TSTP Solution File: LCL258-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL258-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:51:12 EDT 2022
% Result : Unsatisfiable 0.39s 0.56s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of clauses : 108 ( 60 unt; 0 nHn; 46 RR)
% Number of literals : 173 ( 69 equ; 66 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 244 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(p,implies(implies(p,q),q))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_79,implies(X_78,X_80)))
| ~ theorem(implies(implies(X_79,implies(X_78,X_80)),implies(X_78,implies(X_79,X_80))))
| theorem(implies(X_78,implies(X_79,X_80))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_78,implies(X_79,X_80)))),bind(Y,$fot(implies(X_79,implies(X_78,X_80))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77))))
| theorem(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_28)),bind(C,$fot(X_29))]]) ).
cnf(refute_0_3,plain,
implies(X,X_29) = or(not(X),X_29),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X,X_29) != or(not(X),X_29)
| or(not(X),X_29) = implies(X,X_29) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_29))),bind(Y0,$fot(or(not(X),X_29)))]]) ).
cnf(refute_0_8,plain,
or(not(X),X_29) = implies(X,X_29),
inference(resolve,[$cnf( $equal(implies(X,X_29),or(not(X),X_29)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X),X_29) != implies(X,X_29)
| ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29))))
| axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))) ),[0,1,1],$fot(implies(X,X_29))]]) ).
cnf(refute_0_10,plain,
( ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29))))
| axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_13,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_12]) ).
cnf(refute_0_14,plain,
or(not(X),or(X_28,X_29)) = implies(X,or(X_28,X_29)),
inference(subst,[],[refute_0_13:[bind(Y,$fot(or(X_28,X_29)))]]) ).
cnf(refute_0_15,plain,
implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))]]) ).
cnf(refute_0_16,plain,
( implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) != implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))
| or(not(X),or(X_28,X_29)) != implies(X,or(X_28,X_29))
| implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),[1,0],$fot(implies(X,or(X_28,X_29)))]]) ).
cnf(refute_0_17,plain,
( or(not(X),or(X_28,X_29)) != implies(X,or(X_28,X_29))
| implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_28,X_29)),implies(X,or(X_28,X_29))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) != implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))
| ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))
| axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),[0],$fot(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))))]]) ).
cnf(refute_0_20,plain,
( ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))
| axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
axiom(implies(implies(X_43,or(not(X),X_45)),or(not(X),implies(X_43,X_45)))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_43)),bind(X_28,$fot(not(X))),bind(X_29,$fot(X_45))]]) ).
cnf(refute_0_23,plain,
implies(X,implies(X_43,X_45)) = or(not(X),implies(X_43,X_45)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_43,X_45)))]]) ).
cnf(refute_0_24,plain,
( implies(X,implies(X_43,X_45)) != or(not(X),implies(X_43,X_45))
| or(not(X),implies(X_43,X_45)) = implies(X,implies(X_43,X_45)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,implies(X_43,X_45)))),bind(Y0,$fot(or(not(X),implies(X_43,X_45))))]]) ).
cnf(refute_0_25,plain,
or(not(X),implies(X_43,X_45)) = implies(X,implies(X_43,X_45)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_43,X_45)),or(not(X),implies(X_43,X_45))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( or(not(X),implies(X_43,X_45)) != implies(X,implies(X_43,X_45))
| ~ axiom(implies(implies(X_43,or(not(X),X_45)),or(not(X),implies(X_43,X_45))))
| axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_43,or(not(X),X_45)),or(not(X),implies(X_43,X_45)))) ),[0,1],$fot(implies(X,implies(X_43,X_45)))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(implies(implies(X_43,or(not(X),X_45)),or(not(X),implies(X_43,X_45))))
| axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_43,X_45)),implies(X,implies(X_43,X_45))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))),
inference(resolve,[$cnf( axiom(implies(implies(X_43,or(not(X),X_45)),or(not(X),implies(X_43,X_45)))) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
or(not(X),X_45) = implies(X,X_45),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_30,plain,
implies(X_43,or(not(X),X_45)) = implies(X_43,or(not(X),X_45)),
introduced(tautology,[refl,[$fot(implies(X_43,or(not(X),X_45)))]]) ).
