TSTP Solution File: LCL186-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL186-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n024.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 12:58:53 EDT 2022
% Result : Unsatisfiable 12.21s 12.13s
% Output : Proof 12.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL186-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 13:56:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 12.21/12.13 % SZS status Unsatisfiable
% 12.21/12.13 % SZS output start Proof
% 12.21/12.13 The input problem is unsatisfiable because
% 12.21/12.13
% 12.21/12.13 [1] the following set of Horn clauses is unsatisfiable:
% 12.21/12.13
% 12.21/12.13 axiom(or(not(or(A, A)), A))
% 12.21/12.13 axiom(or(not(A), or(B, A)))
% 12.21/12.13 axiom(or(not(or(A, B)), or(B, A)))
% 12.21/12.13 axiom(or(not(or(A, or(B, C))), or(B, or(A, C))))
% 12.21/12.13 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B))))
% 12.21/12.13 axiom(X) ==> theorem(X)
% 12.21/12.13 axiom(or(not(Y), X)) & theorem(Y) ==> theorem(X)
% 12.21/12.13 axiom(or(not(X), Y)) & theorem(or(not(Y), Z)) ==> theorem(or(not(X), Z))
% 12.21/12.13 theorem(or(not(not(p)), or(not(p), q))) ==> \bottom
% 12.21/12.13
% 12.21/12.13 This holds because
% 12.21/12.13
% 12.21/12.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 12.21/12.13
% 12.21/12.13 E:
% 12.21/12.13 axiom(or(not(A), or(B, A))) = true__
% 12.21/12.13 axiom(or(not(or(A, A)), A)) = true__
% 12.21/12.13 axiom(or(not(or(A, B)), or(B, A))) = true__
% 12.21/12.13 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) = true__
% 12.21/12.13 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) = true__
% 12.21/12.13 f1(axiom(X), X) = true__
% 12.21/12.13 f1(true__, X) = theorem(X)
% 12.21/12.13 f2(true__, X) = theorem(X)
% 12.21/12.13 f3(theorem(Y), Y, X) = true__
% 12.21/12.13 f3(true__, Y, X) = f2(axiom(or(not(Y), X)), X)
% 12.21/12.13 f4(true__, X, Z) = theorem(or(not(X), Z))
% 12.21/12.13 f5(theorem(or(not(Y), Z)), X, Y, Z) = true__
% 12.21/12.13 f5(true__, X, Y, Z) = f4(axiom(or(not(X), Y)), X, Z)
% 12.21/12.13 f6(theorem(or(not(not(p)), or(not(p), q)))) = true__
% 12.21/12.13 f6(true__) = false__
% 12.21/12.13 G:
% 12.21/12.13 true__ = false__
% 12.21/12.13
% 12.21/12.13 This holds because
% 12.21/12.13
% 12.21/12.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 12.21/12.13
% 12.21/12.13 f3(true__, or(Y0, Y2), or(not(or(Y0, Y1)), or(Y0, Y2))) = f3(true__, or(not(Y1), Y2), or(not(or(Y0, Y1)), or(Y0, Y2)))
% 12.21/12.13 f3(true__, or(or(Y0, Y2), not(or(Y0, Y1))), or(not(or(Y0, Y1)), or(Y0, Y2))) = f3(true__, or(not(Y1), Y2), or(not(or(Y0, Y1)), or(Y0, Y2)))
% 12.21/12.13 f3(true__, or(or(Y1, Y2), Y0), or(Y0, or(Y1, Y2))) = f3(true__, or(Y1, or(Y0, Y2)), or(Y0, or(Y1, Y2)))
% 12.21/12.13 axiom(or(not(A), or(B, A))) -> true__
% 12.21/12.13 axiom(or(not(or(A, A)), A)) -> true__
% 12.21/12.13 axiom(or(not(or(A, B)), or(B, A))) -> true__
% 12.21/12.13 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) -> true__
% 12.21/12.13 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) -> true__
% 12.21/12.13 f1(axiom(X), X) -> true__
% 12.21/12.13 f1(true__, Y1) -> f3(true__, or(Y1, Y1), Y1)
% 12.21/12.13 f1(true__, or(X1, X0)) -> f3(true__, or(X0, X1), or(X1, X0))
% 12.21/12.13 f1(true__, or(X1, Y0)) -> f3(true__, Y0, or(X1, Y0))
% 12.21/12.13 f1(true__, or(X1, or(X0, X2))) -> f3(true__, or(X0, or(X1, X2)), or(X1, or(X0, X2)))
% 12.21/12.13 f1(true__, or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f1(true__, or(not(or(X0, X0)), X0)) -> true__
% 12.21/12.13 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 12.21/12.13 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 12.21/12.13 f1(true__, or(not(or(X2, X0)), or(X2, X1))) -> f3(true__, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1)))
