TSTP Solution File: LCL190-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 12:58:56 EDT 2022
% Result : Unsatisfiable 10.80s 10.69s
% Output : Proof 10.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n020.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 : Mon Jul 4 03:08:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.80/10.69 % SZS status Unsatisfiable
% 10.80/10.69 % SZS output start Proof
% 10.80/10.69 The input problem is unsatisfiable because
% 10.80/10.69
% 10.80/10.69 [1] the following set of Horn clauses is unsatisfiable:
% 10.80/10.69
% 10.80/10.69 axiom(or(not(or(A, A)), A))
% 10.80/10.69 axiom(or(not(A), or(B, A)))
% 10.80/10.69 axiom(or(not(or(A, B)), or(B, A)))
% 10.80/10.69 axiom(or(not(or(A, or(B, C))), or(B, or(A, C))))
% 10.80/10.69 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B))))
% 10.80/10.69 axiom(X) ==> theorem(X)
% 10.80/10.69 axiom(or(not(Y), X)) & theorem(Y) ==> theorem(X)
% 10.80/10.69 axiom(or(not(X), Y)) & theorem(or(not(Y), Z)) ==> theorem(or(not(X), Z))
% 10.80/10.69 theorem(or(not(or(p, or(q, r))), or(p, or(r, q)))) ==> \bottom
% 10.80/10.69
% 10.80/10.69 This holds because
% 10.80/10.69
% 10.80/10.69 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 10.80/10.69
% 10.80/10.69 E:
% 10.80/10.69 axiom(or(not(A), or(B, A))) = true__
% 10.80/10.69 axiom(or(not(or(A, A)), A)) = true__
% 10.80/10.69 axiom(or(not(or(A, B)), or(B, A))) = true__
% 10.80/10.69 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) = true__
% 10.80/10.69 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) = true__
% 10.80/10.69 f1(axiom(X), X) = true__
% 10.80/10.69 f1(true__, X) = theorem(X)
% 10.80/10.69 f2(true__, X) = theorem(X)
% 10.80/10.69 f3(theorem(Y), Y, X) = true__
% 10.80/10.69 f3(true__, Y, X) = f2(axiom(or(not(Y), X)), X)
% 10.80/10.69 f4(true__, X, Z) = theorem(or(not(X), Z))
% 10.80/10.69 f5(theorem(or(not(Y), Z)), X, Y, Z) = true__
% 10.80/10.69 f5(true__, X, Y, Z) = f4(axiom(or(not(X), Y)), X, Z)
% 10.80/10.69 f6(theorem(or(not(or(p, or(q, r))), or(p, or(r, q))))) = true__
% 10.80/10.69 f6(true__) = false__
% 10.80/10.69 G:
% 10.80/10.69 true__ = false__
% 10.80/10.69
% 10.80/10.69 This holds because
% 10.80/10.69
% 10.80/10.69 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 10.80/10.69
% 10.80/10.69
% 10.80/10.69 axiom(or(not(A), or(B, A))) -> true__
% 10.80/10.69 axiom(or(not(or(A, A)), A)) -> true__
% 10.80/10.69 axiom(or(not(or(A, B)), or(B, A))) -> true__
% 10.80/10.69 axiom(or(not(or(A, or(B, C))), or(B, or(A, C)))) -> true__
% 10.80/10.69 axiom(or(not(or(not(A), B)), or(not(or(C, A)), or(C, B)))) -> true__
% 10.80/10.69 f1(axiom(X), X) -> true__
% 10.80/10.69 f1(true__, or(X1, or(not(or(Y0, Y1)), or(Y1, Y0)))) -> true__
% 10.80/10.69 f1(true__, or(X1, or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2))))) -> true__
% 10.80/10.69 f1(true__, or(X1, or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 10.80/10.69 f1(true__, or(Y1, not(or(Y1, Y1)))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(X0), or(X1, X0)))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(Y2), Y2))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(or(X0, X0)), X0))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(or(X0, or(Y1, X2))), or(X0, X2)))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(or(Y2, Y1)), Y2))) -> true__
% 10.80/10.69 f1(true__, or(Y1, or(not(or(or(Y1, Y2), or(Y1, Y2))), Y2))) -> true__
% 10.80/10.69 f1(true__, or(not(X0), or(X1, X0))) -> true__
% 10.80/10.69 f1(true__, or(not(Y0), or(X2, or(Y1, Y0)))) -> true__
% 10.80/10.69 f1(true__, or(not(Y0), or(Y0, Y1))) -> true__
% 10.80/10.69 f1(true__, or(not(Y2), Y2)) -> true__
