TSTP Solution File: LCL176-3 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL176-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n010.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 12:58:45 EDT 2022
% Result : Unsatisfiable 9.21s 9.09s
% Output : Proof 9.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL176-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 04:49:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.21/9.09 % SZS status Unsatisfiable
% 9.21/9.09 % SZS output start Proof
% 9.21/9.09 The input problem is unsatisfiable because
% 9.21/9.09
% 9.21/9.09 [1] the following set of Horn clauses is unsatisfiable:
% 9.21/9.09
% 9.21/9.09 axiom(implies(or(A, A), A))
% 9.21/9.09 axiom(implies(A, or(B, A)))
% 9.21/9.09 axiom(implies(or(A, B), or(B, A)))
% 9.21/9.09 axiom(implies(or(A, or(B, C)), or(B, or(A, C))))
% 9.21/9.09 axiom(implies(implies(A, B), implies(or(C, A), or(C, B))))
% 9.21/9.09 implies(X, Y) = or(not(X), Y)
% 9.21/9.09 axiom(X) ==> theorem(X)
% 9.21/9.09 theorem(implies(Y, X)) & theorem(Y) ==> theorem(X)
% 9.21/9.09 theorem(implies(p, p)) ==> \bottom
% 9.21/9.09
% 9.21/9.09 This holds because
% 9.21/9.09
% 9.21/9.09 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.21/9.09
% 9.21/9.09 E:
% 9.21/9.09 axiom(implies(A, or(B, A))) = true__
% 9.21/9.09 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true__
% 9.21/9.09 axiom(implies(or(A, A), A)) = true__
% 9.21/9.09 axiom(implies(or(A, B), or(B, A))) = true__
% 9.21/9.09 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true__
% 9.21/9.09 f1(axiom(X), X) = true__
% 9.21/9.09 f1(true__, X) = theorem(X)
% 9.21/9.09 f2(true__, X) = theorem(X)
% 9.21/9.09 f3(theorem(Y), Y, X) = true__
% 9.21/9.09 f3(true__, Y, X) = f2(theorem(implies(Y, X)), X)
% 9.21/9.09 f4(theorem(implies(p, p))) = true__
% 9.21/9.09 f4(true__) = false__
% 9.21/9.09 implies(X, Y) = or(not(X), Y)
% 9.21/9.09 G:
% 9.21/9.09 true__ = false__
% 9.21/9.09
% 9.21/9.09 This holds because
% 9.21/9.09
% 9.21/9.09 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.21/9.09
% 9.21/9.09
% 9.21/9.09 axiom(implies(A, or(B, A))) -> true__
% 9.21/9.09 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) -> true__
% 9.21/9.09 axiom(implies(or(A, A), A)) -> true__
% 9.21/9.09 axiom(implies(or(A, B), or(B, A))) -> true__
% 9.21/9.09 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) -> true__
% 9.21/9.09 axiom(or(not(Y0), or(Y1, Y0))) -> true__
% 9.21/9.09 axiom(or(not(or(Y0, Y0)), Y0)) -> true__
% 9.21/9.09 axiom(or(not(or(Y0, Y1)), or(Y1, Y0))) -> true__
% 9.21/9.09 axiom(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 9.21/9.09 axiom(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))) -> true__
% 9.21/9.09 f1(axiom(X), X) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, not(or(Y0, Y0)))), not(or(Y0, not(or(Y0, Y0))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(Y1, not(or(Y1, Y1))))), not(or(Y0, or(Y1, not(or(Y1, Y1)))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(Y1, or(Y2, not(or(Y2, Y2)))))), not(or(Y0, or(Y1, or(Y2, not(or(Y2, Y2))))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(Y1, or(not(Y2), or(Y3, Y2))))), not(or(Y0, or(Y1, or(not(Y2), or(Y3, Y2)))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(Y1, or(not(or(Y2, Y2)), Y2)))), not(or(Y0, or(Y1, or(not(or(Y2, Y2)), Y2))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(Y1, or(or(Y2, Y3), not(Y3))))), not(or(Y0, or(Y1, or(or(Y2, Y3), not(Y3)))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(not(Y1), Y1))), not(or(Y0, or(not(Y1), Y1)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(not(Y1), or(Y2, Y1)))), not(or(Y0, or(not(Y1), or(Y2, Y1))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(not(or(Y1, Y1)), Y1))), not(or(Y0, or(not(or(Y1, Y1)), Y1)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(not(or(Y1, Y2)), or(Y2, Y1)))), not(or(Y0, or(not(or(Y1, Y2)), or(Y2, Y1))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(Y1, Y2), not(Y2)))), not(or(Y0, or(or(Y1, Y2), not(Y2))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(Y1, Y2), not(or(Y2, Y1))))), not(or(Y0, or(or(Y1, Y2), not(or(Y2, Y1)))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(Y1, not(or(Y1, Y1))), Y2))), not(or(Y0, or(or(Y1, not(or(Y1, Y1))), Y2)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(not(Y1), or(Y2, Y1)), Y3))), not(or(Y0, or(or(not(Y1), or(Y2, Y1)), Y3)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(not(or(Y1, Y1)), Y1), Y2))), not(or(Y0, or(or(not(or(Y1, Y1)), Y1), Y2)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(Y0, or(or(or(Y1, Y2), not(Y2)), Y3))), not(or(Y0, or(or(or(Y1, Y2), not(Y2)), Y3)