% 12.21/12.13 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 12.21/12.13 f2(axiom(or(not(Y), X)), X) -> f3(true__, Y, X)
% 12.21/12.13 f2(true__, X) -> theorem(X)
% 12.21/12.13 f3(f1(true__, Y0), Y0, Y1) -> true__
% 12.21/12.13 f3(f3(true__, X1, or(X0, X1)), or(X0, X1), Y1) -> true__
% 12.21/12.13 f3(f3(true__, or(X1, X0), or(X0, X1)), or(X0, X1), Y1) -> true__
% 12.21/12.13 f3(f3(true__, or(X1, or(X0, X2)), or(X0, or(X1, X2))), or(X0, or(X1, X2)), Y1) -> true__
% 12.21/12.13 f3(f3(true__, or(Y0, Y0), Y0), Y0, Y1) -> true__
% 12.21/12.13 f3(f3(true__, or(not(X1), X2), or(not(or(X0, X1)), or(X0, X2))), or(not(or(X0, X1)), or(X0, X2)), Y1) -> true__
% 12.21/12.13 f3(theorem(Y), Y, X) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(X1), X1), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(X1), or(X2, X1)), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(X1, X1)), X1), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(X1, Y0)), X1), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(Y1, Y2)), or(Y2, Y1)), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(Y1, or(Y0, Y2))), or(Y1, Y2)), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(Y1, or(Y2, Y3))), or(Y2, or(Y1, Y3))), Y0)) -> true__
% 12.21/12.13 f3(true__, Y0, or(or(not(or(or(Y0, Y1), or(Y0, Y1))), Y1), Y0)) -> true__
% 12.21/12.13 f3(true__, Y1, or(not(or(Y1, Y1)), Y1)) -> true__
% 12.21/12.13 f3(true__, Y1, or(not(or(or(Y1, Y1), or(Y1, Y1))), Y1)) -> true__
% 12.21/12.13 f3(true__, Y2, or(not(Y2), Y2)) -> true__
% 12.21/12.13 f3(true__, not(X0), or(or(X1, X0), not(X0))) -> true__
% 12.21/12.13 f3(true__, not(or(X0, X1)), or(or(X1, X0), not(or(X0, X1)))) -> true__
% 12.21/12.13 f3(true__, not(or(Y0, Y1)), or(or(Y0, or(Y2, Y1)), not(or(Y0, Y1)))) -> true__
% 12.21/12.13 f3(true__, not(or(Y0, Y1)), or(or(not(or(not(Y1), Y2)), or(Y0, Y2)), not(or(Y0, Y1)))) -> true__
% 12.21/12.13 f3(true__, not(or(Y0, or(Y1, Y1))), or(or(Y0, Y1), not(or(Y0, or(Y1, Y1))))) -> true__
% 12.21/12.13 f3(true__, not(or(Y0, or(Y1, Y2))), or(or(Y0, or(Y2, Y1)), not(or(Y0, or(Y1, Y2))))) -> true__
% 12.21/12.13 f3(true__, not(or(Y0, or(Y1, Y2))), or(or(Y1, or(Y0, Y2)), not(or(Y0, or(Y1, Y2))))) -> true__
% 12.21/12.13 f3(true__, not(or(Y1, Y1)), or(Y1, not(or(Y1, Y1)))) -> true__
% 12.21/12.13 f3(true__, not(or(not(Y0), Y1)), or(or(not(or(Y2, Y0)), or(Y2, Y1)), not(or(not(Y0), Y1)))) -> true__
% 12.21/12.13 f3(true__, not(or(not(Y0), not(Y0))), or(not(or(Y0, Y0)), not(or(not(Y0), not(Y0))))) -> true__
% 12.21/12.13 f3(true__, not(or(not(or(Y1, Y0)), not(or(Y1, Y0)))), or(not(Y0), not(or(not(or(Y1, Y0)), not(or(Y1, Y0)))))) -> true__
% 12.21/12.13 f3(true__, not(or(not(or(Y1, Y0)), not(or(Y1, Y0)))), or(not(or(Y0, Y1)), not(or(not(or(Y1, Y0)), not(or(Y1, Y0)))))) -> true__
% 12.21/12.13 f3(true__, or(X0, not(or(X0, X0))), or(not(or(X0, X0)), X0)) -> true__
% 12.21/12.13 f3(true__, or(X1, X0), or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(X1, X0), or(not(or(X0, X1)), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(X1, X2), or(not(or(or(X1, or(X2, X2)), or(X1, or(X2, X2)))), or(X1, X2))) -> true__
% 12.21/12.13 f3(true__, or(X1, or(X3, X2)), or(not(or(or(X1, X2), or(X1, X2))), or(X1, or(X3, X2)))) -> true__
% 12.21/12.13 f3(true__, or(X1, or(X3, X2)), or(not(or(or(X1, or(X2, X3)), or(X1, or(X2, X3)))), or(X1, or(X3, X2)))) -> true__
% 12.21/12.13 f3(true__, or(X1, or(not(X0), X0)), or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(X1, or(not(or(X0, X1)), X0)), or(not(or(X0, X1)), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(X1, or(not(or(X0, or(X1, X2))), or(X0, X2))), or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 12.21/12.13 f3(true__, or(X2, X1), or(not(or(or(X1, X2), or(X1, X2))), or(X2, X1))) -> true__
