TSTP Solution File: LCL187-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL187-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:50:23 EDT 2022
% Result : Unsatisfiable 96.77s 96.99s
% Output : CNFRefutation 96.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of clauses : 253 ( 135 unt; 0 nHn; 108 RR)
% Number of literals : 410 ( 111 equ; 158 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 563 ( 39 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_4,axiom,
axiom(implies(or(A,B),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(not(p),q))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_68,or(X_69,X_70)))
| ~ theorem(implies(implies(X_68,or(X_69,X_70)),or(X_69,implies(X_68,X_70))))
| theorem(or(X_69,implies(X_68,X_70))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_69,implies(X_68,X_70)))),bind(Y,$fot(implies(X_68,or(X_69,X_70))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27))))
| theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,or(not(X),X_67)))),
inference(subst,[],[refute_0_3:[bind(X_25,$fot(not(X))),bind(X_26,$fot(X_66)),bind(X_27,$fot(X_67))]]) ).
cnf(refute_0_5,plain,
implies(X,X_67) = or(not(X),X_67),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_67))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( implies(X,X_67) != or(not(X),X_67)
| or(not(X),X_67) = implies(X,X_67) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_67))),bind(Y0,$fot(or(not(X),X_67)))]]) ).
cnf(refute_0_10,plain,
or(not(X),X_67) = implies(X,X_67),
inference(resolve,[$cnf( $equal(implies(X,X_67),or(not(X),X_67)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( or(not(X),X_67) != implies(X,X_67)
| ~ theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,or(not(X),X_67))))
| theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,or(not(X),X_67)))) ),[0,1,1],$fot(implies(X,X_67))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,or(not(X),X_67))))
| theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_67),implies(X,X_67)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,or(not(X),X_67)))) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_15,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_14]) ).
cnf(refute_0_16,plain,
or(not(X),or(X_66,X_67)) = implies(X,or(X_66,X_67)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(or(X_66,X_67)))]]) ).
cnf(refute_0_17,plain,
implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) = implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))))]]) ).
cnf(refute_0_18,plain,
( implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) != implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))
| or(not(X),or(X_66,X_67)) != implies(X,or(X_66,X_67))
| implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) = implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))),implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),[1,0],$fot(implies(X,or(X_66,X_67)))]]) ).
cnf(refute_0_19,plain,
( or(not(X),or(X_66,X_67)) != implies(X,or(X_66,X_67))
| implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) = implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))),implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) = implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_66,X_67)),implies(X,or(X_66,X_67))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))) != implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67)))
| ~ theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))))
| theorem(implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),[0],$fot(implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67))))]]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))))
| theorem(implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67))),implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(implies(implies(X,or(X_66,X_67)),or(X_66,implies(X,X_67)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_66,X_67)),or(X_66,implies(X,X_67)))) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
theorem(implies(implies(X_68,or(X_69,X_70)),or(X_69,implies(X_68,X_70)))),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_68)),bind(X_66,$fot(X_69)),bind(X_67,$fot(X_70))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(X_68,or(X_69,X_70)))
| theorem(or(X_69,implies(X_68,X_70))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_68,or(X_69,X_70)),or(X_69,implies(X_68,X_70)))) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
( ~ theorem(implies(X_51739,or(X_51739,X_51738)))
| theorem(or(X_51739,implies(X_51739,X_51738))) ),
inference(subst,[],[refute_0_25:[bind(X_68,$fot(X_51739)),bind(X_69,$fot(X_51739)),bind(X_70,$fot(X_51738))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(implies(not(not(not(not(X_13910)))),X_13910))
| ~ theorem(not(not(not(not(X_13910)))))
| theorem(X_13910) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_13910)),bind(Y,$fot(not(not(not(not(X_13910))))))]]) ).
cnf(refute_0_28,plain,
( ~ axiom(implies(or(X_5,X_6),or(X_6,X_5)))
| theorem(implies(or(X_5,X_6),or(X_6,X_5))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_29,plain,
axiom(implies(or(X_5,X_6),or(X_6,X_5))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_5)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_30,plain,
theorem(implies(or(X_5,X_6),or(X_6,X_5))),
inference(resolve,[$cnf( axiom(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ theorem(implies(or(X_5,X_6),or(X_6,X_5)))
| ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_6,X_5))),bind(Y,$fot(or(X_5,X_6)))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ theorem(or(X_13905,not(not(not(not(not(X_13905)))))))
| theorem(or(not(not(not(not(not(X_13905))))),X_13905)) ),
inference(subst,[],[refute_0_32:[bind(X_5,$fot(X_13905)),bind(X_6,$fot(not(not(not(not(not(X_13905)))))))]]) ).
cnf(refute_0_34,plain,
( ~ theorem(implies(or(X_1163,X_1162),or(X_1163,not(not(X_1162)))))
| ~ theorem(or(X_1163,X_1162))
| theorem(or(X_1163,not(not(X_1162)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_1163,not(not(X_1162))))),bind(Y,$fot(or(X_1163,X_1162)))]]) ).
cnf(refute_0_35,plain,
theorem(implies(or(not(X_11),X_6),or(X_6,not(X_11)))),
inference(subst,[],[refute_0_30:[bind(X_5,$fot(not(X_11)))]]) ).
cnf(refute_0_36,plain,
implies(X_11,X_6) = or(not(X_11),X_6),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_37,plain,
( implies(X_11,X_6) != or(not(X_11),X_6)
| or(not(X_11),X_6) = implies(X_11,X_6) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X_11,X_6))),bind(Y0,$fot(or(not(X_11),X_6)))]]) ).
cnf(refute_0_38,plain,
or(not(X_11),X_6) = implies(X_11,X_6),
inference(resolve,[$cnf( $equal(implies(X_11,X_6),or(not(X_11),X_6)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( or(not(X_11),X_6) != implies(X_11,X_6)
| ~ theorem(implies(or(not(X_11),X_6),or(X_6,not(X_11))))
| theorem(implies(implies(X_11,X_6),or(X_6,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_6),or(X_6,not(X_11)))) ),[0,0],$fot(implies(X_11,X_6))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(or(not(X_11),X_6),or(X_6,not(X_11))))
| theorem(implies(implies(X_11,X_6),or(X_6,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_6),implies(X_11,X_6)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X_11,X_6),or(X_6,not(X_11)))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_6),or(X_6,not(X_11)))) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))),
inference(subst,[],[refute_0_41:[bind(X_11,$fot(X_21)),bind(X_6,$fot(not(X)))]]) ).
cnf(refute_0_43,plain,
implies(X,not(X_21)) = or(not(X),not(X_21)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_21)))]]) ).