cnf(refute_0_31,plain,
( implies(X_43,or(not(X),X_45)) != implies(X_43,or(not(X),X_45))
| or(not(X),X_45) != implies(X,X_45)
| implies(X_43,or(not(X),X_45)) = implies(X_43,implies(X,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_43,or(not(X),X_45)),implies(X_43,or(not(X),X_45))) ),[1,1],$fot(implies(X,X_45))]]) ).
cnf(refute_0_32,plain,
( or(not(X),X_45) != implies(X,X_45)
| implies(X_43,or(not(X),X_45)) = implies(X_43,implies(X,X_45)) ),
inference(resolve,[$cnf( $equal(implies(X_43,or(not(X),X_45)),implies(X_43,or(not(X),X_45))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(X_43,or(not(X),X_45)) = implies(X_43,implies(X,X_45)),
inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) = implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))),
introduced(tautology,[refl,[$fot(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))))]]) ).
cnf(refute_0_35,plain,
( implies(X_43,or(not(X),X_45)) != implies(X_43,implies(X,X_45))
| implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) != implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))
| implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) = implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))),implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) ),[1,0],$fot(implies(X_43,implies(X,X_45)))]]) ).
cnf(refute_0_36,plain,
( implies(X_43,or(not(X),X_45)) != implies(X_43,implies(X,X_45))
| implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) = implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))),implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) = implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45))),
inference(resolve,[$cnf( $equal(implies(X_43,or(not(X),X_45)),implies(X_43,implies(X,X_45))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))) != implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45)))
| ~ axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))))
| axiom(implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) ),[0],$fot(implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45))))]]) ).
cnf(refute_0_39,plain,
( ~ axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))))
| axiom(implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45))),implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
axiom(implies(implies(X_43,implies(X,X_45)),implies(X,implies(X_43,X_45)))),
inference(resolve,[$cnf( axiom(implies(implies(X_43,or(not(X),X_45)),implies(X,implies(X_43,X_45)))) )],[refute_0_28,refute_0_39]) ).
cnf(refute_0_41,plain,
axiom(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_75)),bind(X_43,$fot(X_76)),bind(X_45,$fot(X_77))]]) ).
cnf(refute_0_42,plain,
theorem(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))),
inference(resolve,[$cnf( axiom(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))) )],[refute_0_41,refute_0_1]) ).
cnf(refute_0_43,plain,
theorem(implies(implies(X_79,implies(X_78,X_80)),implies(X_78,implies(X_79,X_80)))),
inference(subst,[],[refute_0_42:[bind(X_75,$fot(X_78)),bind(X_76,$fot(X_79)),bind(X_77,$fot(X_80))]]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(X_79,implies(X_78,X_80)))
| theorem(implies(X_78,implies(X_79,X_80))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_79,implies(X_78,X_80)),implies(X_78,implies(X_79,X_80)))) )],[refute_0_43,refute_0_0]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(implies(X_78,X_80),implies(X_78,X_80)))
| theorem(implies(X_78,implies(implies(X_78,X_80),X_80))) ),
inference(subst,[],[refute_0_44:[bind(X_79,$fot(implies(X_78,X_80)))]]) ).
cnf(refute_0_46,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_47,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(implies(or(X_313,X_313),X_313)),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_313))]]) ).
cnf(refute_0_49,plain,
( ~ axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31))))
| theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))))]]) ).
cnf(refute_0_50,plain,
axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_30)),bind(B,$fot(X_31)),bind(C,$fot(X_32))]]) ).