% 12.21/12.13 f3(true__, or(X2, Y0), or(not(or(Y0, Y0)), or(X2, Y0))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(X1, X3)), or(not(or(or(X1, or(X2, X3)), or(X1, or(X2, X3)))), or(X2, or(X1, X3)))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(Y1, X3)), or(not(or(or(X2, X3), Y1)), or(X2, or(Y1, X3)))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(Y1, Y0)), or(not(Y0), or(X2, or(Y1, Y0)))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(Y1, Y0)), or(not(or(Y0, Y1)), or(X2, or(Y1, Y0)))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(Y1, or(Y0, Y2))), or(not(or(Y0, or(Y1, Y2))), or(X2, or(Y1, or(Y0, Y2))))) -> true__
% 12.21/12.13 f3(true__, or(X2, or(not(or(Y2, Y0)), or(Y2, Y1))), or(not(or(not(Y0), Y1)), or(X2, or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 12.21/12.13 f3(true__, or(Y0, X1), or(X1, Y0)) -> f3(true__, Y0, or(X1, Y0))
% 12.21/12.13 f3(true__, or(Y0, Y1), or(not(Y0), or(Y0, Y1))) -> true__
% 12.21/12.13 f3(true__, or(Y0, Y2), or(not(or(Y0, or(or(Y0, Y2), Y2))), or(Y0, Y2))) -> true__
% 12.21/12.13 f3(true__, or(Y0, or(not(or(Y0, Y1)), Y2)), or(not(or(Y0, Y1)), or(Y0, Y2))) -> f3(true__, or(not(Y1), Y2), or(not(or(Y0, Y1)), or(Y0, Y2)))
% 12.21/12.13 f3(true__, or(Y1, X2), or(not(or(or(X2, X2), Y1)), or(Y1, X2))) -> true__
% 12.21/12.13 f3(true__, or(Y1, not(or(Y1, Y1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, not(or(X0, X0)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(X1), X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(X1), or(X2, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(X1, X0)), X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(X1, X1)), X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(X1, X2)), or(X2, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3))))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(not(X1), X2)), or(not(or(X3, X1)), or(X3, X2))))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X3, X2)), or(not(or(or(X2, X3), Y1)), or(Y1, or(X3, X2)))) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(X3, Y0)), or(not(or(Y0, Y1)), or(Y1, or(X3, Y0)))) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(Y0, Y2)), or(Y0, or(Y1, Y2))) -> f3(true__, or(Y1, Y2), or(Y0, or(Y1, Y2)))
% 12.21/12.13 f3(true__, or(Y1, or(Y0, Y2)), or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(X0), or(X1, X0))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(Y2), Y2)), Y3) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, X0)), X0)), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, X1)), or(X0, or(X2, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, X1)), or(X1, X0))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, X1)), or(not(or(not(X1), X2)), or(X0, X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, or(X1, X1))), or(X0, X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, or(X1, or(X2, X3)))), or(X0, or(X2, or(X1, X3))))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(X0, or(Y1, X2))), or(X0, X2))), Y3) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(Y2, Y1)), Y2)), Y3) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2)), Y3) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2)), or(not(or(or(Y1, Y2), or(Y1, Y2))), or(Y1, Y2))) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(or(X0, X1), not(X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(or(X0, X1), not(or(X1, X0)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2))))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y1, or(or(not(or(X0, X1)), or(X0, X2)), not(or(not(X1), X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(Y2, Y1), or(not(or(Y2, or(Y1, Y1))), or(Y2, Y1))) -> true__
