TSTP Solution File: LCL182-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL182-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 12:50:19 EDT 2022
% Result : Unsatisfiable 34.54s 34.75s
% Output : CNFRefutation 34.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 37
% Syntax : Number of clauses : 207 ( 107 unt; 0 nHn; 91 RR)
% Number of literals : 342 ( 103 equ; 136 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 : 458 ( 25 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(implies(p,q),implies(not(q),not(p)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31))))
| theorem(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_29)),bind(B,$fot(X_30)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))),
inference(resolve,[$cnf( axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,or(not(X),X_34)))),
inference(subst,[],[refute_0_2:[bind(X_29,$fot(not(X))),bind(X_30,$fot(X_33)),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_4,plain,
implies(X,X_34) = or(not(X),X_34),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X,X_34) != or(not(X),X_34)
| or(not(X),X_34) = implies(X,X_34) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_34))),bind(Y0,$fot(or(not(X),X_34)))]]) ).
cnf(refute_0_9,plain,
or(not(X),X_34) = implies(X,X_34),
inference(resolve,[$cnf( $equal(implies(X,X_34),or(not(X),X_34)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X),X_34) != implies(X,X_34)
| ~ theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,or(not(X),X_34))))
| theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,or(not(X),X_34)))) ),[0,1,1],$fot(implies(X,X_34))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,or(not(X),X_34))))
| theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_34),implies(X,X_34)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,or(not(X),X_34)))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_14,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_13]) ).
cnf(refute_0_15,plain,
or(not(X),or(X_33,X_34)) = implies(X,or(X_33,X_34)),
inference(subst,[],[refute_0_14:[bind(Y,$fot(or(X_33,X_34)))]]) ).
cnf(refute_0_16,plain,
implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) = implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))))]]) ).
cnf(refute_0_17,plain,
( implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) != implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))
| or(not(X),or(X_33,X_34)) != implies(X,or(X_33,X_34))
| implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) = implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))),implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),[1,0],$fot(implies(X,or(X_33,X_34)))]]) ).
cnf(refute_0_18,plain,
( or(not(X),or(X_33,X_34)) != implies(X,or(X_33,X_34))
| implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) = implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))),implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) = implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_33,X_34)),implies(X,or(X_33,X_34))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))) != implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))
| ~ theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))))
| theorem(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),[0],$fot(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34))))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))))
| theorem(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34))),implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_33,X_34)),or(X_33,implies(X,X_34)))) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_58)),bind(X_33,$fot(not(X))),bind(X_34,$fot(X_60))]]) ).
cnf(refute_0_24,plain,
implies(X,implies(X_58,X_60)) = or(not(X),implies(X_58,X_60)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_58,X_60)))]]) ).
cnf(refute_0_25,plain,
( implies(X,implies(X_58,X_60)) != or(not(X),implies(X_58,X_60))
| or(not(X),implies(X_58,X_60)) = implies(X,implies(X_58,X_60)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,implies(X_58,X_60)))),bind(Y0,$fot(or(not(X),implies(X_58,X_60))))]]) ).
cnf(refute_0_26,plain,
or(not(X),implies(X_58,X_60)) = implies(X,implies(X_58,X_60)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_58,X_60)),or(not(X),implies(X_58,X_60))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( or(not(X),implies(X_58,X_60)) != implies(X,implies(X_58,X_60))
| ~ theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60))))
| theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))) ),[0,1],$fot(implies(X,implies(X_58,X_60)))]]) ).
cnf(refute_0_28,plain,
( ~ theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60))))
| theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_58,X_60)),implies(X,implies(X_58,X_60))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
or(not(X),X_60) = implies(X,X_60),
inference(subst,[],[refute_0_14:[bind(Y,$fot(X_60))]]) ).
cnf(refute_0_31,plain,
implies(X_58,or(not(X),X_60)) = implies(X_58,or(not(X),X_60)),
introduced(tautology,[refl,[$fot(implies(X_58,or(not(X),X_60)))]]) ).
cnf(refute_0_32,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,or(not(X),X_60))
| or(not(X),X_60) != implies(X,X_60)
| implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,or(not(X),X_60))) ),[1,1],$fot(implies(X,X_60))]]) ).
cnf(refute_0_33,plain,
( or(not(X),X_60) != implies(X,X_60)
| implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)) ),
inference(resolve,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,or(not(X),X_60))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)),
inference(resolve,[$cnf( $equal(or(not(X),X_60),implies(X,X_60)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),
introduced(tautology,[refl,[$fot(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_36,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,implies(X,X_60))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) != implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),[1,0],$fot(implies(X_58,implies(X,X_60)))]]) ).
cnf(refute_0_37,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,implies(X,X_60))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))),
inference(resolve,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,implies(X,X_60))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) != implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))
| ~ theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),[0],$fot(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_29,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X_58,implies(X,X_60)))
| ~ theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(X,implies(X_58,X_60))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,implies(X_58,X_60)))),bind(Y,$fot(implies(X_58,implies(X,X_60))))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X_58,implies(X,X_60)))
| theorem(implies(X,implies(X_58,X_60))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(not(X_41527),implies(or(X_41528,X_41527),X_41528)))
| theorem(implies(or(X_41528,X_41527),implies(not(X_41527),X_41528))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(or(X_41528,X_41527))),bind(X_58,$fot(not(X_41527))),bind(X_60,$fot(X_41528))]]) ).
