TSTP Solution File: LCL323-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL323-3 : 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 12:51:33 EDT 2022
% Result : Unsatisfiable 147.64s 147.84s
% Output : CNFRefutation 147.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 41
% Syntax : Number of clauses : 243 ( 129 unt; 0 nHn; 103 RR)
% Number of literals : 397 ( 118 equ; 155 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 566 ( 44 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(or(implies(p,q),implies(q,r))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_56,or(X_57,X_58)))
| ~ theorem(implies(implies(X_56,or(X_57,X_58)),or(X_57,implies(X_56,X_58))))
| theorem(or(X_57,implies(X_56,X_58))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_57,implies(X_56,X_58)))),bind(Y,$fot(implies(X_56,or(X_57,X_58))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55))))
| theorem(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55)))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,or(not(X),X_23)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_22)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_3,plain,
implies(X,X_23) = or(not(X),X_23),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X,X_23) != or(not(X),X_23)
| or(not(X),X_23) = implies(X,X_23) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_23))),bind(Y0,$fot(or(not(X),X_23)))]]) ).
cnf(refute_0_8,plain,
or(not(X),X_23) = implies(X,X_23),
inference(resolve,[$cnf( $equal(implies(X,X_23),or(not(X),X_23)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X),X_23) != implies(X,X_23)
| ~ axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,or(not(X),X_23))))
| axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,or(not(X),X_23)))) ),[0,1,1],$fot(implies(X,X_23))]]) ).
cnf(refute_0_10,plain,
( ~ axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,or(not(X),X_23))))
| axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_23),implies(X,X_23)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,or(not(X),X_23)))) )],[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( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_12]) ).
cnf(refute_0_14,plain,
or(not(X),or(X_22,X_23)) = implies(X,or(X_22,X_23)),
inference(subst,[],[refute_0_13:[bind(Y,$fot(or(X_22,X_23)))]]) ).
cnf(refute_0_15,plain,
implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) = implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))))]]) ).
cnf(refute_0_16,plain,
( implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) != implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))
| or(not(X),or(X_22,X_23)) != implies(X,or(X_22,X_23))
| implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) = implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))),implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),[1,0],$fot(implies(X,or(X_22,X_23)))]]) ).
cnf(refute_0_17,plain,
( or(not(X),or(X_22,X_23)) != implies(X,or(X_22,X_23))
| implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) = implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))),implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) = implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_22,X_23)),implies(X,or(X_22,X_23))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))) != implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23)))
| ~ axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))))
| axiom(implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),[0],$fot(implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23))))]]) ).
cnf(refute_0_20,plain,
( ~ axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))))
| axiom(implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23))),implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
axiom(implies(implies(X,or(X_22,X_23)),or(X_22,implies(X,X_23)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_22,X_23)),or(X_22,implies(X,X_23)))) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
axiom(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55)))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_53)),bind(X_22,$fot(X_54)),bind(X_23,$fot(X_55))]]) ).
cnf(refute_0_23,plain,
theorem(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55)))),
inference(resolve,[$cnf( axiom(implies(implies(X_53,or(X_54,X_55)),or(X_54,implies(X_53,X_55)))) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
theorem(implies(implies(X_56,or(X_57,X_58)),or(X_57,implies(X_56,X_58)))),
inference(subst,[],[refute_0_23:[bind(X_53,$fot(X_56)),bind(X_54,$fot(X_57)),bind(X_55,$fot(X_58))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(X_56,or(X_57,X_58)))
| theorem(or(X_57,implies(X_56,X_58))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_56,or(X_57,X_58)),or(X_57,implies(X_56,X_58)))) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
( ~ theorem(implies(X_79981,or(implies(X_79979,X_79981),X_79980)))
| theorem(or(implies(X_79979,X_79981),implies(X_79981,X_79980))) ),
inference(subst,[],[refute_0_25:[bind(X_56,$fot(X_79981)),bind(X_57,$fot(implies(X_79979,X_79981))),bind(X_58,$fot(X_79980))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(implies(not(not(X_8514)),X_8514))
| ~ theorem(not(not(X_8514)))
| theorem(X_8514) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_8514)),bind(Y,$fot(not(not(X_8514))))]]) ).
cnf(refute_0_28,plain,
( ~ axiom(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(or(X_15,X_16),or(X_16,X_15))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_15,X_16),or(X_16,X_15))))]]) ).
cnf(refute_0_29,plain,
axiom(implies(or(X_15,X_16),or(X_16,X_15))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_15)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_30,plain,
theorem(implies(or(X_15,X_16),or(X_16,X_15))),
inference(resolve,[$cnf( axiom(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_16,X_15))),bind(Y,$fot(or(X_15,X_16)))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ theorem(or(X_8513,not(not(not(X_8513)))))
| theorem(or(not(not(not(X_8513))),X_8513)) ),
inference(subst,[],[refute_0_32:[bind(X_15,$fot(X_8513)),bind(X_16,$fot(not(not(not(X_8513)))))]]) ).
cnf(refute_0_34,plain,
theorem(implies(or(not(X),X_18),or(X_18,not(X)))),
inference(subst,[],[refute_0_30:[bind(X_15,$fot(not(X))),bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_35,plain,
implies(X,X_18) = or(not(X),X_18),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_18))]]) ).
cnf(refute_0_36,plain,
( implies(X,X_18) != or(not(X),X_18)
| or(not(X),X_18) = implies(X,X_18) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_18))),bind(Y0,$fot(or(not(X),X_18)))]]) ).
cnf(refute_0_37,plain,
or(not(X),X_18) = implies(X,X_18),
inference(resolve,[$cnf( $equal(implies(X,X_18),or(not(X),X_18)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( or(not(X),X_18) != implies(X,X_18)
| ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) ),[0,0],$fot(implies(X,X_18))]]) ).
cnf(refute_0_39,plain,
( ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_18),implies(X,X_18)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
theorem(implies(implies(X,X_18),or(X_18,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ theorem(implies(X,X_18))
| ~ theorem(implies(implies(X,X_18),or(X_18,not(X))))
| theorem(or(X_18,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X)))),bind(Y,$fot(implies(X,X_18)))]]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X,X_18))
| theorem(or(X_18,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_18),or(X_18,not(X)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X_296,X_296))
| theorem(or(X_296,not(X_296))) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_296)),bind(X_18,$fot(X_296))]]) ).
