TSTP Solution File: LCL239-3 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n013.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 12:59:37 EDT 2022
% Result : Unsatisfiable 12.81s 12.63s
% Output : Proof 12.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 20:27:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 12.81/12.63 % SZS status Unsatisfiable
% 12.81/12.63 % SZS output start Proof
% 12.81/12.63 The input problem is unsatisfiable because
% 12.81/12.63
% 12.81/12.63 [1] the following set of Horn clauses is unsatisfiable:
% 12.81/12.63
% 12.81/12.63 axiom(implies(or(A, A), A))
% 12.81/12.63 axiom(implies(A, or(B, A)))
% 12.81/12.63 axiom(implies(or(A, B), or(B, A)))
% 12.81/12.63 axiom(implies(or(A, or(B, C)), or(B, or(A, C))))
% 12.81/12.63 axiom(implies(implies(A, B), implies(or(C, A), or(C, B))))
% 12.81/12.63 implies(X, Y) = or(not(X), Y)
% 12.81/12.63 axiom(X) ==> theorem(X)
% 12.81/12.63 theorem(implies(Y, X)) & theorem(Y) ==> theorem(X)
% 12.81/12.63 and(P, Q) = not(or(not(P), not(Q)))
% 12.81/12.63 theorem(not(and(p, not(p)))) ==> \bottom
% 12.81/12.63
% 12.81/12.63 This holds because
% 12.81/12.63
% 12.81/12.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 12.81/12.63
% 12.81/12.63 E:
% 12.81/12.63 and(P, Q) = not(or(not(P), not(Q)))
% 12.81/12.63 axiom(implies(A, or(B, A))) = true__
% 12.81/12.63 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true__
% 12.81/12.63 axiom(implies(or(A, A), A)) = true__
% 12.81/12.63 axiom(implies(or(A, B), or(B, A))) = true__
% 12.81/12.63 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true__
% 12.81/12.63 f1(axiom(X), X) = true__
% 12.81/12.63 f1(true__, X) = theorem(X)
% 12.81/12.63 f2(true__, X) = theorem(X)
% 12.81/12.63 f3(theorem(Y), Y, X) = true__
% 12.81/12.63 f3(true__, Y, X) = f2(theorem(implies(Y, X)), X)
% 12.81/12.63 f4(theorem(not(and(p, not(p))))) = true__
% 12.81/12.63 f4(true__) = false__
% 12.81/12.63 implies(X, Y) = or(not(X), Y)
% 12.81/12.63 G:
% 12.81/12.63 true__ = false__
% 12.81/12.63
% 12.81/12.63 This holds because
% 12.81/12.63
% 12.81/12.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 12.81/12.63
% 12.81/12.63
% 12.81/12.63 and(P, Q) -> not(or(not(P), not(Q)))
% 12.81/12.63 axiom(implies(A, or(B, A))) -> true__
% 12.81/12.63 axiom(implies(Y0, implies(X0, Y0))) -> true__
% 12.81/12.63 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) -> true__
% 12.81/12.63 axiom(implies(implies(X0, Y1), or(Y1, not(X0)))) -> true__
% 12.81/12.63 axiom(implies(implies(X0, not(X0)), not(X0))) -> true__
% 12.81/12.63 axiom(implies(implies(X0, or(Y1, Y2)), or(Y1, implies(X0, Y2)))) -> true__
% 12.81/12.63 axiom(implies(implies(Y0, Y1), implies(implies(X0, Y0), implies(X0, Y1)))) -> true__
% 12.81/12.63 axiom(implies(implies(Y0, implies(X0, Y2)), implies(X0, implies(Y0, Y2)))) -> true__
% 12.81/12.63 axiom(implies(implies(Y0, not(X0)), implies(X0, not(Y0)))) -> true__
% 12.81/12.63 axiom(implies(or(A, A), A)) -> true__
% 12.81/12.63 axiom(implies(or(A, B), or(B, A))) -> true__
% 12.81/12.63 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) -> true__
% 12.81/12.63 axiom(implies(or(Y0, implies(X0, Y2)), implies(X0, or(Y0, Y2)))) -> true__
% 12.81/12.63 axiom(implies(or(Y0, not(X0)), implies(X0, Y0))) -> true__
% 12.81/12.63 f1(axiom(X), X) -> true__
% 12.81/12.63 f1(true__, implies(X0, implies(X1, X0))) -> true__
% 12.81/12.63 f1(true__, implies(X0, implies(Y1, or(Y2, Y1)))) -> true__
% 12.81/12.63 f1(true__, implies(X0, implies(Y1, or(Y2, not(or(Y2, Y2)))))) -> true__
% 12.81/12.63 f1(true__, implies(X0, not(implies(X0, not(X0))))) -> true__
% 12.81/12.63 f1(true__, implies(X0, not(not(X0)))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(X1, X0))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(Y1, implies(Y2, Y2)))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(Y1, implies(Y2, or(Y3, Y2))))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(Y1, implies(or(Y2, Y2), Y2)))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(Y1, or(Y2, not(or(Y2, Y2)))))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(or(Y1, Y2), not(Y2)))) -> true__
% 12.81/12.63 f1(true__, implies(X0, or(or(Y1, Y2), not(or(Y2, Y1))))) -> true__
% 12.81/12.63 f1(true__, implies(X1, implies(X2, implies(Y0, Y0)))) -> true__
% 12.81/12.63 f1(true__, implies(X1, implies(Y0, Y0))) -> true__
% 12.81/12.63 f1(true__, implies(X1, implies(Y0, or(or(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.63 f1(true__, implies(X1, implies(or(Y0, Y0), Y0))) -> true__
% 12.81/12.63 f1(true__, implies(X1, implies(or(Y0, Y1), or(Y1, Y0)))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(Y0, not(Y0)))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(Y0, not(or(Y0, Y0))))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(Y0, or(or(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(implies(Y0, Y1), not(Y1)))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(implies(Y0, or(Y1, Y0)), Y2))) -> true__