cnf(refute_0_44,plain,
( implies(X,not(X_21)) != or(not(X),not(X_21))
| or(not(X),not(X_21)) = implies(X,not(X_21)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,not(X_21)))),bind(Y0,$fot(or(not(X),not(X_21))))]]) ).
cnf(refute_0_45,plain,
or(not(X),not(X_21)) = implies(X,not(X_21)),
inference(resolve,[$cnf( $equal(implies(X,not(X_21)),or(not(X),not(X_21))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( or(not(X),not(X_21)) != implies(X,not(X_21))
| ~ theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21))))
| theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))) ),[0,1],$fot(implies(X,not(X_21)))]]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21))))
| theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_21)),implies(X,not(X_21))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))),
inference(resolve,[$cnf( theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ theorem(implies(X_21,not(X)))
| ~ theorem(implies(implies(X_21,not(X)),implies(X,not(X_21))))
| theorem(implies(X,not(X_21))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,not(X_21)))),bind(Y,$fot(implies(X_21,not(X))))]]) ).
cnf(refute_0_50,plain,
( ~ theorem(implies(X_21,not(X)))
| theorem(implies(X,not(X_21))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ theorem(implies(not(X),not(X)))
| theorem(implies(X,not(not(X)))) ),
inference(subst,[],[refute_0_50:[bind(X_21,$fot(not(X)))]]) ).
cnf(refute_0_52,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_53,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_52]) ).
cnf(refute_0_54,plain,
theorem(implies(or(X_61,X_61),X_61)),
inference(subst,[],[refute_0_53:[bind(A,$fot(X_61))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(implies(or(X_61,X_61),X_61))
| ~ theorem(or(X_61,X_61))
| theorem(X_61) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_61)),bind(Y,$fot(or(X_61,X_61)))]]) ).
cnf(refute_0_56,plain,
( ~ theorem(or(X_61,X_61))
| theorem(X_61) ),
inference(resolve,[$cnf( theorem(implies(or(X_61,X_61),X_61)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ theorem(or(implies(X_480,X_480),implies(X_480,X_480)))
| theorem(implies(X_480,X_480)) ),
inference(subst,[],[refute_0_56:[bind(X_61,$fot(implies(X_480,X_480)))]]) ).
cnf(refute_0_58,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_59,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_60,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
theorem(implies(X_478,or(X_477,X_478))),
inference(subst,[],[refute_0_60:[bind(X_3,$fot(X_478)),bind(X_4,$fot(X_477))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(implies(X_478,or(X_477,X_478)))
| theorem(or(X_477,implies(X_478,X_478))) ),
inference(subst,[],[refute_0_25:[bind(X_68,$fot(X_478)),bind(X_69,$fot(X_477)),bind(X_70,$fot(X_478))]]) ).
cnf(refute_0_63,plain,
theorem(or(X_477,implies(X_478,X_478))),
inference(resolve,[$cnf( theorem(implies(X_478,or(X_477,X_478))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
theorem(or(implies(X_480,X_480),implies(X_480,X_480))),
inference(subst,[],[refute_0_63:[bind(X_477,$fot(implies(X_480,X_480))),bind(X_478,$fot(X_480))]]) ).
cnf(refute_0_65,plain,
theorem(implies(X_480,X_480)),
inference(resolve,[$cnf( theorem(or(implies(X_480,X_480),implies(X_480,X_480))) )],[refute_0_64,refute_0_57]) ).
cnf(refute_0_66,plain,
theorem(implies(not(X),not(X))),
inference(subst,[],[refute_0_65:[bind(X_480,$fot(not(X)))]]) ).
cnf(refute_0_67,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(implies(not(X),not(X))) )],[refute_0_66,refute_0_51]) ).
cnf(refute_0_68,plain,
theorem(implies(X_1157,not(not(X_1157)))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_1157))]]) ).
cnf(refute_0_69,plain,
( ~ axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29))))
| theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))))]]) ).
cnf(refute_0_70,plain,
axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_28)),bind(B,$fot(X_29)),bind(C,$fot(X_30))]]) ).
cnf(refute_0_71,plain,
theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),
inference(resolve,[$cnf( axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) )],[refute_0_70,refute_0_69]) ).
cnf(refute_0_72,plain,
( ~ theorem(implies(X_28,X_29))
| ~ theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29))))
| theorem(implies(or(X_30,X_28),or(X_30,X_29))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_30,X_28),or(X_30,X_29)))),bind(Y,$fot(implies(X_28,X_29)))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(implies(X_28,X_29))
| theorem(implies(or(X_30,X_28),or(X_30,X_29))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ theorem(implies(X_1157,not(not(X_1157))))
| theorem(implies(or(X_1159,X_1157),or(X_1159,not(not(X_1157))))) ),
inference(subst,[],[refute_0_73:[bind(X_28,$fot(X_1157)),bind(X_29,$fot(not(not(X_1157)))),bind(X_30,$fot(X_1159))]]) ).
cnf(refute_0_75,plain,
theorem(implies(or(X_1159,X_1157),or(X_1159,not(not(X_1157))))),
inference(resolve,[$cnf( theorem(implies(X_1157,not(not(X_1157)))) )],[refute_0_68,refute_0_74]) ).
cnf(refute_0_76,plain,
theorem(implies(or(X_1163,X_1162),or(X_1163,not(not(X_1162))))),
inference(subst,[],[refute_0_75:[bind(X_1157,$fot(X_1162)),bind(X_1159,$fot(X_1163))]]) ).
cnf(refute_0_77,plain,
( ~ theorem(or(X_1163,X_1162))
| theorem(or(X_1163,not(not(X_1162)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_1163,X_1162),or(X_1163,not(not(X_1162))))) )],[refute_0_76,refute_0_34]) ).
cnf(refute_0_78,plain,
( ~ theorem(or(X_13898,not(not(not(X_13898)))))
| theorem(or(X_13898,not(not(not(not(not(X_13898))))))) ),
inference(subst,[],[refute_0_77:[bind(X_1162,$fot(not(not(not(X_13898))))),bind(X_1163,$fot(X_13898))]]) ).
cnf(refute_0_79,plain,
( ~ theorem(implies(X_11,X_6))
| ~ theorem(implies(implies(X_11,X_6),or(X_6,not(X_11))))
| theorem(or(X_6,not(X_11))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_6,not(X_11)))),bind(Y,$fot(implies(X_11,X_6)))]]) ).