cnf(refute_0_44,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_45,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_44]) ).
cnf(refute_0_46,plain,
theorem(implies(or(X_49,X_49),X_49)),
inference(subst,[],[refute_0_45:[bind(A,$fot(X_49))]]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(or(X_49,X_49),X_49))
| ~ theorem(or(X_49,X_49))
| theorem(X_49) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_49)),bind(Y,$fot(or(X_49,X_49)))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(or(X_49,X_49))
| theorem(X_49) ),
inference(resolve,[$cnf( theorem(implies(or(X_49,X_49),X_49)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(implies(X_295,X_295),implies(X_295,X_295)))
| theorem(implies(X_295,X_295)) ),
inference(subst,[],[refute_0_48:[bind(X_49,$fot(implies(X_295,X_295)))]]) ).
cnf(refute_0_50,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,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_51,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_52,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
theorem(implies(X_293,or(X_292,X_293))),
inference(subst,[],[refute_0_52:[bind(X_3,$fot(X_293)),bind(X_4,$fot(X_292))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(X_293,or(X_292,X_293)))
| theorem(or(X_292,implies(X_293,X_293))) ),
inference(subst,[],[refute_0_25:[bind(X_56,$fot(X_293)),bind(X_57,$fot(X_292)),bind(X_58,$fot(X_293))]]) ).
cnf(refute_0_55,plain,
theorem(or(X_292,implies(X_293,X_293))),
inference(resolve,[$cnf( theorem(implies(X_293,or(X_292,X_293))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
theorem(or(implies(X_295,X_295),implies(X_295,X_295))),
inference(subst,[],[refute_0_55:[bind(X_292,$fot(implies(X_295,X_295))),bind(X_293,$fot(X_295))]]) ).
cnf(refute_0_57,plain,
theorem(implies(X_295,X_295)),
inference(resolve,[$cnf( theorem(or(implies(X_295,X_295),implies(X_295,X_295))) )],[refute_0_56,refute_0_49]) ).
cnf(refute_0_58,plain,
theorem(implies(X_296,X_296)),
inference(subst,[],[refute_0_57:[bind(X_295,$fot(X_296))]]) ).
cnf(refute_0_59,plain,
theorem(or(X_296,not(X_296))),
inference(resolve,[$cnf( theorem(implies(X_296,X_296)) )],[refute_0_58,refute_0_43]) ).
cnf(refute_0_60,plain,
theorem(or(X_8512,not(X_8512))),
inference(subst,[],[refute_0_59:[bind(X_296,$fot(X_8512))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(implies(or(X_2712,X_2711),or(X_2712,not(not(X_2711)))))
| ~ theorem(or(X_2712,X_2711))
| theorem(or(X_2712,not(not(X_2711)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_2712,not(not(X_2711))))),bind(Y,$fot(or(X_2712,X_2711)))]]) ).
cnf(refute_0_62,plain,
theorem(implies(implies(X_24,not(X)),or(not(X),not(X_24)))),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_24)),bind(X_18,$fot(not(X)))]]) ).
cnf(refute_0_63,plain,
implies(X,not(X_24)) = or(not(X),not(X_24)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_24)))]]) ).
cnf(refute_0_64,plain,
( implies(X,not(X_24)) != or(not(X),not(X_24))
| or(not(X),not(X_24)) = implies(X,not(X_24)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,not(X_24)))),bind(Y0,$fot(or(not(X),not(X_24))))]]) ).
cnf(refute_0_65,plain,
or(not(X),not(X_24)) = implies(X,not(X_24)),
inference(resolve,[$cnf( $equal(implies(X,not(X_24)),or(not(X),not(X_24))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( or(not(X),not(X_24)) != implies(X,not(X_24))
| ~ theorem(implies(implies(X_24,not(X)),or(not(X),not(X_24))))
| theorem(implies(implies(X_24,not(X)),implies(X,not(X_24)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_24,not(X)),or(not(X),not(X_24)))) ),[0,1],$fot(implies(X,not(X_24)))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(implies(implies(X_24,not(X)),or(not(X),not(X_24))))
| theorem(implies(implies(X_24,not(X)),implies(X,not(X_24)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_24)),implies(X,not(X_24))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(implies(X_24,not(X)),implies(X,not(X_24)))),
inference(resolve,[$cnf( theorem(implies(implies(X_24,not(X)),or(not(X),not(X_24)))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ theorem(implies(X_24,not(X)))
| ~ theorem(implies(implies(X_24,not(X)),implies(X,not(X_24))))
| theorem(implies(X,not(X_24))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,not(X_24)))),bind(Y,$fot(implies(X_24,not(X))))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(implies(X_24,not(X)))
| theorem(implies(X,not(X_24))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_24,not(X)),implies(X,not(X_24)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(not(X),not(X)))
| theorem(implies(X,not(not(X)))) ),
inference(subst,[],[refute_0_70:[bind(X_24,$fot(not(X)))]]) ).
cnf(refute_0_72,plain,
theorem(implies(not(X),not(X))),
inference(subst,[],[refute_0_57:[bind(X_295,$fot(not(X)))]]) ).
cnf(refute_0_73,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(implies(not(X),not(X))) )],[refute_0_72,refute_0_71]) ).
cnf(refute_0_74,plain,
theorem(implies(X_2700,not(not(X_2700)))),
inference(subst,[],[refute_0_73:[bind(X,$fot(X_2700))]]) ).
cnf(refute_0_75,plain,
( ~ axiom(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33))))
| theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))))]]) ).
cnf(refute_0_76,plain,
axiom(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_32)),bind(B,$fot(X_33)),bind(C,$fot(X_34))]]) ).
cnf(refute_0_77,plain,
theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),
inference(resolve,[$cnf( axiom(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
( ~ theorem(implies(X_32,X_33))
| ~ theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33))))
| theorem(implies(or(X_34,X_32),or(X_34,X_33))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_34,X_32),or(X_34,X_33)))),bind(Y,$fot(implies(X_32,X_33)))]]) ).
