TSTP Solution File: LCL186-10 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n005.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 12:58:52 EDT 2022
% Result : Unsatisfiable 6.18s 6.22s
% Output : Proof 6.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 03:47:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 6.18/6.22 % SZS status Unsatisfiable
% 6.18/6.22 % SZS output start Proof
% 6.18/6.22 The input problem is unsatisfiable because
% 6.18/6.22
% 6.18/6.22 [1] the following set of Horn clauses is unsatisfiable:
% 6.18/6.22
% 6.18/6.22 ifeq(A, A, B, C) = B
% 6.18/6.22 axiom(or(not(or(A, A)), A)) = true
% 6.18/6.22 axiom(or(not(A), or(B, A))) = true
% 6.18/6.22 axiom(or(not(or(A, B)), or(B, A))) = true
% 6.18/6.22 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) = true
% 6.18/6.22 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) = true
% 6.18/6.22 ifeq(axiom(X), true, theorem(X), true) = true
% 6.18/6.22 ifeq(theorem(Y), true, ifeq(axiom(or(not(Y), X)), true, theorem(X), true), true) = true
% 6.18/6.22 ifeq(theorem(or(not(Y), Z)), true, ifeq(axiom(or(not(X), Y)), true, theorem(or(not(X), Z)), true), true) = true
% 6.18/6.22 theorem(or(not(not(p)), or(not(p), q))) = true ==> \bottom
% 6.18/6.22
% 6.18/6.22 This holds because
% 6.18/6.22
% 6.18/6.22 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 6.18/6.22
% 6.18/6.22 E:
% 6.18/6.22 axiom(or(not(A), or(B, A))) = true
% 6.18/6.22 axiom(or(not(or(A, A)), A)) = true
% 6.18/6.22 axiom(or(not(or(A, B)), or(B, A))) = true
% 6.18/6.22 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) = true
% 6.18/6.22 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) = true
% 6.18/6.22 f1(theorem(or(not(not(p)), or(not(p), q)))) = true__
% 6.18/6.22 f1(true) = false__
% 6.18/6.22 ifeq(A, A, B, C) = B
% 6.18/6.22 ifeq(axiom(X), true, theorem(X), true) = true
% 6.18/6.22 ifeq(theorem(Y), true, ifeq(axiom(or(not(Y), X)), true, theorem(X), true), true) = true
% 6.18/6.22 ifeq(theorem(or(not(Y), Z)), true, ifeq(axiom(or(not(X), Y)), true, theorem(or(not(X), Z)), true), true) = true
% 6.18/6.22 G:
% 6.18/6.22 true__ = false__
% 6.18/6.22
% 6.18/6.22 This holds because
% 6.18/6.22
% 6.18/6.22 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 6.18/6.22
% 6.18/6.22
% 6.18/6.22 axiom(or(not(A), or(B, A))) -> true
% 6.18/6.22 axiom(or(not(or(A, A)), A)) -> true
% 6.18/6.22 axiom(or(not(or(A, B)), or(B, A))) -> true
% 6.18/6.22 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) -> true
% 6.18/6.22 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) -> true
% 6.18/6.22 f1(theorem(or(not(not(p)), or(not(p), q)))) -> true__
% 6.18/6.22 f1(true) -> false__
% 6.18/6.22 ifeq(A, A, B, C) -> B
% 6.18/6.22 ifeq(axiom(X), true, theorem(X), true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, not(or(X0, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(X1), X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(X1), or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(X1, X0)), X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(X1, X1)), X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(X1, X2)), or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3))))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(X0), X0)), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(X0), or(X0, X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(X0), or(X1, or(X2, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(X0), or(not(or(X1, X2)), or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(Y2), Y0)), true, theorem(or(not(Y2), or(X1, Y0))), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(Y2), or(X0, X1))), true, theorem(or(not(Y2), or(X1, X0))), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(Y2), or(X0, or(X1, X2)))), true, theorem(or(not(Y2), or(X1, or(X0, X2)))), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(Y2), or(Y1, Y1))), true, theorem(or(not(Y2), Y1)), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(Y2), or(not(X0), X1))), true, theorem(or(not(Y2), or(not(or(X2, X0)), or(X2, X1)))), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, X0)), or(X1, X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, X1)), or(X0, X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, X1)), or(X0, or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, X1)), or(X2, or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, not(or(X0, X0)))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(X1, X1))), or(X0, X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(X1, X2))), or(X0, or(X1, X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(X1, X2))), or(or(X0, X2), X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(not(X1), X1))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(X0, or(or(X0, X1), X1))), or(X0, X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(Y2, Y1)), Y1)), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(X0), X0)), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(X0), or(X0, X1))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(X0), or(X1, X0))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(X0, not(or(X0, X0))))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(X0, or(not(X1), X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(not(X0), X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(not(X0), or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(not(or(X0, X0)), X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(Y0), or(Y1, Y0))), or(or(X0, X1), not(X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(X0, X0)), X0)), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(X0, X1)), or(X1, X0))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(X0, not(or(X0, X0))))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(X0, or(not(X1), X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(not(X0), X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(not(X0), or(X0, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(not(X0), or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(not(or(X0, X0)), X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(Y0, Y0)), Y0)), or(or(X0, X1), not(X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(or(X0, X0), or(X0, X0))), X0)), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(or(X0, X1), X2)), or(X0, or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(or(X0, X1), not(X1))), Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(axiom(or(not(or(or(X0, X1), or(X0, X1))), or(X1, X0))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(or(X0, X1), not(X1))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(or(X0, X1), not(or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(axiom(or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(Y), true, ifeq(axiom(or(not(Y), X)), true, theorem(X), true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(X0, not(or(X0, X0))))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(X0, or(not(X1), X1)))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(X0), X0))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(X0), or(X0, X1)))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(X0), or(X1, X0)))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(or(X0, X0)), X0))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(or(X0, X1)), or(X1, X0)))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, ifeq(axiom(or(not(Y0), or(or(X0, X1), not(X1)))), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, theorem(or(X1, Y0)), true) -> true
% 6.18/6.22 ifeq(theorem(Y0), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(X0, X1)), true, theorem(or(X1, X0)), true) -> true
% 6.18/6.22 ifeq(theorem(or(X0, or(X1, X2))), true, theorem(or(X1, or(X0, X2))), true) -> true
% 6.18/6.22 ifeq(theorem(or(X1, X0)), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(X1, or(X0, X2))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y0, not(or(Y0, Y0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y0, or(not(Y2), Y2))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y0, or(not(or(X0, or(Y0, X2))), or(X0, X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y0, or(not(or(Y2, Y0)), Y2))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y0, or(not(or(or(Y0, Y2), or(Y0, Y2))), Y2))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(Y1, Y1)), true, theorem(Y1), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(X0), X1)), true, theorem(or(not(or(X2, X0)), or(X2, X1))), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y), Z)), true, ifeq(axiom(or(not(X), Y)), true, theorem(or(not(X), Z)), true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), Y1)), true, ifeq(axiom(or(not(or(Y1, Y1)), Y0)), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), Y1)), true, theorem(or(not(or(Y0, Y0)), Y1)), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), or(X1, X0))), true, ifeq(axiom(or(not(or(X0, X1)), Y0)), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), or(X1, Y2))), true, ifeq(axiom(or(not(Y2), Y0)), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), or(X1, or(X0, X2)))), true, ifeq(axiom(or(not(or(X0, or(X1, X2))), Y0)), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), or(X1, or(Y0, Y0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y0), or(not(or(X2, X0)), or(X2, X1)))), true, ifeq(axiom(or(not(or(not(X0), X1)), Y0)), true, true, true), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(Y1), Y1)), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(not(X0)), or(not(or(X2, X0)), or(X2, not(X0))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X1, X0)), Y1)), true, theorem(or(not(or(X0, X1)), Y1)), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X1, X2)), or(X1, or(or(X1, X2), X