% 12.81/12.63 f1(true__, implies(X1, or(implies(or(Y0, Y0), Y0), Y1))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, Y0)) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, implies(Y2, Y0)))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, implies(Y2, or(Y3, Y2))))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, implies(or(Y2, Y2), Y2)))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, not(implies(X0, not(X0)))))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, not(not(X0))))) -> true__
% 12.81/12.63 f1(true__, implies(Y0, implies(X0, or(Y2, Y0)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(Y1, implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(Y1, implies(X0, not(implies(X0, not(X0))))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(Y1, implies(Y2, implies(X0, Y2))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(Y1, implies(implies(X0, not(X0)), not(X0))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(Y1, or(implies(X0, Y3), not(Y3))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(implies(X0, Y2), or(Y2, not(X0))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(implies(X0, not(X0)), not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(implies(Y1, not(X0)), implies(X0, not(Y1))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, implies(or(Y1, not(X0)), implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(X2, implies(Y1, Y0)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(X2, or(Y1, Y0)))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(Y1, implies(X0, not(implies(X0, not(X0))))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(Y1, implies(Y2, implies(X0, Y2))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(Y1, implies(implies(X0, not(X0)), not(X0))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(Y1, or(implies(X0, Y3), not(Y3))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(implies(X0, Y2), not(or(Y2, not(X0)))))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(implies(Y1, implies(X0, Y1)), Y3))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(implies(implies(X0, not(X0)), not(X0)), Y2))) -> true__
% 12.81/12.64 f1(true__, implies(Y0, or(or(Y1, not(X0)), not(implies(X0, Y1))))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, X1), implies(implies(X2, X0), implies(X2, X1)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, X1), implies(or(X2, X0), or(X2, X1)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, X1), or(X1, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, Y1), implies(X0, or(Y2, Y1)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, implies(X1, X2)), implies(X1, implies(X0, X2)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, not(X0)), implies(Y1, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, not(X0)), not(X0))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, not(X0)), or(Y1, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, not(X1)), implies(X1, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, or(Y1, Y1)), implies(X0, Y1))) -> true__
% 12.81/12.64 f1(true__, implies(implies(X0, or(Y1, Y2)), or(Y1, implies(X0, Y2)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(Y0, Y1), implies(Y0, implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, implies(implies(Y0, implies(X0, not(X0))), implies(Y0, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(or(X0, X0), X0)) -> true__
% 12.81/12.64 f1(true__, implies(or(X0, X1), or(X1, X0))) -> true__
% 12.81/12.64 f1(true__, implies(or(X0, implies(X1, X2)), implies(X1, or(X0, X2)))) -> true__
% 12.81/12.64 f1(true__, implies(or(X0, not(X1)), implies(X1, X0))) -> true__
% 12.81/12.64 f1(true__, implies(or(X0, or(X1, X2)), or(X1, or(X0, X2)))) -> true__
% 12.81/12.64 f1(true__, implies(or(X2, Y0), or(X2, or(Y1, Y0)))) -> true__
% 12.81/12.64 f1(true__, implies(or(X2, or(Y0, Y0)), or(X2, Y0))) -> true__
% 12.81/12.64 f1(true__, implies(or(Y0, Y0), implies(X2, Y0))) -> true__
% 12.81/12.64 f1(true__, implies(or(Y0, Y0), or(X2, Y0))) -> true__
% 12.81/12.64 f1(true__, implies(or(Y0, Y1), or(Y0, implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, implies(or(Y0, implies(X0, not(X0))), or(Y0, not(X0)))) -> true__
% 12.81/12.64 f1(true__, implies(or(implies(X0, not(X0)), implies(X0, not(X0))), not(X0))) -> true__