% 10.80/10.69 f1(true__, or(not(Y2), or(not(or(Y3, Y1)), or(Y3, Y2)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(X0, X0)), X0)) -> true__
% 10.80/10.69 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 10.80/10.69 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(X2, X0)), or(not(or(not(X0), X1)), or(X2, X1)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, Y0)), or(X2, Y0))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, Y1)), or(X2, or(Y1, Y0)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, Y1)), or(Y0, Y1))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, not(X1))), or(not(or(X3, X1)), or(X3, Y0)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(X2, or(Y1, or(Y0, Y2))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(Y0, or(Y1, Y2)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(or(Y0, Y2), Y1))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, or(not(X1), Y2))), or(not(or(X3, X1)), or(X3, or(Y0, Y2))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y0, or(or(Y0, Y2), Y2))), or(Y0, Y2))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y2, Y3)), or(Y2, or(Y1, Y3)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y2, or(X0, X1))), or(Y2, or(X1, X0)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y2, or(X0, or(X1, X2)))), or(Y2, or(X1, or(X0, X2))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y2, or(Y1, Y1))), or(Y2, Y1))) -> true__
% 10.80/10.69 f1(true__, or(not(or(Y2, or(not(X0), X1))), or(Y2, or(not(or(X2, X0)), or(X2, X1))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(not(Y0), Y1)), or(X2, or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(not(Y0), Y1)), or(Y2, or(not(or(Y2, Y0)), Y1)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(not(Y0), Y1)), or(not(or(X3, or(Y2, Y0))), or(X3, or(Y2, Y1))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(not(Y0), Y1)), or(or(Y2, Y1), not(or(Y2, Y0))))) -> true__
% 10.80/10.69 f1(true__, or(not(or(or(X1, X2), or(X1, X2))), or(X2, X1))) -> true__
% 10.80/10.69 f1(true__, or(not(or(or(X1, or(X2, X3)), or(X1, or(X2, X3)))), or(X2, or(X1, X3)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(or(X2, X3), Y1)), or(X2, or(Y1, X3)))) -> true__
% 10.80/10.69 f1(true__, or(not(or(or(Y1, Y1), or(Y1, Y1))), Y1)) -> true__
% 10.80/10.69 f1(true__, or(not(or(or(not(Y1), Y2), or(not(Y1), Y2))), or(not(or(Y3, Y1)), or(Y3, Y2)))) -> true__
% 10.80/10.69 f1(true__, or(or(X1, X0), not(X0))) -> true__
% 10.80/10.69 f1(true__, or(or(X1, X0), not(or(X0, X1)))) -> true__
% 10.80/10.69 f1(true__, or(or(Y1, or(Y0, Y2)), not(or(Y0, or(Y1, Y2))))) -> true__
% 10.80/10.69 f1(true__, or(or(not(or(Y2, Y0)), or(Y2, Y1)), not(or(not(Y0), Y1)))) -> true__
% 10.80/10.69 f2(axiom(or(not(Y), X)), X) -> f3(true__, Y, X)
% 10.80/10.69 f2(true__, X) -> theorem(X)
% 10.80/10.69 f3(f1(true__, Y0), Y0, Y1) -> true__
% 10.80/10.69 f3(theorem(Y), Y, X) -> true__
% 10.80/10.69 f3(true__, Y0, or(X1, Y0)) -> f1(true__, or(X1, Y0))
% 10.80/10.69 f3(true__, or(X0, X1), or(X1, X0)) -> f1(true__, or(X1, X0))
% 10.80/10.69 f3(true__, or(X0, not(or(X0, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(X1, X2)), or(X1, or(X0, X2))) -> f1(true__, or(X1, or(X0, X2)))
% 10.80/10.69 f3(true__, or(X0, or(not(X1), X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(X1), or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(X1, X0)), X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(X1, X1)), X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(X1, X2)), or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(not(X1), X2)), or(not(or(X3, X1)), or(X3, X2)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(Y1, Y1), Y1) -> f1(true__, Y1)
% 10.80/10.69 f3(true__, or(not(X0), X0), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1))) -> f1(true__, or(not(or(X2, X0)), or(X2, X1)))