% 12.21/12.13 f3(true__, or(Y2, or(X1, X0)), or(not(or(Y2, or(X0, X1))), or(Y2, or(X1, X0)))) -> true__
% 12.21/12.13 f3(true__, or(Y2, or(X1, Y0)), or(not(or(Y2, Y0)), or(Y2, or(X1, Y0)))) -> true__
% 12.21/12.13 f3(true__, or(Y2, or(X1, or(X0, X2))), or(not(or(Y2, or(X0, or(X1, X2)))), or(Y2, or(X1, or(X0, X2))))) -> true__
% 12.21/12.13 f3(true__, or(Y2, or(not(or(X2, X0)), or(X2, X1))), or(not(or(Y2, or(not(X0), X1))), or(Y2, or(not(or(X2, X0)), or(X2, X1))))) -> true__
% 12.21/12.13 f3(true__, or(Y2, or(not(or(Y2, Y0)), Y1)), or(not(or(not(Y0), Y1)), or(Y2, or(not(or(Y2, Y0)), Y1)))) -> true__
% 12.21/12.13 f3(true__, or(not(X0), or(X0, X1)), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(X0), or(X1, X0)), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(X1), X1), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(X2), or(X0, or(X1, X2))), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(Y1), Y1), or(not(or(Y0, Y1)), or(Y0, Y1))) -> true__
% 12.21/12.13 f3(true__, or(not(Y1), Y2), or(not(or(not(Y2), Y1)), or(not(Y2), Y2))) -> true__
% 12.21/12.13 f3(true__, or(not(Y1), or(Y0, Y1)), or(not(or(Y0, Y1)), or(Y0, or(Y0, Y1)))) -> true__
% 12.21/12.13 f3(true__, or(not(Y1), or(not(or(not(Y1), X1)), X1)), or(not(or(not(or(not(Y1), X1)), Y1)), or(not(or(not(Y1), X1)), or(not(or(not(Y1), X1)), X1)))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), Y1), or(not(or(not(or(Y1, Y1)), Y2)), or(not(or(Y1, Y1)), Y1))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), Y2), or(Y1, or(not(Y2), Y2))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), Y2), or(not(or(Y2, Y2)), or(Y2, Y2))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), or(X1, X0)), or(not(or(not(X0), Y2)), or(not(X0), or(X1, X0)))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), or(X1, X0)), or(not(or(not(or(X0, X1)), Y2)), or(not(or(X0, X1)), or(X1, X0)))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), or(X1, or(X0, X2))), or(not(or(not(or(X0, or(X1, X2))), Y2)), or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))))) -> true__
% 12.21/12.13 f3(true__, or(not(Y2), or(not(or(X2, X0)), or(X2, X1))), or(not(or(not(or(not(X0), X1)), Y2)), or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, X0)), X0), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, X1)), or(X1, X0)), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, or(X2, X1))), or(or(X0, X1), X2)), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, or(Y1, X2))), or(X0, X2)), or(Y1, or(not(or(X0, or(Y1, X2))), or(X0, X2)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X0, or(or(X0, X1), X1))), or(X0, X1)), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(X1, X1)), or(X0, X1)), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1))), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1))), or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, X1)), or(X0, or(X1, X2))), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, not(Y0))), X2), or(not(or(Y0, Y0)), or(not(or(X2, not(Y0))), X2))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, not(or(Y1, Y0)))), X2), or(not(Y0), or(not(or(X2, not(or(Y1, Y0)))), X2))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X2, not(or(Y1, Y0)))), X2), or(not(or(Y0, Y1)), or(not(or(X2, not(or(Y1, Y0)))), X2))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X3, X1)), or(X3, Y0)), or(not(or(Y0, not(X1))), or(not(or(X3, X1)), or(X3, Y0)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X3, X1)), or(X3, or(Y0, Y2))), or(not(or(Y0, or(not(X1), Y2))), or(not(or(X3, X1)), or(X3, or(Y0, Y2))))) -> true__