cnf(refute_0_80,plain,
( ~ theorem(implies(X_11,X_6))
| theorem(or(X_6,not(X_11))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_11,X_6),or(X_6,not(X_11)))) )],[refute_0_41,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ theorem(implies(X_481,X_481))
| theorem(or(X_481,not(X_481))) ),
inference(subst,[],[refute_0_80:[bind(X_11,$fot(X_481)),bind(X_6,$fot(X_481))]]) ).
cnf(refute_0_82,plain,
theorem(implies(X_481,X_481)),
inference(subst,[],[refute_0_65:[bind(X_480,$fot(X_481))]]) ).
cnf(refute_0_83,plain,
theorem(or(X_481,not(X_481))),
inference(resolve,[$cnf( theorem(implies(X_481,X_481)) )],[refute_0_82,refute_0_81]) ).
cnf(refute_0_84,plain,
theorem(or(X_13897,not(X_13897))),
inference(subst,[],[refute_0_83:[bind(X_481,$fot(X_13897))]]) ).
cnf(refute_0_85,plain,
( ~ theorem(or(X_13897,not(X_13897)))
| theorem(or(X_13897,not(not(not(X_13897))))) ),
inference(subst,[],[refute_0_77:[bind(X_1162,$fot(not(X_13897))),bind(X_1163,$fot(X_13897))]]) ).
cnf(refute_0_86,plain,
theorem(or(X_13897,not(not(not(X_13897))))),
inference(resolve,[$cnf( theorem(or(X_13897,not(X_13897))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(or(X_13898,not(not(not(X_13898))))),
inference(subst,[],[refute_0_86:[bind(X_13897,$fot(X_13898))]]) ).
cnf(refute_0_88,plain,
theorem(or(X_13898,not(not(not(not(not(X_13898))))))),
inference(resolve,[$cnf( theorem(or(X_13898,not(not(not(X_13898))))) )],[refute_0_87,refute_0_78]) ).
cnf(refute_0_89,plain,
theorem(or(X_13905,not(not(not(not(not(X_13905))))))),
inference(subst,[],[refute_0_88:[bind(X_13898,$fot(X_13905))]]) ).
cnf(refute_0_90,plain,
theorem(or(not(not(not(not(not(X_13905))))),X_13905)),
inference(resolve,[$cnf( theorem(or(X_13905,not(not(not(not(not(X_13905))))))) )],[refute_0_89,refute_0_33]) ).
cnf(refute_0_91,plain,
or(not(not(not(not(not(X_13905))))),X_13905) = implies(not(not(not(not(X_13905)))),X_13905),
inference(subst,[],[refute_0_15:[bind(X,$fot(not(not(not(not(X_13905)))))),bind(Y,$fot(X_13905))]]) ).
cnf(refute_0_92,plain,
( or(not(not(not(not(not(X_13905))))),X_13905) != implies(not(not(not(not(X_13905)))),X_13905)
| ~ theorem(or(not(not(not(not(not(X_13905))))),X_13905))
| theorem(implies(not(not(not(not(X_13905)))),X_13905)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(not(not(not(X_13905))))),X_13905)) ),[0],$fot(implies(not(not(not(not(X_13905)))),X_13905))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(or(not(not(not(not(not(X_13905))))),X_13905))
| theorem(implies(not(not(not(not(X_13905)))),X_13905)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X_13905))))),X_13905),implies(not(not(not(not(X_13905)))),X_13905)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
theorem(implies(not(not(not(not(X_13905)))),X_13905)),
inference(resolve,[$cnf( theorem(or(not(not(not(not(not(X_13905))))),X_13905)) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(implies(not(not(not(not(X_13910)))),X_13910)),
inference(subst,[],[refute_0_94:[bind(X_13905,$fot(X_13910))]]) ).
cnf(refute_0_96,plain,
( ~ theorem(not(not(not(not(X_13910)))))
| theorem(X_13910) ),
inference(resolve,[$cnf( theorem(implies(not(not(not(not(X_13910)))),X_13910)) )],[refute_0_95,refute_0_27]) ).
cnf(refute_0_97,plain,
( ~ theorem(not(not(not(not(implies(X_51733,or(X_51733,X_51732)))))))
| theorem(implies(X_51733,or(X_51733,X_51732))) ),
inference(subst,[],[refute_0_96:[bind(X_13910,$fot(implies(X_51733,or(X_51733,X_51732))))]]) ).
cnf(refute_0_98,plain,
( ~ theorem(implies(implies(not(X_11277),X_11277),not(not(not(not(X_11277))))))
| ~ theorem(implies(not(X_11277),X_11277))
| theorem(not(not(not(not(X_11277))))) ),
inference(subst,[],[rule_2:[bind(X,$fot(not(not(not(not(X_11277)))))),bind(Y,$fot(implies(not(X_11277),X_11277)))]]) ).
cnf(refute_0_99,plain,
( ~ theorem(or(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))))
| theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))) ),
inference(subst,[],[refute_0_56:[bind(X_61,$fot(implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))))]]) ).
cnf(refute_0_100,plain,
( ~ theorem(implies(X_10711,or(implies(or(X_10710,X_10709),not(not(X_10709))),X_10710)))
| theorem(or(implies(or(X_10710,X_10709),not(not(X_10709))),implies(X_10711,X_10710))) ),
inference(subst,[],[refute_0_25:[bind(X_68,$fot(X_10711)),bind(X_69,$fot(implies(or(X_10710,X_10709),not(not(X_10709))))),bind(X_70,$fot(X_10710))]]) ).
cnf(refute_0_101,plain,
( ~ theorem(implies(or(X_1163,X_1162),or(X_1163,not(not(X_1162)))))
| theorem(or(X_1163,implies(or(X_1163,X_1162),not(not(X_1162))))) ),
inference(subst,[],[refute_0_25:[bind(X_68,$fot(or(X_1163,X_1162))),bind(X_69,$fot(X_1163)),bind(X_70,$fot(not(not(X_1162))))]]) ).
cnf(refute_0_102,plain,
theorem(or(X_1163,implies(or(X_1163,X_1162),not(not(X_1162))))),
inference(resolve,[$cnf( theorem(implies(or(X_1163,X_1162),or(X_1163,not(not(X_1162))))) )],[refute_0_76,refute_0_101]) ).
cnf(refute_0_103,plain,
theorem(or(X_9541,implies(or(X_9541,X_1162),not(not(X_1162))))),
inference(subst,[],[refute_0_102:[bind(X_1163,$fot(X_9541))]]) ).
cnf(refute_0_104,plain,
( ~ theorem(implies(or(X_967,X_968),implies(X_969,or(X_968,X_967))))
| ~ theorem(or(X_967,X_968))
| theorem(implies(X_969,or(X_968,X_967))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_969,or(X_968,X_967)))),bind(Y,$fot(or(X_967,X_968)))]]) ).