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(not(Y0), or(Y1, Y0))), not(or(not(Y0), or(Y1, Y0)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(not(or(Y0, Y0)), Y0)), not(or(not(or(Y0, Y0)), Y0))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(not(or(Y0, Y1)), or(Y1, Y0))), not(or(not(or(Y0, Y1)), or(Y1, Y0)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(Y0, Y1), not(Y1))), not(or(or(Y0, Y1), not(Y1)))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(Y0, Y1), not(or(Y1, Y0)))), not(or(or(Y0, Y1), not(or(Y1, Y0))))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(Y0, not(or(Y0, Y0))), Y1)), not(or(or(Y0, not(or(Y0, Y0))), Y1))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(not(Y0), or(Y1, Y0)), Y2)), not(or(or(not(Y0), or(Y1, Y0)), Y2))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(not(or(Y0, Y0)), Y0), Y1)), not(or(or(not(or(Y0, Y0)), Y0), Y1))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(not(or(Y0, Y1)), or(Y1, Y0)), Y2)), not(or(or(not(or(Y0, Y1)), or(Y1, Y0)), Y2))))) -> true__
% 9.21/9.09 f1(true__, not(or(not(or(or(or(Y0, Y1), not(Y1)), Y2)), not(or(or(or(Y0, Y1), not(Y1)), Y2))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, not(or(Y0, Y0))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(Y1, not(or(Y1, Y1)))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(Y1, or(Y2, not(or(Y2, Y2))))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(Y1, or(not(Y2), or(Y3, Y2)))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(Y1, or(not(or(Y2, Y2)), Y2))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(Y1, or(or(Y2, Y3), not(Y3)))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(not(Y1), Y1)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(not(Y1), or(Y2, Y1))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(not(or(Y1, Y1)), Y1)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(not(or(Y1, Y2)), or(Y2, Y1))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(Y1, Y2), not(Y2))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(Y1, Y2), not(or(Y2, Y1)))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(Y1, not(or(Y1, Y1))), Y2)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(not(Y1), or(Y2, Y1)), Y3)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(not(or(Y1, Y1)), Y1), Y2)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(Y0, or(or(or(Y1, Y2), not(Y2)), Y3)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(not(Y0), or(Y1, Y0)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(not(or(Y0, Y0)), Y0))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(not(or(Y0, Y1)), or(Y1, Y0)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(not(or(or(X1, X2), or(X1, X2))), X2))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(Y0, Y1), not(Y1)))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(Y0, Y1), not(or(Y1, Y0))))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(Y0, not(or(Y0, Y0))), Y1))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(Y0, or(not(or(Y1, Y1)), Y1)), Y2))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(not(Y0), or(Y1, Y0)), Y2))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(not(or(Y0, Y0)), Y0), Y1))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(not(or(Y0, Y1)), or(Y1, Y0)), Y2))) -> true__
% 9.21/9.09 f1(true__, or(X1, or(or(or(Y0, Y1), not(Y1)), Y2))) -> true__
% 9.21/9.09 f1(true__, or(Y0, not(or(Y0, Y0)))) -> true__
% 9.21/9.09 f1(true__, or(Y1, or(not(Y0), Y0))) -> true__
% 9.21/9.09 f1(true__, or(not(X0), or(X1, X0))) -> true__
% 9.21/9.09 f1(true__, or(not(X1), X1)) -> true__
% 9.21/9.09 f1(true__, or(not(or(X0, X0)), X0)) -> true__
% 9.21/9.09 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 9.21/9.09 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 9.21/9.09 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, Y0), not(Y0))) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, Y0), not(or(Y0, Y1)))) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, not(or(Y1, Y1))), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, or(Y2, not(or(Y2, Y2)))), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, or(not(Y2), or(Y3, Y2))), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, or(not(or(Y2, Y2)), Y2)), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(Y1, or(or(Y2, Y3), not(Y3))), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(not(Y1), Y1), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(not(Y1), or(Y2, Y1)), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(not(or(Y1, Y1)), Y1), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(not(or(Y1, Y2)), or(Y2, Y1)), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(or(Y1, Y2), not(Y2)), Y0)) -> true__