% 12.21/12.13 f3(true__, or(not(or(X3, or(Y2, Y0))), or(X3, or(Y2, Y1))), or(not(or(not(Y0), Y1)), or(not(or(X3, or(Y2, Y0))), or(X3, or(Y2, Y1))))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y0, X2)), or(Y0, X2)), or(not(or(Y0, or(Y0, X2))), or(Y0, or(Y0, X2)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y1, Y2)), or(Y1, Y2)), or(not(or(Y0, or(Y1, Y2))), or(Y0, or(Y1, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, Y0)), or(Y2, Y1)), or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, Y0)), or(Y2, or(X1, Y0))), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, Y1)), Y2), or(Y1, or(not(or(Y2, Y1)), Y2))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(X0, X1))), or(Y2, or(X1, X0))), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(X0, or(X1, X2)))), or(Y2, or(X1, or(X0, X2)))), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(Y1, Y1))), or(Y2, Y1)), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(not(X0), X1))), or(Y2, or(not(or(X2, X0)), or(X2, X1)))), Y3) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(not(Y1), Y3))), or(Y2, Y3)), or(not(or(Y1, Y1)), or(not(or(Y2, or(not(Y1), Y3))), or(Y2, Y3)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y2, or(not(or(X1, Y0)), Y3))), or(Y2, Y3)), or(not(Y0), or(not(or(Y2, or(not(or(X1, Y0)), Y3))), or(Y2, Y3)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y3, Y1)), or(Y3, Y2)), or(not(Y2), or(not(or(Y3, Y1)), or(Y3, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(Y3, Y1)), or(Y3, Y2)), or(not(or(or(not(Y1), Y2), or(not(Y1), Y2))), or(not(or(Y3, Y1)), or(Y3, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(not(X0), X1)), or(X2, X1)), or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))), Y1) -> true__
% 12.21/12.13 f3(true__, or(not(or(not(Y2), Y3)), or(Y1, Y3)), or(not(Y2), or(not(or(not(Y2), Y3)), or(Y1, Y3)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(not(Y2), Y3)), or(Y1, Y3)), or(not(or(or(Y1, Y2), or(Y1, Y2))), or(not(or(not(Y2), Y3)), or(Y1, Y3)))) -> true__
% 12.21/12.13 f3(true__, or(not(or(or(X0, X2), X1)), or(X0, or(X1, X2))), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(or(X1, X0), or(X1, X0))), or(X0, X1)), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(or(Y0, Y0), or(Y0, Y0))), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2), or(Y1, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2))) -> true__
% 12.21/12.13 f3(true__, or(not(or(or(not(or(X1, Y0)), Y2), or(not(or(X1, Y0)), Y2))), Y2), or(not(Y0), or(not(or(or(not(or(X1, Y0)), Y2), or(not(or(X1, Y0)), Y2))), Y2))) -> true__
% 12.21/12.13 f3(true__, or(or(X0, X1), not(or(X0, or(X1, X1)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(X0, or(X2, X1)), not(or(X0, X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(X0, or(X2, X1)), not(or(X0, or(X1, X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(X1, X0), not(X0)), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(X1, X0), not(X0)), or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(or(X1, X0), not(or(X0, X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(X1, X0), not(or(X0, X1))), or(not(or(X0, X1)), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(or(X1, or(X0, X2)), not(or(X0, or(X1, X2)))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(Y0, Y1), or(Y0, Y1)), or(Y0, Y1)) -> f3(true__, Y1, or(Y0, Y1))
% 12.21/12.13 f3(true__, or(or(Y0, Y1), or(Y0, Y1)), or(Y0, Y1)) -> f3(true__, or(Y1, Y0), or(Y0, Y1))
% 12.21/12.13 f3(true__, or(or(Y0, Y2), Y1), or(not(or(Y0, or(Y1, Y2))), or(or(Y0, Y2), Y1))) -> true__
% 12.21/12.13 f3(true__, or(or(Y0, or(Y1, Y2)), or(Y0, or(Y1, Y2))), or(Y0, or(Y1, Y2))) -> f3(true__, or(Y1, or(Y0, Y2)), or(Y0, or(Y1, Y2)))