% 12.81/12.64 f1(true__, implies(or(or(X1, X1), or(X1, X1)), X1)) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, Y0), not(implies(Y0, Y0))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, implies(Y1, Y0)), not(implies(Y0, implies(Y1, Y0)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, implies(Y1, implies(Y2, Y1))), not(implies(Y0, implies(Y1, implies(Y2, Y1))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, implies(Y1, or(Y2, Y1))), not(implies(Y0, implies(Y1, or(Y2, Y1))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, implies(or(Y1, Y1), Y1)), not(implies(Y0, implies(or(Y1, Y1), Y1)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, not(implies(Y0, not(Y0)))), not(implies(Y0, not(implies(Y0, not(Y0)))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(Y0, or(Y1, Y0)), not(implies(Y0, or(Y1, Y0)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(implies(Y0, not(Y0)), not(Y0)), not(implies(implies(Y0, not(Y0)), not(Y0)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(or(Y0, Y0), Y0), not(implies(or(Y0, Y0), Y0))))) -> true__
% 12.81/12.64 f1(true__, not(implies(implies(or(Y0, Y1), or(Y1, Y0)), not(implies(or(Y0, Y1), or(Y1, Y0)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(Y0, implies(Y1, implies(Y2, Y1))), not(or(Y0, implies(Y1, implies(Y2, Y1))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(Y0, implies(Y1, or(Y2, Y1))), not(or(Y0, implies(Y1, or(Y2, Y1))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(Y0, implies(or(Y1, Y1), Y1)), not(or(Y0, implies(or(Y1, Y1), Y1)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(Y0, not(or(Y0, Y0))), not(or(Y0, not(or(Y0, Y0))))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(implies(Y0, Y1), not(Y1)), not(or(implies(Y0, Y1), not(Y1)))))) -> true__
% 12.81/12.64 f1(true__, not(implies(or(or(Y0, Y1), not(Y1)), not(or(or(Y0, Y1), not(Y1)))))) -> true__
% 12.81/12.64 f1(true__, not(not(implies(X0, not(not(X0)))))) -> true__
% 12.81/12.64 f1(true__, not(not(implies(Y0, Y0)))) -> true__
% 12.81/12.64 f1(true__, not(not(implies(Y0, or(Y1, Y0))))) -> true__
% 12.81/12.64 f1(true__, not(not(implies(or(Y0, Y0), Y0)))) -> true__
% 12.81/12.64 f1(true__, not(not(or(Y0, not(Y0))))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(Y0, Y0))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(Y0, or(Y1, Y0)))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(Y0, or(Y1, not(or(Y1, Y1)))))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(Y0, or(implies(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(Y0, or(or(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(or(Y0, Y0), Y0))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(or(Y0, Y1), or(Y1, Y0)))) -> true__
% 12.81/12.64 f1(true__, or(X1, implies(or(or(X1, X2), or(X1, X2)), X2))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(X2, implies(Y0, Y0)))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, implies(Y1, or(Y2, Y1))))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, implies(or(Y1, Y1), Y1)))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, not(Y0)))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, not(or(Y0, Y0))))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, or(Y1, not(or(Y1, Y1)))))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, or(implies(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(Y0, or(or(Y1, Y2), not(Y2))))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(implies(Y0, or(Y1, Y0)), Y2))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(implies(or(Y0, Y0), Y0), Y1))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(or(Y0, Y1), not(Y1)))) -> true__
% 12.81/12.64 f1(true__, or(X1, or(or(Y0, Y1), not(or(Y1, Y0))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(X0, implies(Y2, Y2)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(X0, implies(Y2, or(Y3, Y2))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(X0, implies(or(Y2, Y2), Y2)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(X0, not(implies(X0, not(X0)))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(X0, not(not(X0))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(Y1, implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(Y1, implies(X0, not(implies(X0, not(X0))))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(Y1, implies(Y2, implies(X0, Y2))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(Y1, implies(implies(X0, not(X0)), not(X0))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(implies(X0, Y2), or(Y2, not(X0))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(implies(X0, not(X0)), not(X0)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(implies(Y1, not(X0)), implies(X0, not(Y1))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, implies(or(Y1, not(X0)), implies(X0, Y1)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, not(Y0))) -> true__
% 12.81/12.64 f1(true__, or(Y0, not(or(Y0, Y0)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(Y1, implies(X0, not(implies(X0, not(X0))))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(Y1, implies(Y2, implies(X0, Y2))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(Y1, implies(implies(X0, not(X0)), not(X0))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(implies(X0, Y2), not(Y2)))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(implies(X0, Y2), not(or(Y2, not(X0)))))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(implies(Y1, implies(X0, Y1)), Y3))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(implies(implies(X0, not(X0)), not(X0)), Y2))) -> true__