% 10.80/10.69 f3(true__, or(not(X0), or(X0, X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(X0), or(X1, X0)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(X0), or(X1, or(X2, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(X0), or(not(or(X1, X2)), or(X1, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X0)), X0), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X0)), or(X1, X0)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X1)), or(X0, X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X1)), or(X0, or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X1)), or(X1, X0)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X1)), or(X2, or(X1, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, X1)), or(not(or(not(X1), X2)), or(X0, X2))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, not(X1))), or(not(or(X2, X1)), or(X2, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X1))), or(X0, X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X2))), or(X0, or(X1, X2))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X2))), or(X3, or(X1, or(X0, X2)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, X2))), or(or(X0, X2), X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(X1, or(X2, X3)))), or(X0, or(X2, or(X1, X3)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(not(X1), X2))), or(X0, or(not(or(X3, X1)), or(X3, X2)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(not(X1), X2))), or(not(or(X3, X1)), or(X3, or(X0, X2)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(X0, or(or(X0, X1), X1))), or(X0, X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(not(X0), X1)), or(X2, or(not(or(X2, X0)), X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(not(X0), X1)), or(X2, or(not(or(X3, X0)), or(X3, X1)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(not(X0), X1)), or(not(or(X2, or(X3, X0))), or(X2, or(X3, X1)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(not(X0), X1)), or(or(X2, X1), not(or(X2, X0)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(or(X0, X0), or(X0, X0))), X0), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(or(X0, X1), X2)), or(X0, or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(or(X0, X1), or(X0, X1))), or(X1, X0)), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(or(X0, or(X1, X2)), or(X0, or(X1, X2)))), or(X1, or(X0, X2))), Y1) -> true__
% 10.80/10.69 f3(true__, or(not(or(or(not(X0), X1), or(not(X0), X1))), or(not(or(X2, X0)), or(X2, X1))), Y1) -> true__
% 10.80/10.69 f3(true__, or(or(X0, X1), not(X1)), Y1) -> true__
% 10.80/10.69 f3(true__, or(or(X0, X1), not(or(X1, X0))), Y1) -> true__
% 10.80/10.69 f3(true__, or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2)))), Y1) -> true__
% 10.80/10.69 f3(true__, or(or(not(or(X0, X1)), or(X0, X2)), not(or(not(X1), X2))), Y1) -> true__
% 10.80/10.69 f4(axiom(or(not(X), Y)), X, Z) -> f5(true__, X, Y, Z)
% 10.80/10.69 f4(true__, X, Z) -> theorem(or(not(X), Z))
% 10.80/10.69 f5(f1(true__, or(not(Y0), Y1)), Y2, Y0, Y1) -> true__
% 10.80/10.69 f5(theorem(or(not(Y), Z)), X, Y, Z) -> true__
% 10.80/10.69 f5(true__, Y0, or(X1, Y0), Y2) -> f1(true__, or(not(Y0), Y2))
% 10.80/10.69 f5(true__, Y2, Y0, not(or(not(Y0), not(Y0)))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(X1, Y0)) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(X1, or(X2, Y0))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(Y0, X1)) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(X1), X1)) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(X1), or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, X1)), X1)) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, X2)), or(X1, Y0))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, X2)), or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, not(Y0))), X1)) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3)))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(X1, or(not(Y0), X2))), or(X1, X2))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(not(X1), X2)), or(not(or(X3, X1)), or(X3, X2)))) -> true__