cnf(refute_0_105,plain,
theorem(implies(X_62,or(X_4,X_62))),
inference(subst,[],[refute_0_60:[bind(X_3,$fot(X_62))]]) ).
cnf(refute_0_106,plain,
( ~ theorem(X_62)
| ~ theorem(implies(X_62,or(X_4,X_62)))
| theorem(or(X_4,X_62)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_62))),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_107,plain,
( ~ theorem(X_62)
| theorem(or(X_4,X_62)) ),
inference(resolve,[$cnf( theorem(implies(X_62,or(X_4,X_62))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ theorem(implies(or(X_5,X_6),or(X_6,X_5)))
| theorem(or(X_73,implies(or(X_5,X_6),or(X_6,X_5)))) ),
inference(subst,[],[refute_0_107:[bind(X_4,$fot(X_73)),bind(X_62,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_109,plain,
theorem(or(X_73,implies(or(X_5,X_6),or(X_6,X_5)))),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_30,refute_0_108]) ).
cnf(refute_0_110,plain,
theorem(or(X_93,implies(or(X_5,X_6),or(X_6,X_5)))),
inference(subst,[],[refute_0_109:[bind(X_73,$fot(X_93))]]) ).
cnf(refute_0_111,plain,
( ~ theorem(or(X_93,implies(or(X_5,X_6),or(X_6,X_5))))
| theorem(or(implies(or(X_5,X_6),or(X_6,X_5)),X_93)) ),
inference(subst,[],[refute_0_32:[bind(X_5,$fot(X_93)),bind(X_6,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_112,plain,
theorem(or(implies(or(X_5,X_6),or(X_6,X_5)),X_93)),
inference(resolve,[$cnf( theorem(or(X_93,implies(or(X_5,X_6),or(X_6,X_5)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
theorem(or(implies(or(X_5,X_6),or(X_6,X_5)),not(X_139))),
inference(subst,[],[refute_0_112:[bind(X_93,$fot(not(X_139)))]]) ).
cnf(refute_0_114,plain,
theorem(implies(or(X_5,not(X_11)),or(not(X_11),X_5))),
inference(subst,[],[refute_0_30:[bind(X_6,$fot(not(X_11)))]]) ).
cnf(refute_0_115,plain,
implies(X_11,X_5) = or(not(X_11),X_5),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_116,plain,
( implies(X_11,X_5) != or(not(X_11),X_5)
| or(not(X_11),X_5) = implies(X_11,X_5) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X_11,X_5))),bind(Y0,$fot(or(not(X_11),X_5)))]]) ).
cnf(refute_0_117,plain,
or(not(X_11),X_5) = implies(X_11,X_5),
inference(resolve,[$cnf( $equal(implies(X_11,X_5),or(not(X_11),X_5)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( or(not(X_11),X_5) != implies(X_11,X_5)
| ~ theorem(implies(or(X_5,not(X_11)),or(not(X_11),X_5)))
| theorem(implies(or(X_5,not(X_11)),implies(X_11,X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_5,not(X_11)),or(not(X_11),X_5))) ),[0,1],$fot(implies(X_11,X_5))]]) ).
cnf(refute_0_119,plain,
( ~ theorem(implies(or(X_5,not(X_11)),or(not(X_11),X_5)))
| theorem(implies(or(X_5,not(X_11)),implies(X_11,X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_5),implies(X_11,X_5)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
theorem(implies(or(X_5,not(X_11)),implies(X_11,X_5))),
inference(resolve,[$cnf( theorem(implies(or(X_5,not(X_11)),or(not(X_11),X_5))) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ theorem(implies(or(X_5,not(X_11)),implies(X_11,X_5)))
| ~ theorem(or(X_5,not(X_11)))
| theorem(implies(X_11,X_5)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_11,X_5))),bind(Y,$fot(or(X_5,not(X_11))))]]) ).
cnf(refute_0_122,plain,
( ~ theorem(or(X_5,not(X_11)))
| theorem(implies(X_11,X_5)) ),
inference(resolve,[$cnf( theorem(implies(or(X_5,not(X_11)),implies(X_11,X_5))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( ~ theorem(or(implies(or(X_5,X_6),or(X_6,X_5)),not(X_139)))
| theorem(implies(X_139,implies(or(X_5,X_6),or(X_6,X_5)))) ),
inference(subst,[],[refute_0_122:[bind(X_11,$fot(X_139)),bind(X_5,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_124,plain,
theorem(implies(X_139,implies(or(X_5,X_6),or(X_6,X_5)))),
inference(resolve,[$cnf( theorem(or(implies(or(X_5,X_6),or(X_6,X_5)),not(X_139))) )],[refute_0_113,refute_0_123]) ).
cnf(refute_0_125,plain,
theorem(implies(X_928,implies(or(X_5,X_6),or(X_6,X_5)))),
inference(subst,[],[refute_0_124:[bind(X_139,$fot(X_928))]]) ).
cnf(refute_0_126,plain,
( ~ axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49))))
| theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))))]]) ).
cnf(refute_0_127,plain,
axiom(implies(or(X_25,or(not(X),X_27)),or(not(X),or(X_25,X_27)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_25)),bind(B,$fot(not(X))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_128,plain,
implies(X,or(X_25,X_27)) = or(not(X),or(X_25,X_27)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_25,X_27)))]]) ).
cnf(refute_0_129,plain,
( implies(X,or(X_25,X_27)) != or(not(X),or(X_25,X_27))
| or(not(X),or(X_25,X_27)) = implies(X,or(X_25,X_27)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,or(X_25,X_27)))),bind(Y0,$fot(or(not(X),or(X_25,X_27))))]]) ).
cnf(refute_0_130,plain,
or(not(X),or(X_25,X_27)) = implies(X,or(X_25,X_27)),
inference(resolve,[$cnf( $equal(implies(X,or(X_25,X_27)),or(not(X),or(X_25,X_27))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( or(not(X),or(X_25,X_27)) != implies(X,or(X_25,X_27))
| ~ axiom(implies(or(X_25,or(not(X),X_27)),or(not(X),or(X_25,X_27))))
| axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_25,or(not(X),X_27)),or(not(X),or(X_25,X_27)))) ),[0,1],$fot(implies(X,or(X_25,X_27)))]]) ).
cnf(refute_0_132,plain,
( ~ axiom(implies(or(X_25,or(not(X),X_27)),or(not(X),or(X_25,X_27))))
| axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_25,X_27)),implies(X,or(X_25,X_27))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(X_25,or(not(X),X_27)),or(not(X),or(X_25,X_27)))) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
or(not(X),X_27) = implies(X,X_27),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_27))]]) ).