cnf(refute_0_79,plain,
( ~ theorem(implies(X_32,X_33))
| theorem(implies(or(X_34,X_32),or(X_34,X_33))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ theorem(implies(X_2700,not(not(X_2700))))
| theorem(implies(or(X_2702,X_2700),or(X_2702,not(not(X_2700))))) ),
inference(subst,[],[refute_0_79:[bind(X_32,$fot(X_2700)),bind(X_33,$fot(not(not(X_2700)))),bind(X_34,$fot(X_2702))]]) ).
cnf(refute_0_81,plain,
theorem(implies(or(X_2702,X_2700),or(X_2702,not(not(X_2700))))),
inference(resolve,[$cnf( theorem(implies(X_2700,not(not(X_2700)))) )],[refute_0_74,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(implies(or(X_2712,X_2711),or(X_2712,not(not(X_2711))))),
inference(subst,[],[refute_0_81:[bind(X_2700,$fot(X_2711)),bind(X_2702,$fot(X_2712))]]) ).
cnf(refute_0_83,plain,
( ~ theorem(or(X_2712,X_2711))
| theorem(or(X_2712,not(not(X_2711)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_2712,X_2711),or(X_2712,not(not(X_2711))))) )],[refute_0_82,refute_0_61]) ).
cnf(refute_0_84,plain,
( ~ theorem(or(X_8512,not(X_8512)))
| theorem(or(X_8512,not(not(not(X_8512))))) ),
inference(subst,[],[refute_0_83:[bind(X_2711,$fot(not(X_8512))),bind(X_2712,$fot(X_8512))]]) ).
cnf(refute_0_85,plain,
theorem(or(X_8512,not(not(not(X_8512))))),
inference(resolve,[$cnf( theorem(or(X_8512,not(X_8512))) )],[refute_0_60,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(or(X_8513,not(not(not(X_8513))))),
inference(subst,[],[refute_0_85:[bind(X_8512,$fot(X_8513))]]) ).
cnf(refute_0_87,plain,
theorem(or(not(not(not(X_8513))),X_8513)),
inference(resolve,[$cnf( theorem(or(X_8513,not(not(not(X_8513))))) )],[refute_0_86,refute_0_33]) ).
cnf(refute_0_88,plain,
or(not(not(not(X_8513))),X_8513) = implies(not(not(X_8513)),X_8513),
inference(subst,[],[refute_0_13:[bind(X,$fot(not(not(X_8513)))),bind(Y,$fot(X_8513))]]) ).
cnf(refute_0_89,plain,
( or(not(not(not(X_8513))),X_8513) != implies(not(not(X_8513)),X_8513)
| ~ theorem(or(not(not(not(X_8513))),X_8513))
| theorem(implies(not(not(X_8513)),X_8513)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(not(X_8513))),X_8513)) ),[0],$fot(implies(not(not(X_8513)),X_8513))]]) ).
cnf(refute_0_90,plain,
( ~ theorem(or(not(not(not(X_8513))),X_8513))
| theorem(implies(not(not(X_8513)),X_8513)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X_8513))),X_8513),implies(not(not(X_8513)),X_8513)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
theorem(implies(not(not(X_8513)),X_8513)),
inference(resolve,[$cnf( theorem(or(not(not(not(X_8513))),X_8513)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(implies(not(not(X_8514)),X_8514)),
inference(subst,[],[refute_0_91:[bind(X_8513,$fot(X_8514))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(not(not(X_8514)))
| theorem(X_8514) ),
inference(resolve,[$cnf( theorem(implies(not(not(X_8514)),X_8514)) )],[refute_0_92,refute_0_27]) ).
cnf(refute_0_94,plain,
( ~ theorem(not(not(implies(X_79978,or(implies(X_79976,X_79978),X_79977)))))
| theorem(implies(X_79978,or(implies(X_79976,X_79978),X_79977))) ),
inference(subst,[],[refute_0_93:[bind(X_8514,$fot(implies(X_79978,or(implies(X_79976,X_79978),X_79977))))]]) ).
cnf(refute_0_95,plain,
( ~ theorem(implies(implies(not(X_25828),X_25828),not(not(X_25828))))
| ~ theorem(implies(not(X_25828),X_25828))
| theorem(not(not(X_25828))) ),
inference(subst,[],[rule_2:[bind(X,$fot(not(not(X_25828)))),bind(Y,$fot(implies(not(X_25828),X_25828)))]]) ).
cnf(refute_0_96,plain,
theorem(implies(or(not(not(X_2700)),X_2700),or(not(not(X_2700)),not(not(X_2700))))),
inference(subst,[],[refute_0_81:[bind(X_2702,$fot(not(not(X_2700))))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(implies(X_2490,or(X_2491,X_2491)))
| ~ theorem(implies(implies(X_2490,or(X_2491,X_2491)),implies(X_2490,X_2491)))
| theorem(implies(X_2490,X_2491)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_2490,X_2491))),bind(Y,$fot(implies(X_2490,or(X_2491,X_2491))))]]) ).
cnf(refute_0_98,plain,
theorem(implies(or(X_2484,X_2484),X_2484)),
inference(subst,[],[refute_0_45:[bind(A,$fot(X_2484))]]) ).
cnf(refute_0_99,plain,
theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))),
inference(subst,[],[refute_0_77:[bind(X_32,$fot(X_43)),bind(X_33,$fot(X_44)),bind(X_34,$fot(not(X)))]]) ).
cnf(refute_0_100,plain,
implies(X,X_44) = or(not(X),X_44),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_44))]]) ).
cnf(refute_0_101,plain,
( implies(X,X_44) != or(not(X),X_44)
| or(not(X),X_44) = implies(X,X_44) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_44))),bind(Y0,$fot(or(not(X),X_44)))]]) ).
cnf(refute_0_102,plain,
or(not(X),X_44) = implies(X,X_44),
inference(resolve,[$cnf( $equal(implies(X,X_44),or(not(X),X_44)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( or(not(X),X_44) != implies(X,X_44)
| ~ theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44))))
| theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))) ),[0,1,1],$fot(implies(X,X_44))]]) ).
cnf(refute_0_104,plain,
( ~ theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44))))
| theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_44),implies(X,X_44)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))),
inference(resolve,[$cnf( theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
or(not(X),X_43) = implies(X,X_43),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_107,plain,
implies(or(not(X),X_43),implies(X,X_44)) = implies(or(not(X),X_43),implies(X,X_44)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_43),implies(X,X_44)))]]) ).