cnf(refute_0_51,plain,
theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))),
inference(resolve,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))) )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
( ~ theorem(implies(X_30,X_31))
| ~ theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31))))
| theorem(implies(or(X_32,X_30),or(X_32,X_31))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_32,X_30),or(X_32,X_31)))),bind(Y,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_53,plain,
( ~ theorem(implies(X_30,X_31))
| theorem(implies(or(X_32,X_30),or(X_32,X_31))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(or(X_313,X_313),X_313))
| theorem(implies(or(X_314,or(X_313,X_313)),or(X_314,X_313))) ),
inference(subst,[],[refute_0_53:[bind(X_30,$fot(or(X_313,X_313))),bind(X_31,$fot(X_313)),bind(X_32,$fot(X_314))]]) ).
cnf(refute_0_55,plain,
theorem(implies(or(X_314,or(X_313,X_313)),or(X_314,X_313))),
inference(resolve,[$cnf( theorem(implies(or(X_313,X_313),X_313)) )],[refute_0_48,refute_0_54]) ).
cnf(refute_0_56,plain,
theorem(implies(or(X_316,or(not(X),not(X))),or(X_316,not(X)))),
inference(subst,[],[refute_0_55:[bind(X_313,$fot(not(X))),bind(X_314,$fot(X_316))]]) ).
cnf(refute_0_57,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_58,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_59,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ theorem(implies(or(X_316,or(not(X),not(X))),or(X_316,not(X))))
| theorem(implies(or(X_316,implies(X,not(X))),or(X_316,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_316,or(not(X),not(X))),or(X_316,not(X)))) ),[0,0,1],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(implies(or(X_316,or(not(X),not(X))),or(X_316,not(X))))
| theorem(implies(or(X_316,implies(X,not(X))),or(X_316,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
theorem(implies(or(X_316,implies(X,not(X))),or(X_316,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(X_316,or(not(X),not(X))),or(X_316,not(X)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
theorem(implies(or(not(X),implies(X_321,not(X_321))),or(not(X),not(X_321)))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_321)),bind(X_316,$fot(not(X)))]]) ).
cnf(refute_0_64,plain,
implies(X,not(X_321)) = or(not(X),not(X_321)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_321)))]]) ).
cnf(refute_0_65,plain,
( implies(X,not(X_321)) != or(not(X),not(X_321))
| or(not(X),not(X_321)) = implies(X,not(X_321)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,not(X_321)))),bind(Y0,$fot(or(not(X),not(X_321))))]]) ).
cnf(refute_0_66,plain,
or(not(X),not(X_321)) = implies(X,not(X_321)),
inference(resolve,[$cnf( $equal(implies(X,not(X_321)),or(not(X),not(X_321))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( or(not(X),not(X_321)) != implies(X,not(X_321))
| ~ theorem(implies(or(not(X),implies(X_321,not(X_321))),or(not(X),not(X_321))))
| theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_321,not(X_321))),or(not(X),not(X_321)))) ),[0,1],$fot(implies(X,not(X_321)))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(implies(or(not(X),implies(X_321,not(X_321))),or(not(X),not(X_321))))
| theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_321)),implies(X,not(X_321))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_321,not(X_321))),or(not(X),not(X_321)))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
or(not(X),implies(X_321,not(X_321))) = implies(X,implies(X_321,not(X_321))),
inference(subst,[],[refute_0_13:[bind(Y,$fot(implies(X_321,not(X_321))))]]) ).
cnf(refute_0_71,plain,
implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) = implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))))]]) ).
cnf(refute_0_72,plain,
( implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) != implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))
| or(not(X),implies(X_321,not(X_321))) != implies(X,implies(X_321,not(X_321)))
| implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) = implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))),implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) ),[1,0],$fot(implies(X,implies(X_321,not(X_321))))]]) ).
cnf(refute_0_73,plain,
( or(not(X),implies(X_321,not(X_321))) != implies(X,implies(X_321,not(X_321)))
| implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) = implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))),implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) = implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_321,not(X_321))),implies(X,implies(X_321,not(X_321)))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
( implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))) != implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))
| ~ theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))))
| theorem(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) ),[0],$fot(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))))]]) ).