cnf(refute_0_135,plain,
or(X_25,or(not(X),X_27)) = or(X_25,or(not(X),X_27)),
introduced(tautology,[refl,[$fot(or(X_25,or(not(X),X_27)))]]) ).
cnf(refute_0_136,plain,
( or(X_25,or(not(X),X_27)) != or(X_25,or(not(X),X_27))
| or(not(X),X_27) != implies(X,X_27)
| or(X_25,or(not(X),X_27)) = or(X_25,implies(X,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_25,or(not(X),X_27)),or(X_25,or(not(X),X_27))) ),[1,1],$fot(implies(X,X_27))]]) ).
cnf(refute_0_137,plain,
( or(not(X),X_27) != implies(X,X_27)
| or(X_25,or(not(X),X_27)) = or(X_25,implies(X,X_27)) ),
inference(resolve,[$cnf( $equal(or(X_25,or(not(X),X_27)),or(X_25,or(not(X),X_27))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
or(X_25,or(not(X),X_27)) = or(X_25,implies(X,X_27)),
inference(resolve,[$cnf( $equal(or(not(X),X_27),implies(X,X_27)) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) = implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))),
introduced(tautology,[refl,[$fot(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))))]]) ).
cnf(refute_0_140,plain,
( implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) != implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))
| or(X_25,or(not(X),X_27)) != or(X_25,implies(X,X_27))
| implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) = implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))),implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) ),[1,0],$fot(or(X_25,implies(X,X_27)))]]) ).
cnf(refute_0_141,plain,
( or(X_25,or(not(X),X_27)) != or(X_25,implies(X,X_27))
| implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) = implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27))) ),
inference(resolve,[$cnf( $equal(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))),implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) = implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27))),
inference(resolve,[$cnf( $equal(or(X_25,or(not(X),X_27)),or(X_25,implies(X,X_27))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))) != implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27)))
| ~ axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))))
| axiom(implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) ),[0],$fot(implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27))))]]) ).
cnf(refute_0_144,plain,
( ~ axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))))
| axiom(implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27))),implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
axiom(implies(or(X_25,implies(X,X_27)),implies(X,or(X_25,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(X_25,or(not(X),X_27)),implies(X,or(X_25,X_27)))) )],[refute_0_133,refute_0_144]) ).
cnf(refute_0_146,plain,
axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(subst,[],[refute_0_145:[bind(X,$fot(X_47)),bind(X_25,$fot(X_48)),bind(X_27,$fot(X_49))]]) ).
cnf(refute_0_147,plain,
theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(resolve,[$cnf( axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) )],[refute_0_146,refute_0_126]) ).
cnf(refute_0_148,plain,
theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,or(not(X),X_52)))),
inference(subst,[],[refute_0_147:[bind(X_47,$fot(X_50)),bind(X_48,$fot(not(X))),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_149,plain,
implies(X,X_52) = or(not(X),X_52),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_52))]]) ).
cnf(refute_0_150,plain,
( implies(X,X_52) != or(not(X),X_52)
| or(not(X),X_52) = implies(X,X_52) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_52))),bind(Y0,$fot(or(not(X),X_52)))]]) ).
cnf(refute_0_151,plain,
or(not(X),X_52) = implies(X,X_52),
inference(resolve,[$cnf( $equal(implies(X,X_52),or(not(X),X_52)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( or(not(X),X_52) != implies(X,X_52)
| ~ theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,or(not(X),X_52))))
| theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,or(not(X),X_52)))) ),[0,1,1],$fot(implies(X,X_52))]]) ).
cnf(refute_0_153,plain,
( ~ theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,or(not(X),X_52))))
| theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_52),implies(X,X_52)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,or(not(X),X_52)))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
or(not(X),implies(X_50,X_52)) = implies(X,implies(X_50,X_52)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(implies(X_50,X_52)))]]) ).
cnf(refute_0_156,plain,
implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) = implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))))]]) ).
cnf(refute_0_157,plain,
( implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) != implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))
| or(not(X),implies(X_50,X_52)) != implies(X,implies(X_50,X_52))
| implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) = implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))),implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),[1,0],$fot(implies(X,implies(X_50,X_52)))]]) ).
cnf(refute_0_158,plain,
( or(not(X),implies(X_50,X_52)) != implies(X,implies(X_50,X_52))
| implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) = implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))),implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) = implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_50,X_52)),implies(X,implies(X_50,X_52))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))) != implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))
| ~ theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))))
| theorem(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),[0],$fot(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52))))]]) ).
cnf(refute_0_161,plain,
( ~ theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))))
| theorem(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52))),implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
theorem(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) )],[refute_0_154,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ theorem(implies(X,implies(X_50,X_52)))
| ~ theorem(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52))))
| theorem(implies(X_50,implies(X,X_52))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_50,implies(X,X_52)))),bind(Y,$fot(implies(X,implies(X_50,X_52))))]]) ).
cnf(refute_0_164,plain,
( ~ theorem(implies(X,implies(X_50,X_52)))
| theorem(implies(X_50,implies(X,X_52))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_50,X_52)),implies(X_50,implies(X,X_52)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( ~ theorem(implies(X_928,implies(or(X_5,X_6),or(X_6,X_5))))
| theorem(implies(or(X_5,X_6),implies(X_928,or(X_6,X_5)))) ),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_928)),bind(X_50,$fot(or(X_5,X_6))),bind(X_52,$fot(or(X_6,X_5)))]]) ).
cnf(refute_0_166,plain,
theorem(implies(or(X_5,X_6),implies(X_928,or(X_6,X_5)))),
inference(resolve,[$cnf( theorem(implies(X_928,implies(or(X_5,X_6),or(X_6,X_5)))) )],[refute_0_125,refute_0_165]) ).
cnf(refute_0_167,plain,
theorem(implies(or(X_967,X_968),implies(X_969,or(X_968,X_967)))),
inference(subst,[],[refute_0_166:[bind(X_5,$fot(X_967)),bind(X_6,$fot(X_968)),bind(X_928,$fot(X_969))]]) ).
cnf(refute_0_168,plain,
( ~ theorem(or(X_967,X_968))
| theorem(implies(X_969,or(X_968,X_967))) ),
inference(resolve,[$cnf( theorem(implies(or(X_967,X_968),implies(X_969,or(X_968,X_967)))) )],[refute_0_167,refute_0_104]) ).