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X1, Y2)), Y1)), true, theorem(or(not(Y2), Y1)), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X1, or(X0, X2))), Y1)), true, theorem(or(not(or(X0, or(X1, X2))), Y1)), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X2, X0)), or(X2, X1))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, Y1)), or(X1, Y1))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, Y1)), or(X1, or(Y1, Y0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, not(X0))), or(not(or(X2, X0)), or(X2, Y0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(X0, X1))), or(X1, X0))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(X0, or(X1, X2)))), or(X1, or(X0, X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(Y1, Y2))), or(X1, or(Y1, or(Y0, Y2))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(Y1, Y2))), or(or(Y0, Y2), Y1))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(Y2, Y2))), Y2)), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(not(X0), X1))), or(not(or(X2, X0)), or(X2, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(not(X0), Y2))), or(not(or(X2, X0)), or(X2, or(Y0, Y2))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(Y0, or(or(Y0, Y2), Y2))), or(Y0, Y2))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(not(or(X2, X0)), or(X2, X1))), Y1)), true, theorem(or(not(or(not(X0), X1)), Y1)), true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(not(or(Y0, Y1)), or(Y0, Y2))), or(X1, or(not(Y1), Y2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(not(or(Y0, Y1)), or(Y0, Y2))), or(Y2, not(Y1)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(not(or(Y0, Y1)), or(Y0, not(Y1)))), not(Y1))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(not(or(Y0, Y1)), or(Y0, or(X1, X2)))), or(X1, or(not(Y1), X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(not(or(or(X1, X2), Y1)), or(X1, or(Y1, X2)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(X1, X0), not(X0))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(X1, X0), not(or(X0, X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(X1, or(X0, X2)), not(or(X0, or(X1, X2))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(X0), or(X1, X0)), or(not(X0), or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(or(X0, X0)), X0), or(not(or(X0, X0)), X0))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(or(X0, X1)), or(X1, X0)), or(not(or(X0, X1)), or(X1, X0)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))), or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(or(X2, X0)), or(X2, X1)), not(or(not(X0), X1)))), true, true, true) -> true
% 6.18/6.22 ifeq(theorem(or(or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))), or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))))), true, true, true) -> true
% 6.18/6.22 theorem(or(Y1, not(Y1))) -> true
% 6.18/6.22 theorem(or(Y1, not(or(Y1, Y1)))) -> true
% 6.18/6.22 theorem(or(Y1, not(or(or(Y1, Y1), or(Y1, Y1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, not(or(X0, X0))))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(X1), X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(X1), or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(or(X1, X0)), X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(or(X1, X1)), X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(or(X1, X2)), or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2))))) -> true
% 6.18/6.22 theorem(or(Y1, or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(X0), or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(X0), or(X1, X0)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(X0), or(X1, or(X2, X0))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(X0), or(not(or(X1, X2)), or(X1, X0))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(Y1), Y2))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(Y2), Y2))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, X0)), X0))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, X0)), or(X1, X0)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, X1)), or(X0, or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, X1)), or(X1, X0)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, X1)), or(X2, or(X1, X0))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(X1, X1))), or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(X1, X2))), or(or(X0, X2), X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(Y1, X2))), or(X0, X2)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(X0, or(or(X0, X1), X1))), or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(Y1, Y2)), Y2))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(Y2, Y1)), Y2))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(or(X0, X0), or(X0, X0))), X0))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(or(X0, X1), X2)), or(X0, or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(or(X0, X1), or(X0, X1))), or(X1, X0)))) -> true