% 12.81/12.64 f1(true__, or(Y0, or(or(Y1, not(X0)), not(implies(X0, Y1))))) -> true__
% 12.81/12.64 f1(true__, or(implies(X0, Y1), not(or(Y1, not(X0))))) -> true__
% 12.81/12.64 f1(true__, or(implies(Y0, implies(X0, Y0)), Y2)) -> true__
% 12.81/12.64 f1(true__, or(implies(Y0, not(X0)), not(implies(X0, not(Y0))))) -> true__
% 12.81/12.64 f1(true__, or(implies(Y1, Y0), not(Y0))) -> true__
% 12.81/12.64 f1(true__, or(implies(Y1, or(Y2, Y1)), Y0)) -> true__
% 12.81/12.64 f1(true__, or(implies(implies(X0, not(X0)), not(X0)), Y1)) -> true__
% 12.81/12.64 f1(true__, or(implies(or(Y1, Y1), Y1), Y0)) -> true__
% 12.81/12.64 f1(true__, or(or(Y0, not(X0)), not(implies(X0, Y0)))) -> true__
% 12.81/12.64 f1(true__, or(or(Y1, Y0), not(Y0))) -> true__
% 12.81/12.64 f1(true__, or(or(Y1, Y0), not(or(Y0, Y1)))) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, X0), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, not(implies(X2, not(X2)))))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(X2, or(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(implies(X2, not(X2)), not(X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, implies(or(X2, X2), X2))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, not(implies(X1, not(X1))))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, or(X2, X0))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, or(X2, not(or(X2, X2))))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, or(implies(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(X1, or(or(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(implies(X1, X2), or(X2, not(X1)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(implies(X1, not(X1)), not(X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(implies(X1, not(X2)), implies(X2, not(X1)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(or(X1, X1), X1)), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(or(X1, X2), or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, implies(or(X1, not(X2)), implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, not(implies(X0, not(X0)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, not(not(X0))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(X2, X0))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(X2, not(implies(X2, not(X2)))))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(X2, or(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(implies(X2, not(X2)), not(X2)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, implies(or(X2, X2), X2))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, not(X1))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, not(or(X1, X1)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, or(X2, X0))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, or(X2, not(or(X2, X2))))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, or(implies(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.64 f2(f1(true__, implies(implies(X0, or(X1, or(or(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(implies(X1, X2), not(X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(implies(X1, implies(X2, X1)), X3)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(implies(X1, or(X2, X1)), X3)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(implies(implies(X1, not(X1)), not(X1)), X2)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(implies(or(X1, X1), X1), X2)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(or(X1, X2), not(X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(X0, or(or(X1, X2), not(or(X2, X1)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, X1), implies(X0, implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, X1), implies(X0, or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, X1), implies(implies(X2, X0), implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, X1), implies(or(X2, X0), or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, X1), or(X1, not(X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, implies(X1, X2)), implies(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, not(X0)), implies(X1, not(X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, not(X0)), not(X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, not(X0)), or(X1, not(X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, not(X1)), implies(X1, not(X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, or(X1, X1)), implies(X0, X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(implies(X0, or(X1, X2)), or(X1, implies(X0, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X0), X0), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X0), implies(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X0), or(