% 12.21/12.13 f3(true__, or(or(Y1, or(Y0, Y2)), not(or(Y0, or(Y1, Y2)))), or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(or(Y2, Y1), not(or(Y2, Y0))), or(not(or(not(Y0), Y1)), or(or(Y2, Y1), not(or(Y2, Y0))))) -> true__
% 12.21/12.13 f3(true__, or(or(not(X0), or(X1, X0)), or(not(X0), or(X1, X0))), or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f3(true__, or(or(not(X1), X1), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(X1), or(X2, X1)), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X0, X0)), X0), or(not(or(X0, X0)), X0)), or(not(or(X0, X0)), X0)) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X1, X1)), X1), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X1, X2)), or(X2, X1)), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X1, Y0)), X1), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3))), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X1, or(Y0, X2))), or(X1, X2)), Y0), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(X2, X0)), or(X2, X1)), not(or(not(X0), X1))), Y2) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(Y0, Y1)), or(Y0, Y2)), or(not(or(Y0, Y1)), or(Y0, Y2))), or(not(or(Y0, Y1)), or(Y0, Y2))) -> f3(true__, or(not(Y1), Y2), or(not(or(Y0, Y1)), or(Y0, Y2)))
% 12.21/12.13 f3(true__, or(or(not(or(Y0, Y1)), or(Y1, Y0)), or(not(or(Y0, Y1)), or(Y1, Y0))), or(not(or(Y0, Y1)), or(Y1, Y0))) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2))), or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))), or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(Y2, Y0)), or(Y2, Y1)), not(or(not(Y0), Y1))), or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1))), or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))), or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))) -> true__
% 12.21/12.13 f3(true__, or(or(not(or(or(Y0, X1), or(Y0, X1))), X1), Y0), Y2) -> true__
% 12.21/12.13 f4(axiom(or(not(X), Y)), X, Z) -> f5(true__, X, Y, Z)
% 12.21/12.13 f4(true__, X, Z) -> theorem(or(not(X), Z))
% 12.21/12.13 f5(f1(true__, or(not(Y0), Y1)), Y2, Y0, Y1) -> true__
% 12.21/12.13 f5(f3(true__, Y1, or(not(Y0), Y1)), Y2, Y0, Y1) -> true__
% 12.21/12.13 f5(f3(true__, or(X1, or(not(Y0), X2)), or(not(Y0), or(X1, X2))), Y2, Y0, or(X1, X2)) -> true__
% 12.21/12.13 f5(f3(true__, or(Y1, not(Y0)), or(not(Y0), Y1)), Y2, Y0, Y1) -> true__
% 12.21/12.13 f5(f3(true__, or(not(X1), X2), or(not(or(X0, X1)), or(X0, X2))), Y2, or(X0, X1), or(X0, X2)) -> true__
% 12.21/12.13 f5(f3(true__, or(or(not(Y0), Y1), or(not(Y0), Y1)), or(not(Y0), Y1)), Y2, Y0, Y1) -> true__
% 12.21/12.13 f5(theorem(or(not(Y), Z)), X, Y, Z) -> true__
% 12.21/12.13 f5(true__, Y0, or(X1, Y0), Y2) -> f1(true__, or(not(Y0), Y2))
% 12.21/12.13 f5(true__, Y2, Y0, or(X1, Y0)) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, Y1) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, not(or(not(Y1), not(Y1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, not(or(X0, X0)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(X1, Y1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(X1), X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(X1), or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(X1, X0)), X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(X1, X1)), X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(X1, X2)), or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3))))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(not(X1), X2)), or(not(or(X3, X1)), or(X3, X2))))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(Y1, X1)) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(X0), or(X1, X0))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, X0)), X0)) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, X1)), or(X0, or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, X1)), or(not(or(not(X1), X2)), or(X0, X2)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, or(X1, X1))), or(X0, X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(or(X0, X1), not(X1))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(or(X0, X1), not(or(X1, X0)))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2))))) -> true__