cnf(refute_0_108,plain,
( implies(or(not(X),X_43),implies(X,X_44)) != implies(or(not(X),X_43),implies(X,X_44))
| or(not(X),X_43) != implies(X,X_43)
| implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(or(not(X),X_43),implies(X,X_44))) ),[1,0],$fot(implies(X,X_43))]]) ).
cnf(refute_0_109,plain,
( or(not(X),X_43) != implies(X,X_43)
| implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(or(not(X),X_43),implies(X,X_44))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)),
inference(resolve,[$cnf( $equal(or(not(X),X_43),implies(X,X_43)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),
introduced(tautology,[refl,[$fot(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))]]) ).
cnf(refute_0_112,plain,
( implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) != implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))
| implies(or(not(X),X_43),implies(X,X_44)) != implies(implies(X,X_43),implies(X,X_44))
| implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),[1,1],$fot(implies(implies(X,X_43),implies(X,X_44)))]]) ).
cnf(refute_0_113,plain,
( implies(or(not(X),X_43),implies(X,X_44)) != implies(implies(X,X_43),implies(X,X_44))
| implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(implies(X,X_43),implies(X,X_44))) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) != implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))
| ~ theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))
| theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),[0],$fot(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))))]]) ).
cnf(refute_0_116,plain,
( ~ theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))
| theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))),
inference(resolve,[$cnf( theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) )],[refute_0_105,refute_0_116]) ).
cnf(refute_0_118,plain,
( ~ theorem(implies(X_43,X_44))
| ~ theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))))
| theorem(implies(implies(X,X_43),implies(X,X_44))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X,X_43),implies(X,X_44)))),bind(Y,$fot(implies(X_43,X_44)))]]) ).
cnf(refute_0_119,plain,
( ~ theorem(implies(X_43,X_44))
| theorem(implies(implies(X,X_43),implies(X,X_44))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ theorem(implies(or(X_2484,X_2484),X_2484))
| theorem(implies(implies(X_2482,or(X_2484,X_2484)),implies(X_2482,X_2484))) ),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_2482)),bind(X_43,$fot(or(X_2484,X_2484))),bind(X_44,$fot(X_2484))]]) ).
cnf(refute_0_121,plain,
theorem(implies(implies(X_2482,or(X_2484,X_2484)),implies(X_2482,X_2484))),
inference(resolve,[$cnf( theorem(implies(or(X_2484,X_2484),X_2484)) )],[refute_0_98,refute_0_120]) ).
cnf(refute_0_122,plain,
theorem(implies(implies(X_2490,or(X_2491,X_2491)),implies(X_2490,X_2491))),
inference(subst,[],[refute_0_121:[bind(X_2482,$fot(X_2490)),bind(X_2484,$fot(X_2491))]]) ).
cnf(refute_0_123,plain,
( ~ theorem(implies(X_2490,or(X_2491,X_2491)))
| theorem(implies(X_2490,X_2491)) ),
inference(resolve,[$cnf( theorem(implies(implies(X_2490,or(X_2491,X_2491)),implies(X_2490,X_2491))) )],[refute_0_122,refute_0_97]) ).
cnf(refute_0_124,plain,
( ~ theorem(implies(or(not(not(X_2700)),X_2700),or(not(not(X_2700)),not(not(X_2700)))))
| theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))) ),
inference(subst,[],[refute_0_123:[bind(X_2490,$fot(or(not(not(X_2700)),X_2700))),bind(X_2491,$fot(not(not(X_2700))))]]) ).
cnf(refute_0_125,plain,
theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))),
inference(resolve,[$cnf( theorem(implies(or(not(not(X_2700)),X_2700),or(not(not(X_2700)),not(not(X_2700))))) )],[refute_0_96,refute_0_124]) ).
cnf(refute_0_126,plain,
or(not(not(X_2700)),X_2700) = implies(not(X_2700),X_2700),
inference(subst,[],[refute_0_13:[bind(X,$fot(not(X_2700))),bind(Y,$fot(X_2700))]]) ).
cnf(refute_0_127,plain,
implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) = implies(or(not(not(X_2700)),X_2700),not(not(X_2700))),
introduced(tautology,[refl,[$fot(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))))]]) ).
cnf(refute_0_128,plain,
( implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) != implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))
| or(not(not(X_2700)),X_2700) != implies(not(X_2700),X_2700)
| implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) = implies(implies(not(X_2700),X_2700),not(not(X_2700))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))),implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))) ),[1,0],$fot(implies(not(X_2700),X_2700))]]) ).
cnf(refute_0_129,plain,
( or(not(not(X_2700)),X_2700) != implies(not(X_2700),X_2700)
| implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) = implies(implies(not(X_2700),X_2700),not(not(X_2700))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))),implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) = implies(implies(not(X_2700),X_2700),not(not(X_2700))),
inference(resolve,[$cnf( $equal(or(not(not(X_2700)),X_2700),implies(not(X_2700),X_2700)) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
( implies(or(not(not(X_2700)),X_2700),not(not(X_2700))) != implies(implies(not(X_2700),X_2700),not(not(X_2700)))
| ~ theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))))
| theorem(implies(implies(not(X_2700),X_2700),not(not(X_2700)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))) ),[0],$fot(implies(implies(not(X_2700),X_2700),not(not(X_2700))))]]) ).
cnf(refute_0_132,plain,
( ~ theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))))
| theorem(implies(implies(not(X_2700),X_2700),not(not(X_2700)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_2700)),X_2700),not(not(X_2700))),implies(implies(not(X_2700),X_2700),not(not(X_2700)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
theorem(implies(implies(not(X_2700),X_2700),not(not(X_2700)))),
inference(resolve,[$cnf( theorem(implies(or(not(not(X_2700)),X_2700),not(not(X_2700)))) )],[refute_0_125,refute_0_132]) ).
cnf(refute_0_134,plain,
theorem(implies(implies(not(X_25828),X_25828),not(not(X_25828)))),
inference(subst,[],[refute_0_133:[bind(X_2700,$fot(X_25828))]]) ).