cnf(refute_0_45,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_46,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_45]) ).
cnf(refute_0_47,plain,
theorem(implies(or(X_67,X_67),X_67)),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_67))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(implies(or(X_67,X_67),X_67))
| ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_67)),bind(Y,$fot(or(X_67,X_67)))]]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(resolve,[$cnf( theorem(implies(or(X_67,X_67),X_67)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)),implies(not(X_41524),implies(or(X_41526,X_41524),X_41526))))
| theorem(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526))) ),
inference(subst,[],[refute_0_49:[bind(X_67,$fot(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526))))]]) ).
cnf(refute_0_51,plain,
( ~ axiom(implies(or(X_13,X_14),or(X_14,X_13)))
| theorem(implies(or(X_13,X_14),or(X_14,X_13))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_52,plain,
axiom(implies(or(X_13,X_14),or(X_14,X_13))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_53,plain,
theorem(implies(or(X_13,X_14),or(X_14,X_13))),
inference(resolve,[$cnf( axiom(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(or(X_13,X_14),or(X_14,X_13)))
| ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_14,X_13))),bind(Y,$fot(or(X_13,X_14)))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ theorem(or(X_5804,implies(or(X_5805,X_5804),X_5805)))
| theorem(or(implies(or(X_5805,X_5804),X_5805),X_5804)) ),
inference(subst,[],[refute_0_55:[bind(X_13,$fot(X_5804)),bind(X_14,$fot(implies(or(X_5805,X_5804),X_5805)))]]) ).
cnf(refute_0_57,plain,
theorem(implies(or(X_5803,X_5802),or(X_5802,X_5803))),
inference(subst,[],[refute_0_53:[bind(X_13,$fot(X_5803)),bind(X_14,$fot(X_5802))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(X,or(X_33,X_34)))
| ~ theorem(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34))))
| theorem(or(X_33,implies(X,X_34))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_33,implies(X,X_34)))),bind(Y,$fot(implies(X,or(X_33,X_34))))]]) ).
cnf(refute_0_59,plain,
( ~ theorem(implies(X,or(X_33,X_34)))
| theorem(or(X_33,implies(X,X_34))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,or(X_33,X_34)),or(X_33,implies(X,X_34)))) )],[refute_0_22,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ theorem(implies(or(X_5803,X_5802),or(X_5802,X_5803)))
| theorem(or(X_5802,implies(or(X_5803,X_5802),X_5803))) ),
inference(subst,[],[refute_0_59:[bind(X,$fot(or(X_5803,X_5802))),bind(X_33,$fot(X_5802)),bind(X_34,$fot(X_5803))]]) ).
cnf(refute_0_61,plain,
theorem(or(X_5802,implies(or(X_5803,X_5802),X_5803))),
inference(resolve,[$cnf( theorem(implies(or(X_5803,X_5802),or(X_5802,X_5803))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
theorem(or(X_5804,implies(or(X_5805,X_5804),X_5805))),
inference(subst,[],[refute_0_61:[bind(X_5802,$fot(X_5804)),bind(X_5803,$fot(X_5805))]]) ).
cnf(refute_0_63,plain,
theorem(or(implies(or(X_5805,X_5804),X_5805),X_5804)),
inference(resolve,[$cnf( theorem(or(X_5804,implies(or(X_5805,X_5804),X_5805))) )],[refute_0_62,refute_0_56]) ).
cnf(refute_0_64,plain,
theorem(or(implies(or(X_5805,X_32884),X_5805),X_32884)),
inference(subst,[],[refute_0_63:[bind(X_5804,$fot(X_32884))]]) ).
cnf(refute_0_65,plain,
( ~ theorem(implies(or(X_7302,X_7301),or(X_7302,not(not(X_7301)))))
| ~ theorem(or(X_7302,X_7301))
| theorem(or(X_7302,not(not(X_7301)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_7302,not(not(X_7301))))),bind(Y,$fot(or(X_7302,X_7301)))]]) ).
cnf(refute_0_66,plain,
theorem(implies(or(not(X),X_16),or(X_16,not(X)))),
inference(subst,[],[refute_0_53:[bind(X_13,$fot(not(X))),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_67,plain,
implies(X,X_16) = or(not(X),X_16),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_16))]]) ).
cnf(refute_0_68,plain,
( implies(X,X_16) != or(not(X),X_16)
| or(not(X),X_16) = implies(X,X_16) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_16))),bind(Y0,$fot(or(not(X),X_16)))]]) ).