cnf(refute_0_76,plain,
( ~ theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))))
| theorem(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321))),implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
theorem(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_321,not(X_321))),implies(X,not(X_321)))) )],[refute_0_69,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ theorem(X_526)
| ~ theorem(implies(X_526,implies(X_527,X_527)))
| theorem(implies(X_527,X_527)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_527,X_527))),bind(Y,$fot(X_526))]]) ).
cnf(refute_0_79,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_80,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_81,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_80,refute_0_79]) ).
cnf(refute_0_82,plain,
theorem(implies(X_3,or(not(X_11),X_3))),
inference(subst,[],[refute_0_81:[bind(X_4,$fot(not(X_11)))]]) ).
cnf(refute_0_83,plain,
implies(X_11,X_3) = or(not(X_11),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_84,plain,
( implies(X_11,X_3) != or(not(X_11),X_3)
| or(not(X_11),X_3) = implies(X_11,X_3) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X_11,X_3))),bind(Y0,$fot(or(not(X_11),X_3)))]]) ).
cnf(refute_0_85,plain,
or(not(X_11),X_3) = implies(X_11,X_3),
inference(resolve,[$cnf( $equal(implies(X_11,X_3),or(not(X_11),X_3)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( or(not(X_11),X_3) != implies(X_11,X_3)
| ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) ),[0,1],$fot(implies(X_11,X_3))]]) ).
cnf(refute_0_87,plain,
( ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_3),implies(X_11,X_3)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
theorem(implies(X_3,implies(X_11,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
theorem(implies(X_525,implies(X_523,X_525))),
inference(subst,[],[refute_0_88:[bind(X_11,$fot(X_523)),bind(X_3,$fot(X_525))]]) ).
cnf(refute_0_90,plain,
( ~ theorem(implies(X_525,implies(X_523,X_525)))
| theorem(implies(X_523,implies(X_525,X_525))) ),
inference(subst,[],[refute_0_44:[bind(X_78,$fot(X_523)),bind(X_79,$fot(X_525)),bind(X_80,$fot(X_525))]]) ).
cnf(refute_0_91,plain,
theorem(implies(X_523,implies(X_525,X_525))),
inference(resolve,[$cnf( theorem(implies(X_525,implies(X_523,X_525))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(implies(X_526,implies(X_527,X_527))),
inference(subst,[],[refute_0_91:[bind(X_523,$fot(X_526)),bind(X_525,$fot(X_527))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(X_526)
| theorem(implies(X_527,X_527)) ),
inference(resolve,[$cnf( theorem(implies(X_526,implies(X_527,X_527))) )],[refute_0_92,refute_0_78]) ).
cnf(refute_0_94,plain,
( ~ theorem(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))))
| theorem(implies(X_662,X_662)) ),
inference(subst,[],[refute_0_93:[bind(X_526,$fot(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321))))),bind(X_527,$fot(X_662))]]) ).
cnf(refute_0_95,plain,
theorem(implies(X_662,X_662)),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_321,not(X_321))),implies(X,not(X_321)))) )],[refute_0_77,refute_0_94]) ).
cnf(refute_0_96,plain,
theorem(implies(implies(X_78,X_80),implies(X_78,X_80))),
inference(subst,[],[refute_0_95:[bind(X_662,$fot(implies(X_78,X_80)))]]) ).
cnf(refute_0_97,plain,
theorem(implies(X_78,implies(implies(X_78,X_80),X_80))),
inference(resolve,[$cnf( theorem(implies(implies(X_78,X_80),implies(X_78,X_80))) )],[refute_0_96,refute_0_45]) ).
cnf(refute_0_98,plain,
theorem(implies(p,implies(implies(p,q),q))),
inference(subst,[],[refute_0_97:[bind(X_78,$fot(p)),bind(X_80,$fot(q))]]) ).
cnf(refute_0_99,plain,
$false,
inference(resolve,[$cnf( theorem(implies(p,implies(implies(p,q),q))) )],[refute_0_98,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL258-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 08:21:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56
% 0.39/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.57
%------------------------------------------------------------------------------