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X1), or(X0, implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X1), or(X0, or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, X1), or(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, implies(X1, X2)), implies(X1, or(X0, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, not(X1)), implies(X1, X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, or(X1, X1)), or(X0, X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(X0, or(X1, X2)), or(X1, or(X0, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(implies(or(or(X0, X0), or(X0, X0)), X0), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(not(not(implies(X0, X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(X2, not(implies(X2, not(X2)))))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(X2, or(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(implies(X2, not(X2)), not(X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, implies(or(X2, X2), X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, not(implies(X1, not(X1))))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, or(X2, not(or(X2, X2))))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, or(implies(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(X1, or(or(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(implies(X1, X2), or(X2, not(X1)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(implies(X1, not(X1)), not(X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(implies(X1, not(X2)), implies(X2, not(X1)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(or(X1, X1), X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(or(X1, X2), or(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, implies(or(X1, not(X2)), implies(X2, X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, not(X0)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, not(or(X0, X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(X2, X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(X2, implies(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(X2, not(implies(X2, not(X2)))))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(X2, or(X3, X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(implies(X2, not(X2)), not(X2)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, implies(or(X2, X2), X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, not(X1))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, not(or(X1, X1)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, or(X2, not(or(X2, X2))))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, or(implies(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(X1, or(or(X2, X3), not(X3)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(implies(X1, X2), not(X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(implies(X1, implies(X2, X1)), X3)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(implies(X1, or(X2, X1)), X3)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(implies(implies(X1, not(X1)), not(X1)), X2)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(implies(or(X1, X1), X1), X2)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(or(X1, X2), not(X2))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(X0, or(or(X1, X2), not(or(X2, X1)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(X0, X1), not(X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(X0, X1), not(or(X1, not(X0)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(X0, implies(X1, X0)), X2), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(X0, not(X1)), not(implies(X1, not(X0)))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(X0, or(X1, X0)), X2), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(implies(X0, not(X0)), not(X0)), X1), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(implies(or(X0, X0), X0), X1), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(or(X0, X1), not(X1)), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(or(X0, X1), not(or(X1, X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(f1(true__, implies(or(or(X0, not(X1)), not(implies(X1, X0))), Y1)), Y1) -> true__
% 12.81/12.65 f2(true__, X) -> theorem(X)
% 12.81/12.65 f3(f1(true__, Y0), Y0, Y1) -> true__
% 12.81/12.65 f3(theorem(Y), Y, X) -> true__
% 12.81/12.65 f3(true__, Y, X) -> f2(theorem(implies(Y, X)), X)
% 12.81/12.65 f4(f1(true__, not(not(implies(p, not(not(p))))))) -> true__
% 12.81/12.65 f4(theorem(not(and(p, not(p))))) -> true__
% 12.81/12.65 f4(true__) -> false__
% 12.81/12.65 false__ -> true__
% 12.81/12.65 or(not(X), Y) -> implies(X, Y)
% 12.81/12.65 theorem(X) -> f1(true__, X)
% 12.81/12.65 with the LPO induced by
% 12.81/12.65 p > f4 > and > not > f3 > f2 > theorem > f1 > or > axiom > implies > false__ > true__
% 12.81/12.65
% 12.81/12.65 % SZS output end Proof
% 12.81/12.65
%------------------------------------------------------------------------------