cnf(refute_0_135,plain,
( ~ theorem(implies(not(X_25828),X_25828))
| theorem(not(not(X_25828))) ),
inference(resolve,[$cnf( theorem(implies(implies(not(X_25828),X_25828),not(not(X_25828)))) )],[refute_0_134,refute_0_95]) ).
cnf(refute_0_136,plain,
( ~ theorem(implies(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641))),implies(X_79642,or(implies(X_79640,X_79642),X_79641))))
| theorem(not(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641))))) ),
inference(subst,[],[refute_0_135:[bind(X_25828,$fot(implies(X_79642,or(implies(X_79640,X_79642),X_79641))))]]) ).
cnf(refute_0_137,plain,
theorem(implies(X_50,or(X_4,X_50))),
inference(subst,[],[refute_0_52:[bind(X_3,$fot(X_50))]]) ).
cnf(refute_0_138,plain,
( ~ theorem(X_50)
| ~ theorem(implies(X_50,or(X_4,X_50)))
| theorem(or(X_4,X_50)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_50))),bind(Y,$fot(X_50))]]) ).
cnf(refute_0_139,plain,
( ~ theorem(X_50)
| theorem(or(X_4,X_50)) ),
inference(resolve,[$cnf( theorem(implies(X_50,or(X_4,X_50))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ theorem(implies(X_3,or(X_4,X_3)))
| theorem(or(X_68,implies(X_3,or(X_4,X_3)))) ),
inference(subst,[],[refute_0_139:[bind(X_4,$fot(X_68)),bind(X_50,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_141,plain,
theorem(or(X_68,implies(X_3,or(X_4,X_3)))),
inference(resolve,[$cnf( theorem(implies(X_3,or(X_4,X_3))) )],[refute_0_52,refute_0_140]) ).
cnf(refute_0_142,plain,
theorem(or(X_3270,implies(X_3269,or(X_4,X_3269)))),
inference(subst,[],[refute_0_141:[bind(X_3,$fot(X_3269)),bind(X_68,$fot(X_3270))]]) ).
cnf(refute_0_143,plain,
( ~ theorem(implies(or(X_75,implies(X_74,X_76)),implies(X_74,or(X_75,X_76))))
| ~ theorem(or(X_75,implies(X_74,X_76)))
| theorem(implies(X_74,or(X_75,X_76))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_74,or(X_75,X_76)))),bind(Y,$fot(or(X_75,implies(X_74,X_76))))]]) ).
cnf(refute_0_144,plain,
( ~ axiom(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23))))
| theorem(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23)))))]]) ).
cnf(refute_0_145,plain,
axiom(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_21)),bind(B,$fot(X_22)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_146,plain,
theorem(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23)))),
inference(resolve,[$cnf( axiom(implies(or(X_21,or(X_22,X_23)),or(X_22,or(X_21,X_23)))) )],[refute_0_145,refute_0_144]) ).
cnf(refute_0_147,plain,
theorem(implies(or(X_40,or(not(X),X_42)),or(not(X),or(X_40,X_42)))),
inference(subst,[],[refute_0_146:[bind(X_21,$fot(X_40)),bind(X_22,$fot(not(X))),bind(X_23,$fot(X_42))]]) ).
cnf(refute_0_148,plain,
implies(X,or(X_40,X_42)) = or(not(X),or(X_40,X_42)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_40,X_42)))]]) ).
cnf(refute_0_149,plain,
( implies(X,or(X_40,X_42)) != or(not(X),or(X_40,X_42))
| or(not(X),or(X_40,X_42)) = implies(X,or(X_40,X_42)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,or(X_40,X_42)))),bind(Y0,$fot(or(not(X),or(X_40,X_42))))]]) ).
cnf(refute_0_150,plain,
or(not(X),or(X_40,X_42)) = implies(X,or(X_40,X_42)),
inference(resolve,[$cnf( $equal(implies(X,or(X_40,X_42)),or(not(X),or(X_40,X_42))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( or(not(X),or(X_40,X_42)) != implies(X,or(X_40,X_42))
| ~ theorem(implies(or(X_40,or(not(X),X_42)),or(not(X),or(X_40,X_42))))
| theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_40,or(not(X),X_42)),or(not(X),or(X_40,X_42)))) ),[0,1],$fot(implies(X,or(X_40,X_42)))]]) ).
cnf(refute_0_152,plain,
( ~ theorem(implies(or(X_40,or(not(X),X_42)),or(not(X),or(X_40,X_42))))
| theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_40,X_42)),implies(X,or(X_40,X_42))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))),
inference(resolve,[$cnf( theorem(implies(or(X_40,or(not(X),X_42)),or(not(X),or(X_40,X_42)))) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
or(not(X),X_42) = implies(X,X_42),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_155,plain,
or(X_40,or(not(X),X_42)) = or(X_40,or(not(X),X_42)),
introduced(tautology,[refl,[$fot(or(X_40,or(not(X),X_42)))]]) ).
cnf(refute_0_156,plain,
( or(X_40,or(not(X),X_42)) != or(X_40,or(not(X),X_42))
| or(not(X),X_42) != implies(X,X_42)
| or(X_40,or(not(X),X_42)) = or(X_40,implies(X,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_40,or(not(X),X_42)),or(X_40,or(not(X),X_42))) ),[1,1],$fot(implies(X,X_42))]]) ).
cnf(refute_0_157,plain,
( or(not(X),X_42) != implies(X,X_42)
| or(X_40,or(not(X),X_42)) = or(X_40,implies(X,X_42)) ),
inference(resolve,[$cnf( $equal(or(X_40,or(not(X),X_42)),or(X_40,or(not(X),X_42))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
or(X_40,or(not(X),X_42)) = or(X_40,implies(X,X_42)),
inference(resolve,[$cnf( $equal(or(not(X),X_42),implies(X,X_42)) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) = implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))),
introduced(tautology,[refl,[$fot(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))))]]) ).
cnf(refute_0_160,plain,
( implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) != implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))
| or(X_40,or(not(X),X_42)) != or(X_40,implies(X,X_42))
| implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) = implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))),implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) ),[1,0],$fot(or(X_40,implies(X,X_42)))]]) ).
