y2))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y0, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3))), equivalent(X2, equivalent(equivalent(equivalent(Y2, Y1), Y0), Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(equivalent(Y2, Y1), Y0), Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y0, equivalent(Y2, Y3)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3)))), equivalent(X2, equivalent(Y0, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3)))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y0, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X2, equivalent(Y1, Y2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X2, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y1, Y2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), Y2))), equivalent(X2, Y2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, Y3)))), equivalent(X2, Y3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, Y3)))), equivalent(equivalent(X3, X2), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(Y1, Y3)))), equivalent(X2, equivalent(Y2, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(Y1, Y3)))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y2, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), Y3)))), equivalent(X2, Y3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), Y3)))), equivalent(equivalent(X3, X2), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(Y1, Y3))), equivalent(X2, equivalent(Y2, equivalent(Y0, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3)), equivalent(X2, equivalent(equivalent(Y1, Y2), Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))), equivalent(X2, equivalent(equivalent(equivalent(Y3, Y4), equivalent(equivalent(Y4, Y3), Y5)), Y5)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))), equivalent(equivalent(X3, X2), equivalent(X3, equivalent(Y3, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), Y3)), equivalent(X2, Y3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), Y3)), equivalent(equivalent(X3, X2), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, X1), equivalent(equivalent(X0, X3), equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), equivalent(X0, X1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, Y1), equivalent(equivalent(Y0, X3), equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, Y3), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), X3), Y3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(Y0, equivalent(Y1, Y2)), X2)))), equivalent(X3, X2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, equivalent(Y1, Y2)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), X3), equivalent(Y3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, X2)))), equivalent(X3, equivalent(equivalent(X4, X1), equivalent(X4, X2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X3, equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(Y0, X3), equivalent(equivalent(equivalent(Y2, Y1), Y0), Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X4, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(X1, X3))))), equivalent(X4, equivalent(X2, X3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(X4, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))))), equivalent(X4, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(X3, equivalent(Y2, Y0)), equivalent(X3, equivalent(Y2, Y1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(X3, equivalent(Y2, Y0)), equivalent(X3, equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(X3, equivalent(Y2, equivalent(Y3, Y0))), equivalent(X3, equivalent(Y2, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(equivalent(X4, Y2), equivalent(X4, Y1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(equivalent(X4, Y2), equivalent(X4, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, Y1), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(X2, X4)), equivalent(equivalent(equivalent(X2, X3), Y0), equivalent(X3, X4)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(equivalent(X3, Y0), equivalent(X3, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(equivalent(X3, equivalent(X4, Y0)), equivalent(X3, equivalent(X4, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2))))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(Y0, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(X3, X2), X4)), equivalent(equivalent(equivalent(X2, X3), Y0), X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(X3, equivalent(equivalent(Y2, Y1), Y0)), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, equivalent(Y2, Y1)), equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))), equivalent(equivalent(X3, Y0), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))), equivalent(equivalent(X3, equivalent(X4, Y0)), equivalent(X3, equivalent(X4, Y3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(Y0, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(X2, equivalent(Y0, equivalent(Y1, Y2))), equivalent(X2, X3)))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(Y0, equivalent(Y1, Y2)), X2))), X2)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(Y2, Y3), equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), equivalent(X1, X3)))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), equivalent(equivalent(X2, X1), X3)))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X1, X3), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, equivalent(X1, X2))))), equivalent(X3, X2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X1, X3), equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(X1, X2))))), equivalent(X3, X2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X1, X3), equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), equivalent(X1, X2))), equivalent(X3, X2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, equivalent(equivalent(X1, X2), X3))))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, equivalent(X1, X2)), equivalent(Y0, Y2))), Y2)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(X1, X2), X3))))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(Y0, equivalent(Y1, equivalent(X1, X2))), equivalent(Y0, equivalent(Y1, Y3)))), Y3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(equivalent(Y0, Y1), equivalent(X1, X2)), equivalent(Y1, Y3))), equivalent(Y0, Y3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2))), equivalent(X1, X2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(X2, X1), equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), equivalent(equivalent(X1, X2), X3))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(X3, Y1), equivalent(X3, Y2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(X3, equivalent(X4, Y1)), equivalent(X3, equivalent(X4, Y2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), equivalent(Y1, Y2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, equivalent(X2, X3))), equivalent(Y1, equivalent(equivalent(X4, X2), equivalent(X4, X3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, equivalent(equivalent(X2, X3), X4))), equivalent(equivalent(equivalent(X3, X2), Y1), X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, equivalent(equivalent(X2, X3), equivalent(X2, X4)))), equivalent(Y1, equivalent(X3, X4)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X4)))), equivalent(Y1, X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), Y2)), Y2)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), Y2)), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), Y2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, X2))), equivalent(equivalent(X3, X1), equivalent(X3, X2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, X2))), equivalent(equivalent(X3, equivalent(X4, X1)), equivalent(X3, equivalent(X4, X2))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, equivalent(X2, X3)))), equivalent(X1, equivalent