% 12.21/12.13 f5(true__, Y2, Y1, or(or(not(or(X0, X1)), or(X0, X2)), not(or(not(X1), X2)))) -> true__
% 12.21/12.13 f5(true__, Y2, or(X0, X1), or(X1, X0)) -> true__
% 12.21/12.13 f5(true__, Y2, or(X0, or(X1, X2)), or(X1, or(X0, X2))) -> true__
% 12.21/12.13 f5(true__, Y2, or(X0, or(X2, X1)), or(or(X0, X1), X2)) -> true__
% 12.21/12.13 f5(true__, Y2, or(X0, or(or(X0, X1), X1)), or(X0, X1)) -> true__
% 12.21/12.13 f5(true__, Y2, or(X1, X1), or(X0, X1)) -> true__
% 12.21/12.13 f5(true__, Y2, or(X2, X1), or(X0, or(X1, X2))) -> true__
% 12.21/12.13 f5(true__, Y2, or(Y1, Y1), Y1) -> true__
% 12.21/12.13 f5(true__, Y2, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1))) -> true__
% 12.21/12.13 f5(true__, Y2, or(or(X0, X2), X1), or(X0, or(X1, X2))) -> true__
% 12.21/12.13 f5(true__, Y2, or(or(X1, X0), or(X1, X0)), or(X0, X1)) -> true__
% 12.21/12.13 f5(true__, Y2, or(or(Y0, Y0), or(Y0, Y0)), Y0) -> true__
% 12.21/12.13 f5(true__, Y3, Y1, or(not(Y2), Y2)) -> true__
% 12.21/12.13 f5(true__, Y3, Y1, or(not(or(X0, or(not(Y1), X2))), or(X0, X2))) -> true__
% 12.21/12.13 f5(true__, Y3, Y1, or(not(or(Y2, not(Y1))), Y2)) -> true__
% 12.21/12.13 f5(true__, Y3, Y1, or(not(or(or(not(Y1), Y2), or(not(Y1), Y2))), Y2)) -> true__
% 12.21/12.13 f5(true__, Y3, or(X2, X0), or(not(or(not(X0), X1)), or(X2, X1))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, Y0), or(Y2, not(or(not(Y0), not(Y0))))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, Y0), or(Y2, or(X1, Y0))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, Y0), or(Y2, or(not(X1), X1))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, or(X0, X1)), or(Y2, or(X1, X0))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, or(X0, or(X1, X2))), or(Y2, or(X1, or(X0, X2)))) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, or(Y1, Y1)), or(Y2, Y1)) -> true__
% 12.21/12.13 f5(true__, Y3, or(Y2, or(not(X0), X1)), or(Y2, or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 12.21/12.13 f5(true__, or(X0, X1), or(X1, X0), Y2) -> f1(true__, or(not(or(X0, X1)), Y2))
% 12.21/12.13 f5(true__, or(X0, or(X1, X2)), or(X1, or(X0, X2)), Y2) -> f1(true__, or(not(or(X0, or(X1, X2))), Y2))
% 12.21/12.13 f5(true__, or(Y1, Y1), Y1, Y2) -> f1(true__, or(not(or(Y1, Y1)), Y2))
% 12.21/12.13 f5(true__, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1)), Y2) -> f1(true__, or(not(or(not(X0), X1)), Y2))
% 12.21/12.13 f6(f1(true__, or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(f3(true__, or(not(p), or(not(not(p)), q)), or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(f3(true__, or(not(p), q), or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(f3(true__, or(or(not(not(p)), or(not(p), q)), or(not(not(p)), or(not(p), q))), or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(f3(true__, or(or(not(p), q), not(not(p))), or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(theorem(or(not(not(p)), or(not(p), q)))) -> true__
% 12.21/12.13 f6(true__) -> false__
% 12.21/12.13 false__ -> true__
% 12.21/12.13 theorem(X) -> f1(true__, X)
% 12.21/12.13 with the LPO induced by
% 12.21/12.13 q > p > f6 > f4 > f5 > f2 > theorem > f1 > f3 > not > axiom > or > false__ > true__
% 12.21/12.13
% 12.21/12.13 % SZS output end Proof
% 12.21/12.13
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