cnf(refute_0_161,plain,
( or(X_40,or(not(X),X_42)) != or(X_40,implies(X,X_42))
| implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) = implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42))) ),
inference(resolve,[$cnf( $equal(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))),implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) = implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42))),
inference(resolve,[$cnf( $equal(or(X_40,or(not(X),X_42)),or(X_40,implies(X,X_42))) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
( implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))) != implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42)))
| ~ theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))))
| theorem(implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) ),[0],$fot(implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42))))]]) ).
cnf(refute_0_164,plain,
( ~ theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))))
| theorem(implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42))),implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
theorem(implies(or(X_40,implies(X,X_42)),implies(X,or(X_40,X_42)))),
inference(resolve,[$cnf( theorem(implies(or(X_40,or(not(X),X_42)),implies(X,or(X_40,X_42)))) )],[refute_0_153,refute_0_164]) ).
cnf(refute_0_166,plain,
theorem(implies(or(X_75,implies(X_74,X_76)),implies(X_74,or(X_75,X_76)))),
inference(subst,[],[refute_0_165:[bind(X,$fot(X_74)),bind(X_40,$fot(X_75)),bind(X_42,$fot(X_76))]]) ).
cnf(refute_0_167,plain,
( ~ theorem(or(X_75,implies(X_74,X_76)))
| theorem(implies(X_74,or(X_75,X_76))) ),
inference(resolve,[$cnf( theorem(implies(or(X_75,implies(X_74,X_76)),implies(X_74,or(X_75,X_76)))) )],[refute_0_166,refute_0_143]) ).
cnf(refute_0_168,plain,
( ~ theorem(or(X_3270,implies(X_3269,or(X_4,X_3269))))
| theorem(implies(X_3269,or(X_3270,or(X_4,X_3269)))) ),
inference(subst,[],[refute_0_167:[bind(X_74,$fot(X_3269)),bind(X_75,$fot(X_3270)),bind(X_76,$fot(or(X_4,X_3269)))]]) ).
cnf(refute_0_169,plain,
theorem(implies(X_3269,or(X_3270,or(X_4,X_3269)))),
inference(resolve,[$cnf( theorem(or(X_3270,implies(X_3269,or(X_4,X_3269)))) )],[refute_0_142,refute_0_168]) ).
cnf(refute_0_170,plain,
theorem(implies(X_3272,or(X_3273,or(not(X),X_3272)))),
inference(subst,[],[refute_0_169:[bind(X_3269,$fot(X_3272)),bind(X_3270,$fot(X_3273)),bind(X_4,$fot(not(X)))]]) ).
cnf(refute_0_171,plain,
implies(X,X_3272) = or(not(X),X_3272),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_3272))]]) ).
cnf(refute_0_172,plain,
( implies(X,X_3272) != or(not(X),X_3272)
| or(not(X),X_3272) = implies(X,X_3272) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_3272))),bind(Y0,$fot(or(not(X),X_3272)))]]) ).
cnf(refute_0_173,plain,
or(not(X),X_3272) = implies(X,X_3272),
inference(resolve,[$cnf( $equal(implies(X,X_3272),or(not(X),X_3272)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
( or(not(X),X_3272) != implies(X,X_3272)
| ~ theorem(implies(X_3272,or(X_3273,or(not(X),X_3272))))
| theorem(implies(X_3272,or(X_3273,implies(X,X_3272)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3272,or(X_3273,or(not(X),X_3272)))) ),[0,1,1],$fot(implies(X,X_3272))]]) ).
cnf(refute_0_175,plain,
( ~ theorem(implies(X_3272,or(X_3273,or(not(X),X_3272))))
| theorem(implies(X_3272,or(X_3273,implies(X,X_3272)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_3272),implies(X,X_3272)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
theorem(implies(X_3272,or(X_3273,implies(X,X_3272)))),
inference(resolve,[$cnf( theorem(implies(X_3272,or(X_3273,or(not(X),X_3272)))) )],[refute_0_170,refute_0_175]) ).
cnf(refute_0_177,plain,
theorem(implies(X_79621,or(X_79619,implies(X,X_79621)))),
inference(subst,[],[refute_0_176:[bind(X_3272,$fot(X_79621)),bind(X_3273,$fot(X_79619))]]) ).
cnf(refute_0_178,plain,
( ~ theorem(implies(X_4981,or(X_4979,X_4980)))
| ~ theorem(implies(implies(X_4981,or(X_4979,X_4980)),implies(X_4982,implies(X_4981,or(X_4980,X_4979)))))
| theorem(implies(X_4982,implies(X_4981,or(X_4980,X_4979)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_4982,implies(X_4981,or(X_4980,X_4979))))),bind(Y,$fot(implies(X_4981,or(X_4979,X_4980))))]]) ).
cnf(refute_0_179,plain,
theorem(implies(X_3,or(not(X_7),X_3))),
inference(subst,[],[refute_0_52:[bind(X_4,$fot(not(X_7)))]]) ).
cnf(refute_0_180,plain,
implies(X_7,X_3) = or(not(X_7),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_181,plain,
( implies(X_7,X_3) != or(not(X_7),X_3)
| or(not(X_7),X_3) = implies(X_7,X_3) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X_7,X_3))),bind(Y0,$fot(or(not(X_7),X_3)))]]) ).
cnf(refute_0_182,plain,
or(not(X_7),X_3) = implies(X_7,X_3),
inference(resolve,[$cnf( $equal(implies(X_7,X_3),or(not(X_7),X_3)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
( or(not(X_7),X_3) != implies(X_7,X_3)
| ~ theorem(implies(X_3,or(not(X_7),X_3)))
| theorem(implies(X_3,implies(X_7,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) ),[0,1],$fot(implies(X_7,X_3))]]) ).
cnf(refute_0_184,plain,
( ~ theorem(implies(X_3,or(not(X_7),X_3)))
| theorem(implies(X_3,implies(X_7,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),X_3),implies(X_7,X_3)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
theorem(implies(X_3,implies(X_7,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) )],[refute_0_179,refute_0_184]) ).
cnf(refute_0_186,plain,
theorem(implies(X_50,implies(X_7,X_50))),
inference(subst,[],[refute_0_185:[bind(X_3,$fot(X_50))]]) ).