% 6.18/6.22 theorem(or(Y1, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2))) -> true
% 6.18/6.22 theorem(or(Y1, or(or(X0, X1), not(X1)))) -> true
% 6.18/6.22 theorem(or(Y1, or(or(X0, X1), not(or(X1, X0))))) -> true
% 6.18/6.22 theorem(or(Y1, or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2)))))) -> true
% 6.18/6.22 theorem(or(not(X0), or(X1, X0))) -> true
% 6.18/6.22 theorem(or(not(Y1), not(or(not(or(Y0, Y1)), not(or(Y0, Y1)))))) -> true
% 6.18/6.22 theorem(or(not(Y1), or(X1, or(Y0, Y1)))) -> true
% 6.18/6.22 theorem(or(not(Y1), or(Y1, Y0))) -> true
% 6.18/6.22 theorem(or(not(Y1), or(not(or(X2, X0)), or(X2, Y1)))) -> true
% 6.18/6.22 theorem(or(not(Y1), or(or(Y0, Y1), X1))) -> true
% 6.18/6.22 theorem(or(not(Y2), Y2)) -> true
% 6.18/6.22 theorem(or(not(or(X0, X0)), X0)) -> true
% 6.18/6.22 theorem(or(not(or(X0, X1)), or(X1, X0))) -> true
% 6.18/6.22 theorem(or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true
% 6.18/6.22 theorem(or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1)))) -> true
% 6.18/6.22 theorem(or(not(or(Y0, Y0)), not(or(not(Y0), not(Y0))))) -> true
% 6.18/6.22 theorem(or(not(or(Y0, Y0)), or(X1, Y0))) -> true
% 6.18/6.22 theorem(or(not(or(Y0, Y0)), or(Y0, X1))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, Y0)), or(X1, or(Y0, Y1)))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, Y0)), or(Y1, Y0))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, not(X0))), or(not(or(X2, X0)), or(X2, Y1)))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, or(Y0, Y2))), or(X1, or(Y0, or(Y1, Y2))))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, or(Y0, Y2))), or(Y1, or(Y0, Y2)))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, or(Y0, Y2))), or(or(Y1, Y2), Y0))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, or(not(X0), Y2))), or(not(or(X2, X0)), or(X2, or(Y1, Y2))))) -> true
% 6.18/6.22 theorem(or(not(or(Y1, or(or(Y1, Y2), Y2))), or(Y1, Y2))) -> true
% 6.18/6.22 theorem(or(not(or(Y2, Y0)), or(Y2, or(X1, Y0)))) -> true
% 6.18/6.22 theorem(or(not(or(Y2, or(X0, X1))), or(Y2, or(X1, X0)))) -> true
% 6.18/6.22 theorem(or(not(or(Y2, or(X0, or(X1, X2)))), or(Y2, or(X1, or(X0, X2))))) -> true
% 6.18/6.22 theorem(or(not(or(Y2, or(Y1, Y1))), or(Y2, Y1))) -> true
% 6.18/6.22 theorem(or(not(or(Y2, or(not(X0), X1))), or(Y2, or(not(or(X2, X0)), or(X2, X1))))) -> true
% 6.18/6.22 theorem(or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true
% 6.18/6.22 theorem(or(not(or(not(Y1), Y2)), or(X1, or(not(or(Y0, Y1)), or(Y0, Y2))))) -> true
% 6.18/6.22 theorem(or(not(or(not(Y1), Y2)), or(Y0, or(not(or(Y0, Y1)), Y2)))) -> true
% 6.18/6.22 theorem(or(not(or(not(Y1), Y2)), or(not(or(X2, or(Y0, Y1))), or(X2, or(Y0, Y2))))) -> true
% 6.18/6.22 theorem(or(not(or(not(Y1), Y2)), or(or(Y0, Y2), not(or(Y0, Y1))))) -> true
% 6.18/6.22 theorem(or(not(or(or(X0, X1), or(X0, X1))), or(X1, X0))) -> true
% 6.18/6.22 theorem(or(not(or(or(X0, or(X1, X2)), or(X0, or(X1, X2)))), or(X1, or(X0, X2)))) -> true
% 6.18/6.22 theorem(or(not(or(or(X1, X2), Y0)), or(X1, or(Y0, X2)))) -> true
% 6.18/6.22 theorem(or(not(or(or(Y1, Y1), or(Y1, Y1))), Y1)) -> true
% 6.18/6.22 theorem(or(not(or(or(not(X0), X1), or(not(X0), X1))), or(not(or(X2, X0)), or(X2, X1)))) -> true
% 6.18/6.22 theorem(or(or(X0, X1), not(X0))) -> true
% 6.18/6.22 theorem(or(or(X0, X1), not(or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(or(X0, X1), not(or(X0, or(X1, X1))))) -> true
% 6.18/6.22 theorem(or(or(X0, or(X2, X1)), not(or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(or(X1, X0), not(X0))) -> true
% 6.18/6.22 theorem(or(or(X1, X0), not(or(X0, X0)))) -> true
% 6.18/6.22 theorem(or(or(X1, X0), not(or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(or(X1, X0), not(or(or(X0, X1), or(X0, X1))))) -> true
% 6.18/6.22 theorem(or(or(X1, or(X0, X2)), not(or(X0, or(X1, X2))))) -> true
% 6.18/6.22 theorem(or(or(X1, or(X2, X0)), not(X0))) -> true
% 6.18/6.22 theorem(or(or(X2, or(X1, X0)), not(or(X0, X1)))) -> true
% 6.18/6.22 theorem(or(or(not(X1), X1), Y0)) -> true
% 6.18/6.22 theorem(or(or(not(X1), or(X2, X1)), Y0)) -> true
% 6.18/6.22 theorem(or(or(not(or(X1, X1)), X1), Y0)) -> true
% 6.18/6.22 theorem(or(or(not(or(X1, X2)), or(X1, X0)), not(X0))) -> true
% 6.18/6.22 theorem(or(or(not(or(X1, X2)), or(X2, X1)), Y0)) -> true
% 6.18/6.22 theorem(or(or(not(or(X1, Y0)), X1), Y0)) -> true
% 6.18/6.22 theorem(or(or(not(or(X2, X0)), or(X2, X1)), not(or(not(X0), X1)))) -> true
% 6.18/6.22 theorem(or(or(not(or(or(Y0, X1), or(Y0, X1))), X1), Y0)) -> true
% 6.18/6.22 true__ -> false__
% 6.18/6.22 with the LPO induced by
% 6.18/6.22 q > p > f1 > theorem > not > true > or > axiom > ifeq > true__ > false__
% 6.18/6.22
% 6.18/6.22 % SZS output end Proof
% 6.18/6.22
%------------------------------------------------------------------------------