% 10.80/10.69 f5(true__, Y2, Y0, or(not(or(or(not(Y0), X1), or(not(Y0), X1))), X1)) -> true__
% 10.80/10.69 f5(true__, Y2, Y1, Y1) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X0), or(X1, X0)) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X1), or(X0, X1)) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X1), or(X0, or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X1), or(X1, X0)) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X1), or(X2, or(X1, X0))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, X1), or(not(or(not(X1), X2)), or(X0, X2))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, not(X1)), or(not(or(X2, X1)), or(X2, X0))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X1)), or(X0, X1)) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X2)), or(X0, or(X1, X2))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X2)), or(X0, or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X2)), or(X1, or(X0, X2))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X2)), or(X3, or(X1, or(X0, X2)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, X2)), or(or(X0, X2), X1)) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(X1, or(X2, X3))), or(X0, or(X2, or(X1, X3)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(not(X1), X2)), or(X0, or(not(or(X3, X1)), or(X3, X2)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(not(X1), X2)), or(not(or(X3, X1)), or(X3, or(X0, X2)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(X0, or(or(X0, X1), X1)), or(X0, X1)) -> true__
% 10.80/10.69 f5(true__, Y2, or(Y1, Y1), Y1) -> true__
% 10.80/10.69 f5(true__, Y2, or(not(X0), X1), or(X2, or(not(or(X2, X0)), X1))) -> true__
% 10.80/10.69 f5(true__, Y2, or(not(X0), X1), or(X2, or(not(or(X3, X0)), or(X3, X1)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, or(not(X0), X1), or(not(or(X2, or(X3, X0))), or(X2, or(X3, X1)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(not(X0), X1), or(or(X2, X1), not(or(X2, X0)))) -> true__
% 10.80/10.69 f5(true__, Y2, or(or(X0, X1), X2), or(X0, or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, Y2, or(or(X0, X1), or(X0, X1)), or(X1, X0)) -> true__
% 10.80/10.69 f5(true__, Y2, or(or(X0, or(X1, X2)), or(X0, or(X1, X2))), or(X1, or(X0, X2))) -> true__
% 10.80/10.69 f5(true__, Y2, or(or(Y1, Y1), or(Y1, Y1)), Y1) -> true__
% 10.80/10.69 f5(true__, Y2, or(or(not(X0), X1), or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1))) -> true__
% 10.80/10.69 f5(true__, or(X0, X1), or(X1, X0), Y2) -> f1(true__, or(not(or(X0, X1)), Y2))
% 10.80/10.69 f5(true__, or(X0, or(X1, X2)), or(X1, or(X0, X2)), Y2) -> f1(true__, or(not(or(X0, or(X1, X2))), Y2))
% 10.80/10.69 f5(true__, or(Y1, Y1), Y1, Y2) -> f1(true__, or(not(or(Y1, Y1)), Y2))
% 10.80/10.69 f5(true__, or(not(X0), X1), or(not(or(X2, X0)), or(X2, X1)), Y2) -> f1(true__, or(not(or(not(X0), X1)), Y2))
% 10.80/10.69 f6(f1(true__, or(not(or(p, or(q, r))), or(p, or(r, q))))) -> true__
% 10.80/10.69 f6(theorem(or(not(or(p, or(q, r))), or(p, or(r, q))))) -> true__
% 10.80/10.69 f6(true__) -> false__
% 10.80/10.69 false__ -> true__
% 10.80/10.69 theorem(X) -> f1(true__, X)
% 10.80/10.69 with the LPO induced by
% 10.80/10.69 r > q > p > f6 > f4 > f5 > not > or > f3 > f2 > theorem > f1 > axiom > false__ > true__
% 10.80/10.69
% 10.80/10.69 % SZS output end Proof
% 10.80/10.69
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