cnf(refute_0_169,plain,
( ~ theorem(or(X_9541,implies(or(X_9541,X_1162),not(not(X_1162)))))
| theorem(implies(X_9543,or(implies(or(X_9541,X_1162),not(not(X_1162))),X_9541))) ),
inference(subst,[],[refute_0_168:[bind(X_967,$fot(X_9541)),bind(X_968,$fot(implies(or(X_9541,X_1162),not(not(X_1162))))),bind(X_969,$fot(X_9543))]]) ).
cnf(refute_0_170,plain,
theorem(implies(X_9543,or(implies(or(X_9541,X_1162),not(not(X_1162))),X_9541))),
inference(resolve,[$cnf( theorem(or(X_9541,implies(or(X_9541,X_1162),not(not(X_1162))))) )],[refute_0_103,refute_0_169]) ).
cnf(refute_0_171,plain,
theorem(implies(X_10711,or(implies(or(X_10710,X_10709),not(not(X_10709))),X_10710))),
inference(subst,[],[refute_0_170:[bind(X_1162,$fot(X_10709)),bind(X_9541,$fot(X_10710)),bind(X_9543,$fot(X_10711))]]) ).
cnf(refute_0_172,plain,
theorem(or(implies(or(X_10710,X_10709),not(not(X_10709))),implies(X_10711,X_10710))),
inference(resolve,[$cnf( theorem(implies(X_10711,or(implies(or(X_10710,X_10709),not(not(X_10709))),X_10710))) )],[refute_0_171,refute_0_100]) ).
cnf(refute_0_173,plain,
theorem(or(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(or(not(not(X_10712)),X_10712),not(not(X_10712))))),
inference(subst,[],[refute_0_172:[bind(X_10709,$fot(X_10712)),bind(X_10710,$fot(not(not(X_10712)))),bind(X_10711,$fot(or(not(not(X_10712)),X_10712)))]]) ).
cnf(refute_0_174,plain,
theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))),
inference(resolve,[$cnf( theorem(or(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(or(not(not(X_10712)),X_10712),not(not(X_10712))))) )],[refute_0_173,refute_0_99]) ).
cnf(refute_0_175,plain,
or(not(not(X_10712)),X_10712) = implies(not(X_10712),X_10712),
inference(subst,[],[refute_0_15:[bind(X,$fot(not(X_10712))),bind(Y,$fot(X_10712))]]) ).
cnf(refute_0_176,plain,
implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) = implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),
introduced(tautology,[refl,[$fot(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))))]]) ).
cnf(refute_0_177,plain,
( implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) != implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))
| or(not(not(X_10712)),X_10712) != implies(not(X_10712),X_10712)
| implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) = implies(implies(not(X_10712),X_10712),not(not(X_10712))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))) ),[1,0],$fot(implies(not(X_10712),X_10712))]]) ).
cnf(refute_0_178,plain,
( or(not(not(X_10712)),X_10712) != implies(not(X_10712),X_10712)
| implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) = implies(implies(not(X_10712),X_10712),not(not(X_10712))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) = implies(implies(not(X_10712),X_10712),not(not(X_10712))),
inference(resolve,[$cnf( $equal(or(not(not(X_10712)),X_10712),implies(not(X_10712),X_10712)) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
( implies(or(not(not(X_10712)),X_10712),not(not(X_10712))) != implies(implies(not(X_10712),X_10712),not(not(X_10712)))
| ~ theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))))
| theorem(implies(implies(not(X_10712),X_10712),not(not(X_10712)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))) ),[0],$fot(implies(implies(not(X_10712),X_10712),not(not(X_10712))))]]) ).
cnf(refute_0_181,plain,
( ~ theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))))
| theorem(implies(implies(not(X_10712),X_10712),not(not(X_10712)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_10712)),X_10712),not(not(X_10712))),implies(implies(not(X_10712),X_10712),not(not(X_10712)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
theorem(implies(implies(not(X_10712),X_10712),not(not(X_10712)))),
inference(resolve,[$cnf( theorem(implies(or(not(not(X_10712)),X_10712),not(not(X_10712)))) )],[refute_0_174,refute_0_181]) ).
cnf(refute_0_183,plain,
( ~ theorem(implies(X_1068,X_1069))
| ~ theorem(implies(implies(X_1068,X_1069),implies(X_1068,not(not(X_1069)))))
| theorem(implies(X_1068,not(not(X_1069)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1068,not(not(X_1069))))),bind(Y,$fot(implies(X_1068,X_1069)))]]) ).
cnf(refute_0_184,plain,
theorem(implies(X_1066,not(not(X_1066)))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_1066))]]) ).
cnf(refute_0_185,plain,
( ~ axiom(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33))))
| theorem(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))))]]) ).
cnf(refute_0_186,plain,
axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),or(not(X),X_29)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_28)),bind(B,$fot(X_29)),bind(C,$fot(not(X)))]]) ).
cnf(refute_0_187,plain,
implies(X,X_29) = or(not(X),X_29),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_188,plain,
( implies(X,X_29) != or(not(X),X_29)
| or(not(X),X_29) = implies(X,X_29) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_29))),bind(Y0,$fot(or(not(X),X_29)))]]) ).
cnf(refute_0_189,plain,
or(not(X),X_29) = implies(X,X_29),
inference(resolve,[$cnf( $equal(implies(X,X_29),or(not(X),X_29)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
( or(not(X),X_29) != implies(X,X_29)
| ~ axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),or(not(X),X_29))))
| axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),or(not(X),X_29)))) ),[0,1,1],$fot(implies(X,X_29))]]) ).
cnf(refute_0_191,plain,
( ~ axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),or(not(X),X_29))))
| axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),or(not(X),X_29)))) )],[refute_0_186,refute_0_191]) ).
cnf(refute_0_193,plain,
or(not(X),X_28) = implies(X,X_28),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_28))]]) ).
cnf(refute_0_194,plain,
implies(or(not(X),X_28),implies(X,X_29)) = implies(or(not(X),X_28),implies(X,X_29)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_28),implies(X,X_29)))]]) ).
cnf(refute_0_195,plain,
( implies(or(not(X),X_28),implies(X,X_29)) != implies(or(not(X),X_28),implies(X,X_29))
| or(not(X),X_28) != implies(X,X_28)
| implies(or(not(X),X_28),implies(X,X_29)) = implies(implies(X,X_28),implies(X,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_28),implies(X,X_29)),implies(or(not(X),X_28),implies(X,X_29))) ),[1,0],$fot(implies(X,X_28))]]) ).
cnf(refute_0_196,plain,
( or(not(X),X_28) != implies(X,X_28)
| implies(or(not(X),X_28),implies(X,X_29)) = implies(implies(X,X_28),implies(X,X_29)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_28),implies(X,X_29)),implies(or(not(X),X_28),implies(X,X_29))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(or(not(X),X_28),implies(X,X_29)) = implies(implies(X,X_28),implies(X,X_29)),
inference(resolve,[$cnf( $equal(or(not(X),X_28),implies(X,X_28)) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) = implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))),
introduced(tautology,[refl,[$fot(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))))]]) ).