cnf(refute_0_187,plain,
( ~ theorem(X_50)
| ~ theorem(implies(X_50,implies(X_7,X_50)))
| theorem(implies(X_7,X_50)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_7,X_50))),bind(Y,$fot(X_50))]]) ).
cnf(refute_0_188,plain,
( ~ theorem(X_50)
| theorem(implies(X_7,X_50)) ),
inference(resolve,[$cnf( theorem(implies(X_50,implies(X_7,X_50))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( ~ theorem(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535))))
| theorem(implies(X_7,implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535))))) ),
inference(subst,[],[refute_0_188:[bind(X_50,$fot(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535)))))]]) ).
cnf(refute_0_190,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(implies(X_2482,or(X_15,X_16)),implies(X_2482,or(X_16,X_15)))) ),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_2482)),bind(X_43,$fot(or(X_15,X_16))),bind(X_44,$fot(or(X_16,X_15)))]]) ).
cnf(refute_0_191,plain,
theorem(implies(implies(X_2482,or(X_15,X_16)),implies(X_2482,or(X_16,X_15)))),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_30,refute_0_190]) ).
cnf(refute_0_192,plain,
theorem(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535)))),
inference(subst,[],[refute_0_191:[bind(X_15,$fot(X_2535)),bind(X_16,$fot(X_2536)),bind(X_2482,$fot(X_2537))]]) ).
cnf(refute_0_193,plain,
theorem(implies(X_7,implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535))))),
inference(resolve,[$cnf( theorem(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535)))) )],[refute_0_192,refute_0_189]) ).
cnf(refute_0_194,plain,
theorem(implies(X_4919,implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535))))),
inference(subst,[],[refute_0_193:[bind(X_7,$fot(X_4919))]]) ).
cnf(refute_0_195,plain,
( ~ theorem(implies(X_81,implies(X_80,X_82)))
| ~ theorem(implies(implies(X_81,implies(X_80,X_82)),implies(X_80,implies(X_81,X_82))))
| theorem(implies(X_80,implies(X_81,X_82))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_80,implies(X_81,X_82)))),bind(Y,$fot(implies(X_81,implies(X_80,X_82))))]]) ).
cnf(refute_0_196,plain,
( ~ axiom(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79))))
| theorem(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79)))))]]) ).
cnf(refute_0_197,plain,
axiom(implies(implies(X_53,or(not(X),X_55)),or(not(X),implies(X_53,X_55)))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_53)),bind(X_22,$fot(not(X))),bind(X_23,$fot(X_55))]]) ).
cnf(refute_0_198,plain,
implies(X,implies(X_53,X_55)) = or(not(X),implies(X_53,X_55)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_53,X_55)))]]) ).
cnf(refute_0_199,plain,
( implies(X,implies(X_53,X_55)) != or(not(X),implies(X_53,X_55))
| or(not(X),implies(X_53,X_55)) = implies(X,implies(X_53,X_55)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,implies(X_53,X_55)))),bind(Y0,$fot(or(not(X),implies(X_53,X_55))))]]) ).
cnf(refute_0_200,plain,
or(not(X),implies(X_53,X_55)) = implies(X,implies(X_53,X_55)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_53,X_55)),or(not(X),implies(X_53,X_55))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( or(not(X),implies(X_53,X_55)) != implies(X,implies(X_53,X_55))
| ~ axiom(implies(implies(X_53,or(not(X),X_55)),or(not(X),implies(X_53,X_55))))
| axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_53,or(not(X),X_55)),or(not(X),implies(X_53,X_55)))) ),[0,1],$fot(implies(X,implies(X_53,X_55)))]]) ).
cnf(refute_0_202,plain,
( ~ axiom(implies(implies(X_53,or(not(X),X_55)),or(not(X),implies(X_53,X_55))))
| axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_53,X_55)),implies(X,implies(X_53,X_55))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))),
inference(resolve,[$cnf( axiom(implies(implies(X_53,or(not(X),X_55)),or(not(X),implies(X_53,X_55)))) )],[refute_0_197,refute_0_202]) ).
cnf(refute_0_204,plain,
or(not(X),X_55) = implies(X,X_55),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_55))]]) ).
cnf(refute_0_205,plain,
implies(X_53,or(not(X),X_55)) = implies(X_53,or(not(X),X_55)),
introduced(tautology,[refl,[$fot(implies(X_53,or(not(X),X_55)))]]) ).
cnf(refute_0_206,plain,
( implies(X_53,or(not(X),X_55)) != implies(X_53,or(not(X),X_55))
| or(not(X),X_55) != implies(X,X_55)
| implies(X_53,or(not(X),X_55)) = implies(X_53,implies(X,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_53,or(not(X),X_55)),implies(X_53,or(not(X),X_55))) ),[1,1],$fot(implies(X,X_55))]]) ).
cnf(refute_0_207,plain,
( or(not(X),X_55) != implies(X,X_55)
| implies(X_53,or(not(X),X_55)) = implies(X_53,implies(X,X_55)) ),
inference(resolve,[$cnf( $equal(implies(X_53,or(not(X),X_55)),implies(X_53,or(not(X),X_55))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(X_53,or(not(X),X_55)) = implies(X_53,implies(X,X_55)),
inference(resolve,[$cnf( $equal(or(not(X),X_55),implies(X,X_55)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) = implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))),
introduced(tautology,[refl,[$fot(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))))]]) ).
cnf(refute_0_210,plain,
( implies(X_53,or(not(X),X_55)) != implies(X_53,implies(X,X_55))
| implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) != implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))
| implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) = implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))),implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) ),[1,0],$fot(implies(X_53,implies(X,X_55)))]]) ).
cnf(refute_0_211,plain,
( implies(X_53,or(not(X),X_55)) != implies(X_53,implies(X,X_55))
| implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) = implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))),implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) = implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55))),
inference(resolve,[$cnf( $equal(implies(X_53,or(not(X),X_55)),implies(X_53,implies(X,X_55))) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
( implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))) != implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55)))
| ~ axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))))
| axiom(implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) ),[0],$fot(implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55))))]]) ).
cnf(refute_0_214,plain,
( ~ axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))))
| axiom(implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55))),implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55)))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
axiom(implies(implies(X_53,implies(X,X_55)),implies(X,implies(X_53,X_55)))),
inference(resolve,[$cnf( axiom(implies(implies(X_53,or(not(X),X_55)),implies(X,implies(X_53,X_55)))) )],[refute_0_203,refute_0_214]) ).