(equivalent(X4, X2), equivalent(X4, X3))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, equivalent(equivalent(X2, X3), X4)))), equivalent(equivalent(equivalent(X3, X2), X1), X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, equivalent(equivalent(X2, X3), equivalent(X2, X4))))), equivalent(X1, equivalent(X3, X4)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(X1, equivalent(equivalent(X2, X3), equivalent(equivalent(X3, X2), X4))))), equivalent(X1, X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(X1, X3)))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(X1, X3)))), equivalent(equivalent(X4, X2), equivalent(X4, X3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3)))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, X2), equivalent(equivalent(X3, equivalent(X2, X1)), equivalent(X3, X4))))), X4)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(X1, equivalent(X2, X3)), equivalent(X1, equivalent(equivalent(X3, X2), X4))))), X4)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)))), equivalent(X4, X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), equivalent(equivalent(equivalent(X1, X2), equivalent(equivalent(X3, X1), equivalent(X3, X2))), X4))), X4)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, equivalent(X1, X2)))), equivalent(equivalent(X3, X1), equivalent(X3, X2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, equivalent(equivalent(X1, X2), equivalent(X1, X3))))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, Y2), X2), equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, Y1), X2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(X1, X2)), equivalent(Y0, equivalent(X1, X3))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(X1, X2)), equivalent(Y0, equivalent(equivalent(X2, X1), X3))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(Y1, Y3))), equivalent(equivalent(X3, Y2), equivalent(X3, Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(X1, X2)))), equivalent(equivalent(X3, X1), equivalent(X3, X2)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(X1, X2), equivalent(X1, X3))))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, equivalent(X1, X2))), equivalent(Y0, equivalent(Y1, equivalent(X1, X3)))), equivalent(X2, X3))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(Y1, equivalent(X1, X2))), equivalent(Y0, equivalent(Y1, equivalent(equivalent(X2, X1), X3)))), X3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(Y0, equivalent(X2, X3))), equivalent(X4, X4))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y0, equivalent(equivalent(X1, X2), equivalent(equivalent(X3, X1), equivalent(X3, X2)))), equivalent(Y0, Y2)), Y2)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y1, X3), equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X3, Y2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y1, Y3), equivalent(Y1, Y2)), equivalent(Y3, Y2))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(Y2, Y1), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3)), Y3)) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(Y0, Y0))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(Y0, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), Y0)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(equivalent(Y3, Y2), equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y3, Y0)), equivalent(Y2, equivalent(Y3, Y1)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2)))))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3)), equivalent(equivalent(equivalent(Y2, Y1), Y0), Y3)))) -> true__
% 7.19/7.16 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3))), equivalent(Y0, equivalent(Y2, Y3))))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y0, equivalent(Y2, Y1)), Y3))), Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(Y0, equivalent(equivalent(Y1, Y2), equivalent(equivalent(Y2, Y1), Y3))), equivalent(Y0, Y3)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(Y3, Y1), equivalent(Y3, Y2))))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y1, Y0), Y2)), Y2))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, equivalent(Y1, Y0)), equivalent(Y2, Y3))), Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(Y1, Y3))), equivalent(Y2, Y3)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(Y0, equivalent(Y1, Y2)), equivalent(Y0, equivalent(equivalent(Y2, Y1), Y3))), Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(Y1, Y3)), equivalent(Y2, equivalent(Y0, Y3))))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(Y1, Y2), Y3)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, Y2)), equivalent(Y3, Y3)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(X1, X2), equivalent(X1, X3)), equivalent(X2, X3)), equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), Y3), Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), Y2), equivalent(Y1, Y3)), equivalent(equivalent(X3, Y2), equivalent(X3, equivalent(Y0, Y3))))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), Y3), equivalent(equivalent(X3, equivalent(Y1, Y2)), equivalent(X3, Y3)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(Y1, X3)), equivalent(Y2, X3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2)), equivalent(equivalent(Y2, Y1), X3)), X3)) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), Y3), equivalent(equivalent(equivalent(equivalent(X2, X3), equivalent(X2, X4)), equivalent(X3, X4)), Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), equivalent(X1, X2)), equivalent(equivalent(X3, X1), equivalent(X3, X2)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), equivalent(equivalent(X1, X2), equivalent(X1, X3))), equivalent(X2, X3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y0, Y1), equivalent(equivalent(Y2, Y0), equivalent(Y2, Y1))), equivalent(equivalent(X1, X2), equivalent(equivalent(X2, X1), X3))), X3)) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), X3), equivalent(equivalent(Y2, Y3), X3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y2, Y3), equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3))), X3), X3)) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y2, equivalent(Y3, Y0)), X3), equivalent(Y0, Y1)), equivalent(X3, equivalent(Y2, equivalent(Y3, Y1))))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y3, Y1), X2), equivalent(Y1, Y2)), equivalent(X2, equivalent(Y3, Y2)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(Y3, Y1), X3), equivalent(equivalent(Y0, Y1), equivalent(Y0, Y2))), equivalent(X3, equivalent(Y3, Y2)))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(X2, X1), Y1), equivalent(X1, X2)), equivalent(Y1, Y3)), Y3)) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(Y2, Y1), Y0), X3), equivalent(Y0, equivalent(equivalent(Y1, Y2), Y3))), equivalent(X3, Y3))) -> true__
% 7.19/7.17 f1(true__, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y1, Y2), equivalent(Y1, Y3)), equivalent(Y2, Y3)), X3), Y0), equivalent(X3, Y0))) -> true__
% 7.19/7.17 f2(f1(true__, Y0), Y0, Y1) -> true__
% 7.19/7.17 f2(is_a_theorem(X), X, Y) -> true__
% 7.19/7.17 f2(true__, X, Y) -> f1(is_a_theorem(equivalent(X, Y)), Y)
% 7.19/7.17 f3(f1(true__, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) -> true__
% 7.19/7.17 f3(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))) -> true__
% 7.19/7.17 f3(true__) -> false__
% 7.19/7.17 is_a_theorem(Y) -> f1(true__, Y)
% 7.19/7.17 is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, U)), equivalent(Z, U)), X))) -> true__
% 7.19/7.17 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z)) -> true__
% 7.19/7.17 true__ -> false__
% 7.19/7.17 with the LPO induced by
% 7.19/7.17 e > c > b > a > f2 > equivalent > f3 > is_a_theorem > f1 > true__ > false__
% 7.19/7.17
% 7.19/7.17 % SZS output end Proof
% 7.19/7.17
%------------------------------------------------------------------------------