% 9.21/9.09 f1(true__, or(or(or(Y1, Y2), not(or(Y2, Y1))), Y0)) -> true__
% 9.21/9.09 f2(f1(true__, or(not(not(or(not(or(X0, not(or(X0, X0)))), not(or(X0, not(or(X0, X0))))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(not(or(not(or(not(X0), or(X1, X0))), not(or(not(X0), or(X1, X0)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(not(or(not(or(not(or(X0, X0)), X0)), not(or(not(or(X0, X0)), X0))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(not(or(not(or(or(X0, X1), not(X1))), not(or(or(X0, X1), not(X1)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, not(or(X0, X0)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, not(or(X1, X1))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(X2, not(or(X2, X2)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(X2, or(X3, not(or(X3, X3))))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(X2, or(not(X3), or(X4, X3)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(X2, or(not(or(X3, X3)), X3))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(X2, or(or(X3, X4), not(X4)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(not(X2), or(X3, X2))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(not(or(X2, X2)), X2)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(not(or(X2, X3)), or(X3, X2))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(X2, X3), not(X3))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(X2, X3), not(or(X3, X2)))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(X2, not(or(X2, X2))), X3)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(not(X2), or(X3, X2)), X4)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(not(or(X2, X2)), X2), X3)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(X1, or(or(or(X2, X3), not(X3)), X4)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(not(X1), X1))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(not(X1), or(X2, X1)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(not(or(X1, X1)), X1))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(not(or(X1, X2)), or(X2, X1)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(X1, X2), not(X2)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(X1, X2), not(or(X2, X1))))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(X1, not(or(X1, X1))), X2))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(X1, or(not(or(X2, X2)), X2)), X3))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(not(X1), or(X2, X1)), X3))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(not(or(X1, X1)), X1), X2))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(not(or(X1, X2)), or(X2, X1)), X3))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(X0, or(or(or(X1, X2), not(X2)), X3))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(X0), X0)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(X0), or(X1, X0))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(or(X0, X0)), X0)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(or(X0, X1)), or(X1, X0))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, X1), not(X1))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, X1), not(or(X1, X0)))), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, not(or(X0, X0))), X1)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, or(X1, not(or(X1, X1)))), X2)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, or(not(X1), or(X2, X1))), X3)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, or(not(or(X1, X1)), X1)), X2)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(X0, or(or(X1, X2), not(X2))), X3)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(not(X0), or(X1, X0)), X2)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(not(or(X0, X0)), X0), X1)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(not(or(X0, X1)), or(X1, X0)), X2)), Y1)), Y1) -> true__
% 9.21/9.09 f2(f1(true__, or(not(or(or(or(X0, X1), not(X1)), X2)), Y1)), Y1) -> true__
% 9.21/9.09 f2(true__, X) -> theorem(X)
% 9.21/9.09 f3(f1(true__, Y0), Y0, Y1) -> true__
% 9.21/9.09 f3(theorem(Y), Y, X) -> true__
% 9.21/9.09 f3(true__, Y, X) -> f2(theorem(implies(Y, X)), X)
% 9.21/9.09 f4(f1(true__, or(not(p), p))) -> true__
% 9.21/9.09 f4(theorem(implies(p, p))) -> true__
% 9.21/9.09 f4(true__) -> false__
% 9.21/9.09 false__ -> true__
% 9.21/9.09 implies(X, Y) -> or(not(X), Y)
% 9.21/9.09 theorem(X) -> f1(true__, X)
% 9.21/9.09 with the LPO induced by
% 9.21/9.09 p > f4 > f3 > implies > f2 > theorem > f1 > not > or > axiom > false__ > true__
% 9.21/9.09
% 9.21/9.09 % SZS output end Proof
% 9.21/9.09
%------------------------------------------------------------------------------