cnf(refute_0_216,plain,
axiom(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79)))),
inference(subst,[],[refute_0_215:[bind(X,$fot(X_77)),bind(X_53,$fot(X_78)),bind(X_55,$fot(X_79))]]) ).
cnf(refute_0_217,plain,
theorem(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79)))),
inference(resolve,[$cnf( axiom(implies(implies(X_78,implies(X_77,X_79)),implies(X_77,implies(X_78,X_79)))) )],[refute_0_216,refute_0_196]) ).
cnf(refute_0_218,plain,
theorem(implies(implies(X_81,implies(X_80,X_82)),implies(X_80,implies(X_81,X_82)))),
inference(subst,[],[refute_0_217:[bind(X_77,$fot(X_80)),bind(X_78,$fot(X_81)),bind(X_79,$fot(X_82))]]) ).
cnf(refute_0_219,plain,
( ~ theorem(implies(X_81,implies(X_80,X_82)))
| theorem(implies(X_80,implies(X_81,X_82))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_81,implies(X_80,X_82)),implies(X_80,implies(X_81,X_82)))) )],[refute_0_218,refute_0_195]) ).
cnf(refute_0_220,plain,
( ~ theorem(implies(X_4919,implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535)))))
| theorem(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_4919,implies(X_2537,or(X_2536,X_2535))))) ),
inference(subst,[],[refute_0_219:[bind(X_80,$fot(implies(X_2537,or(X_2535,X_2536)))),bind(X_81,$fot(X_4919)),bind(X_82,$fot(implies(X_2537,or(X_2536,X_2535))))]]) ).
cnf(refute_0_221,plain,
theorem(implies(implies(X_2537,or(X_2535,X_2536)),implies(X_4919,implies(X_2537,or(X_2536,X_2535))))),
inference(resolve,[$cnf( theorem(implies(X_4919,implies(implies(X_2537,or(X_2535,X_2536)),implies(X_2537,or(X_2536,X_2535))))) )],[refute_0_194,refute_0_220]) ).
cnf(refute_0_222,plain,
theorem(implies(implies(X_4981,or(X_4979,X_4980)),implies(X_4982,implies(X_4981,or(X_4980,X_4979))))),
inference(subst,[],[refute_0_221:[bind(X_2535,$fot(X_4979)),bind(X_2536,$fot(X_4980)),bind(X_2537,$fot(X_4981)),bind(X_4919,$fot(X_4982))]]) ).
cnf(refute_0_223,plain,
( ~ theorem(implies(X_4981,or(X_4979,X_4980)))
| theorem(implies(X_4982,implies(X_4981,or(X_4980,X_4979)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_4981,or(X_4979,X_4980)),implies(X_4982,implies(X_4981,or(X_4980,X_4979))))) )],[refute_0_222,refute_0_178]) ).
cnf(refute_0_224,plain,
( ~ theorem(implies(X_79621,or(X_79619,implies(X,X_79621))))
| theorem(implies(X_79622,implies(X_79621,or(implies(X,X_79621),X_79619)))) ),
inference(subst,[],[refute_0_223:[bind(X_4979,$fot(X_79619)),bind(X_4980,$fot(implies(X,X_79621))),bind(X_4981,$fot(X_79621)),bind(X_4982,$fot(X_79622))]]) ).
cnf(refute_0_225,plain,
theorem(implies(X_79622,implies(X_79621,or(implies(X,X_79621),X_79619)))),
inference(resolve,[$cnf( theorem(implies(X_79621,or(X_79619,implies(X,X_79621)))) )],[refute_0_177,refute_0_224]) ).
cnf(refute_0_226,plain,
theorem(implies(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641))),implies(X_79642,or(implies(X_79640,X_79642),X_79641)))),
inference(subst,[],[refute_0_225:[bind(X,$fot(X_79640)),bind(X_79619,$fot(X_79641)),bind(X_79621,$fot(X_79642)),bind(X_79622,$fot(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641)))))]]) ).
cnf(refute_0_227,plain,
theorem(not(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641))))),
inference(resolve,[$cnf( theorem(implies(not(implies(X_79642,or(implies(X_79640,X_79642),X_79641))),implies(X_79642,or(implies(X_79640,X_79642),X_79641)))) )],[refute_0_226,refute_0_136]) ).
cnf(refute_0_228,plain,
theorem(not(not(implies(X_79978,or(implies(X_79976,X_79978),X_79977))))),
inference(subst,[],[refute_0_227:[bind(X_79640,$fot(X_79976)),bind(X_79641,$fot(X_79977)),bind(X_79642,$fot(X_79978))]]) ).
cnf(refute_0_229,plain,
theorem(implies(X_79978,or(implies(X_79976,X_79978),X_79977))),
inference(resolve,[$cnf( theorem(not(not(implies(X_79978,or(implies(X_79976,X_79978),X_79977))))) )],[refute_0_228,refute_0_94]) ).
cnf(refute_0_230,plain,
theorem(implies(X_79981,or(implies(X_79979,X_79981),X_79980))),
inference(subst,[],[refute_0_229:[bind(X_79976,$fot(X_79979)),bind(X_79977,$fot(X_79980)),bind(X_79978,$fot(X_79981))]]) ).
cnf(refute_0_231,plain,
theorem(or(implies(X_79979,X_79981),implies(X_79981,X_79980))),
inference(resolve,[$cnf( theorem(implies(X_79981,or(implies(X_79979,X_79981),X_79980))) )],[refute_0_230,refute_0_26]) ).
cnf(refute_0_232,plain,
theorem(or(implies(p,q),implies(q,r))),
inference(subst,[],[refute_0_231:[bind(X_79979,$fot(p)),bind(X_79980,$fot(r)),bind(X_79981,$fot(q))]]) ).
cnf(refute_0_233,plain,
$false,
inference(resolve,[$cnf( theorem(or(implies(p,q),implies(q,r))) )],[refute_0_232,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL323-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.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 : Sat Jul 2 22:55:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 147.64/147.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 147.64/147.84
% 147.64/147.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 147.64/147.86
%------------------------------------------------------------------------------