cnf(refute_0_199,plain,
( implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) != implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))
| implies(or(not(X),X_28),implies(X,X_29)) != implies(implies(X,X_28),implies(X,X_29))
| implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) = implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))),implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) ),[1,1],$fot(implies(implies(X,X_28),implies(X,X_29)))]]) ).
cnf(refute_0_200,plain,
( implies(or(not(X),X_28),implies(X,X_29)) != implies(implies(X,X_28),implies(X,X_29))
| implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) = implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))),implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) = implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_28),implies(X,X_29)),implies(implies(X,X_28),implies(X,X_29))) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
( implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))) != implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29)))
| ~ axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))))
| axiom(implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) ),[0],$fot(implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29))))]]) ).
cnf(refute_0_203,plain,
( ~ axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))))
| axiom(implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29))),implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
axiom(implies(implies(X_28,X_29),implies(implies(X,X_28),implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(implies(X_28,X_29),implies(or(not(X),X_28),implies(X,X_29)))) )],[refute_0_192,refute_0_203]) ).
cnf(refute_0_205,plain,
axiom(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))),
inference(subst,[],[refute_0_204:[bind(X,$fot(X_31)),bind(X_28,$fot(X_32)),bind(X_29,$fot(X_33))]]) ).
cnf(refute_0_206,plain,
theorem(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))) )],[refute_0_205,refute_0_185]) ).
cnf(refute_0_207,plain,
( ~ theorem(implies(X_32,X_33))
| ~ theorem(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33))))
| theorem(implies(implies(X_31,X_32),implies(X_31,X_33))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X_31,X_32),implies(X_31,X_33)))),bind(Y,$fot(implies(X_32,X_33)))]]) ).
cnf(refute_0_208,plain,
( ~ theorem(implies(X_32,X_33))
| theorem(implies(implies(X_31,X_32),implies(X_31,X_33))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_32,X_33),implies(implies(X_31,X_32),implies(X_31,X_33)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
( ~ theorem(implies(X_1066,not(not(X_1066))))
| theorem(implies(implies(X_1065,X_1066),implies(X_1065,not(not(X_1066))))) ),
inference(subst,[],[refute_0_208:[bind(X_31,$fot(X_1065)),bind(X_32,$fot(X_1066)),bind(X_33,$fot(not(not(X_1066))))]]) ).
cnf(refute_0_210,plain,
theorem(implies(implies(X_1065,X_1066),implies(X_1065,not(not(X_1066))))),
inference(resolve,[$cnf( theorem(implies(X_1066,not(not(X_1066)))) )],[refute_0_184,refute_0_209]) ).
cnf(refute_0_211,plain,
theorem(implies(implies(X_1068,X_1069),implies(X_1068,not(not(X_1069))))),
inference(subst,[],[refute_0_210:[bind(X_1065,$fot(X_1068)),bind(X_1066,$fot(X_1069))]]) ).
cnf(refute_0_212,plain,
( ~ theorem(implies(X_1068,X_1069))
| theorem(implies(X_1068,not(not(X_1069)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_1068,X_1069),implies(X_1068,not(not(X_1069))))) )],[refute_0_211,refute_0_183]) ).
cnf(refute_0_213,plain,
( ~ theorem(implies(implies(not(X_10712),X_10712),not(not(X_10712))))
| theorem(implies(implies(not(X_10712),X_10712),not(not(not(not(X_10712)))))) ),
inference(subst,[],[refute_0_212:[bind(X_1068,$fot(implies(not(X_10712),X_10712))),bind(X_1069,$fot(not(not(X_10712))))]]) ).
cnf(refute_0_214,plain,
theorem(implies(implies(not(X_10712),X_10712),not(not(not(not(X_10712)))))),
inference(resolve,[$cnf( theorem(implies(implies(not(X_10712),X_10712),not(not(X_10712)))) )],[refute_0_182,refute_0_213]) ).
cnf(refute_0_215,plain,
theorem(implies(implies(not(X_11277),X_11277),not(not(not(not(X_11277)))))),
inference(subst,[],[refute_0_214:[bind(X_10712,$fot(X_11277))]]) ).
cnf(refute_0_216,plain,
( ~ theorem(implies(not(X_11277),X_11277))
| theorem(not(not(not(not(X_11277))))) ),
inference(resolve,[$cnf( theorem(implies(implies(not(X_11277),X_11277),not(not(not(not(X_11277)))))) )],[refute_0_215,refute_0_98]) ).
cnf(refute_0_217,plain,
( ~ theorem(implies(not(implies(X_51730,or(X_51730,X_51729))),implies(X_51730,or(X_51730,X_51729))))
| theorem(not(not(not(not(implies(X_51730,or(X_51730,X_51729))))))) ),
inference(subst,[],[refute_0_216:[bind(X_11277,$fot(implies(X_51730,or(X_51730,X_51729))))]]) ).
cnf(refute_0_218,plain,
( ~ theorem(implies(X_51717,implies(X_51718,or(X_51717,X_51716))))
| theorem(implies(X_51718,implies(X_51717,or(X_51717,X_51716)))) ),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_51717)),bind(X_50,$fot(X_51718)),bind(X_52,$fot(or(X_51717,X_51716)))]]) ).
cnf(refute_0_219,plain,
theorem(implies(X_51698,or(X_51697,X_51698))),
inference(subst,[],[refute_0_60:[bind(X_3,$fot(X_51698)),bind(X_4,$fot(X_51697))]]) ).
cnf(refute_0_220,plain,
( ~ theorem(implies(X_8678,or(X_8679,X_8680)))
| ~ theorem(implies(implies(X_8678,or(X_8679,X_8680)),implies(X_8678,implies(X_8681,or(X_8680,X_8679)))))
| theorem(implies(X_8678,implies(X_8681,or(X_8680,X_8679)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_8678,implies(X_8681,or(X_8680,X_8679))))),bind(Y,$fot(implies(X_8678,or(X_8679,X_8680))))]]) ).
cnf(refute_0_221,plain,
( ~ theorem(implies(or(X_5,X_6),implies(X_928,or(X_6,X_5))))
| theorem(implies(implies(X_1065,or(X_5,X_6)),implies(X_1065,implies(X_928,or(X_6,X_5))))) ),
inference(subst,[],[refute_0_208:[bind(X_31,$fot(X_1065)),bind(X_32,$fot(or(X_5,X_6))),bind(X_33,$fot(implies(X_928,or(X_6,X_5))))]]) ).
cnf(refute_0_222,plain,
theorem(implies(implies(X_1065,or(X_5,X_6)),implies(X_1065,implies(X_928,or(X_6,X_5))))),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),implies(X_928,or(X_6,X_5)))) )],[refute_0_166,refute_0_221]) ).
cnf(refute_0_223,plain,
theorem(implies(implies(X_8678,or(X_8679,X_8680)),implies(X_8678,implies(X_8681,or(X_8680,X_8679))))),
inference(subst,[],[refute_0_222:[bind(X_1065,$fot(X_8678)),bind(X_5,$fot(X_8679)),bind(X_6,$fot(X_8680)),bind(X_928,$fot(X_8681))]]) ).
cnf(refute_0_224,plain,
( ~ theorem(implies(X_8678,or(X_8679,X_8680)))
| theorem(implies(X_8678,implies(X_8681,or(X_8680,X_8679)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_8678,or(X_8679,X_8680)),implies(X_8678,implies(X_8681,or(X_8680,X_8679))))) )],[refute_0_223,refute_0_220]) ).
cnf(refute_0_225,plain,
( ~ theorem(implies(X_51698,or(X_51697,X_51698)))
| theorem(implies(X_51698,implies(X_51699,or(X_51698,X_51697)))) ),
inference(subst,[],[refute_0_224:[bind(X_8678,$fot(X_51698)),bind(X_8679,$fot(X_51697)),bind(X_8680,$fot(X_51698)),bind(X_8681,$fot(X_51699))]]) ).
cnf(refute_0_226,plain,
theorem(implies(X_51698,implies(X_51699,or(X_51698,X_51697)))),
inference(resolve,[$cnf( theorem(implies(X_51698,or(X_51697,X_51698))) )],[refute_0_219,refute_0_225]) ).
cnf(refute_0_227,plain,
theorem(implies(X_51717,implies(X_51718,or(X_51717,X_51716)))),
inference(subst,[],[refute_0_226:[bind(X_51697,$fot(X_51716)),bind(X_51698,$fot(X_51717)),bind(X_51699,$fot(X_51718))]]) ).
cnf(refute_0_228,plain,
theorem(implies(X_51718,implies(X_51717,or(X_51717,X_51716)))),
inference(resolve,[$cnf( theorem(implies(X_51717,implies(X_51718,or(X_51717,X_51716)))) )],[refute_0_227,refute_0_218]) ).
cnf(refute_0_229,plain,
theorem(implies(not(implies(X_51730,or(X_51730,X_51729))),implies(X_51730,or(X_51730,X_51729)))),
inference(subst,[],[refute_0_228:[bind(X_51716,$fot(X_51729)),bind(X_51717,$fot(X_51730)),bind(X_51718,$fot(not(implies(X_51730,or(X_51730,X_51729)))))]]) ).
cnf(refute_0_230,plain,
theorem(not(not(not(not(implies(X_51730,or(X_51730,X_51729))))))),
inference(resolve,[$cnf( theorem(implies(not(implies(X_51730,or(X_51730,X_51729))),implies(X_51730,or(X_51730,X_51729)))) )],[refute_0_229,refute_0_217]) ).
cnf(refute_0_231,plain,
theorem(not(not(not(not(implies(X_51733,or(X_51733,X_51732))))))),
inference(subst,[],[refute_0_230:[bind(X_51729,$fot(X_51732)),bind(X_51730,$fot(X_51733))]]) ).
cnf(refute_0_232,plain,
theorem(implies(X_51733,or(X_51733,X_51732))),
inference(resolve,[$cnf( theorem(not(not(not(not(implies(X_51733,or(X_51733,X_51732))))))) )],[refute_0_231,refute_0_97]) ).
cnf(refute_0_233,plain,
theorem(implies(X_51739,or(X_51739,X_51738))),
inference(subst,[],[refute_0_232:[bind(X_51732,$fot(X_51738)),bind(X_51733,$fot(X_51739))]]) ).
cnf(refute_0_234,plain,
theorem(or(X_51739,implies(X_51739,X_51738))),
inference(resolve,[$cnf( theorem(implies(X_51739,or(X_51739,X_51738))) )],[refute_0_233,refute_0_26]) ).
cnf(refute_0_235,plain,
theorem(or(not(X),implies(not(X),X_51740))),
inference(subst,[],[refute_0_234:[bind(X_51738,$fot(X_51740)),bind(X_51739,$fot(not(X)))]]) ).
cnf(refute_0_236,plain,
implies(X,implies(not(X),X_51740)) = or(not(X),implies(not(X),X_51740)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(not(X),X_51740)))]]) ).
cnf(refute_0_237,plain,
( implies(X,implies(not(X),X_51740)) != or(not(X),implies(not(X),X_51740))
| or(not(X),implies(not(X),X_51740)) = implies(X,implies(not(X),X_51740)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,implies(not(X),X_51740)))),bind(Y0,$fot(or(not(X),implies(not(X),X_51740))))]]) ).
cnf(refute_0_238,plain,
or(not(X),implies(not(X),X_51740)) = implies(X,implies(not(X),X_51740)),
inference(resolve,[$cnf( $equal(implies(X,implies(not(X),X_51740)),or(not(X),implies(not(X),X_51740))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( or(not(X),implies(not(X),X_51740)) != implies(X,implies(not(X),X_51740))
| ~ theorem(or(not(X),implies(not(X),X_51740)))
| theorem(implies(X,implies(not(X),X_51740))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(not(X),X_51740))) ),[0],$fot(implies(X,implies(not(X),X_51740)))]]) ).
cnf(refute_0_240,plain,
( ~ theorem(or(not(X),implies(not(X),X_51740)))
| theorem(implies(X,implies(not(X),X_51740))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(not(X),X_51740)),implies(X,implies(not(X),X_51740))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
theorem(implies(X,implies(not(X),X_51740))),
inference(resolve,[$cnf( theorem(or(not(X),implies(not(X),X_51740))) )],[refute_0_235,refute_0_240]) ).
cnf(refute_0_242,plain,
theorem(implies(p,implies(not(p),q))),
inference(subst,[],[refute_0_241:[bind(X,$fot(p)),bind(X_51740,$fot(q))]]) ).
cnf(refute_0_243,plain,
$false,
inference(resolve,[$cnf( theorem(implies(p,implies(not(p),q))) )],[refute_0_242,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL187-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 10:50:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 96.77/96.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 96.77/96.99
% 96.77/96.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.85/97.02
%------------------------------------------------------------------------------