cnf(refute_0_69,plain,
or(not(X),X_16) = implies(X,X_16),
inference(resolve,[$cnf( $equal(implies(X,X_16),or(not(X),X_16)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( or(not(X),X_16) != implies(X,X_16)
| ~ theorem(implies(or(not(X),X_16),or(X_16,not(X))))
| theorem(implies(implies(X,X_16),or(X_16,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_16),or(X_16,not(X)))) ),[0,0],$fot(implies(X,X_16))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(or(not(X),X_16),or(X_16,not(X))))
| theorem(implies(implies(X,X_16),or(X_16,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_16),implies(X,X_16)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
theorem(implies(implies(X,X_16),or(X_16,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_16),or(X_16,not(X)))) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_25)),bind(X_16,$fot(not(X)))]]) ).
cnf(refute_0_74,plain,
implies(X,not(X_25)) = or(not(X),not(X_25)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_75,plain,
( implies(X,not(X_25)) != or(not(X),not(X_25))
| or(not(X),not(X_25)) = implies(X,not(X_25)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,not(X_25)))),bind(Y0,$fot(or(not(X),not(X_25))))]]) ).
cnf(refute_0_76,plain,
or(not(X),not(X_25)) = implies(X,not(X_25)),
inference(resolve,[$cnf( $equal(implies(X,not(X_25)),or(not(X),not(X_25))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( or(not(X),not(X_25)) != implies(X,not(X_25))
| ~ theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25))))
| theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))) ),[0,1],$fot(implies(X,not(X_25)))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25))))
| theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_25)),implies(X,not(X_25))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))),
inference(resolve,[$cnf( theorem(implies(implies(X_25,not(X)),or(not(X),not(X_25)))) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ theorem(implies(X_25,not(X)))
| ~ theorem(implies(implies(X_25,not(X)),implies(X,not(X_25))))
| theorem(implies(X,not(X_25))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,not(X_25)))),bind(Y,$fot(implies(X_25,not(X))))]]) ).
cnf(refute_0_81,plain,
( ~ theorem(implies(X_25,not(X)))
| theorem(implies(X,not(X_25))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_25,not(X)),implies(X,not(X_25)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ theorem(implies(not(X),not(X)))
| theorem(implies(X,not(not(X)))) ),
inference(subst,[],[refute_0_81:[bind(X_25,$fot(not(X)))]]) ).
cnf(refute_0_83,plain,
( ~ theorem(or(X_951,not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))))))
| theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951)) ),
inference(subst,[],[refute_0_55:[bind(X_13,$fot(X_951)),bind(X_14,$fot(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))))))]]) ).
cnf(refute_0_84,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_85,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(implies(X_68,or(B,X_68))),
inference(subst,[],[refute_0_85:[bind(A,$fot(X_68))]]) ).
cnf(refute_0_87,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,or(B,X_68)))
| theorem(or(B,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_88,plain,
( ~ theorem(X_68)
| theorem(or(B,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,or(B,X_68))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ theorem(not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490)))))
| theorem(or(B,not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490)))))) ),
inference(subst,[],[refute_0_88:[bind(X_68,$fot(not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490))))))]]) ).
cnf(refute_0_90,plain,
( ~ theorem(X_235)
| ~ theorem(implies(X_235,not(implies(X_235,not(X_235)))))
| theorem(not(implies(X_235,not(X_235)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(not(implies(X_235,not(X_235))))),bind(Y,$fot(X_235))]]) ).
cnf(refute_0_91,plain,
theorem(implies(or(not(X_7),not(X_7)),not(X_7))),
inference(subst,[],[refute_0_46:[bind(A,$fot(not(X_7)))]]) ).
cnf(refute_0_92,plain,
implies(X_7,not(X_7)) = or(not(X_7),not(X_7)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(not(X_7)))]]) ).
cnf(refute_0_93,plain,
( implies(X_7,not(X_7)) != or(not(X_7),not(X_7))
| or(not(X_7),not(X_7)) = implies(X_7,not(X_7)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_7,not(X_7)))),bind(Y0,$fot(or(not(X_7),not(X_7))))]]) ).
cnf(refute_0_94,plain,
or(not(X_7),not(X_7)) = implies(X_7,not(X_7)),
inference(resolve,[$cnf( $equal(implies(X_7,not(X_7)),or(not(X_7),not(X_7))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( or(not(X_7),not(X_7)) != implies(X_7,not(X_7))
| ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) ),[0,0],$fot(implies(X_7,not(X_7)))]]) ).
cnf(refute_0_96,plain,
( ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),not(X_7)),implies(X_7,not(X_7))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
theorem(implies(implies(X_7,not(X_7)),not(X_7))),
inference(resolve,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ theorem(implies(X,X_16))
| ~ theorem(implies(implies(X,X_16),or(X_16,not(X))))
| theorem(or(X_16,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_16,not(X)))),bind(Y,$fot(implies(X,X_16)))]]) ).
cnf(refute_0_99,plain,
( ~ theorem(implies(X,X_16))
| theorem(or(X_16,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_16),or(X_16,not(X)))) )],[refute_0_72,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ theorem(implies(implies(X_7,not(X_7)),not(X_7)))
| theorem(or(not(X_7),not(implies(X_7,not(X_7))))) ),
inference(subst,[],[refute_0_99:[bind(X,$fot(implies(X_7,not(X_7)))),bind(X_16,$fot(not(X_7)))]]) ).
cnf(refute_0_101,plain,
theorem(or(not(X_7),not(implies(X_7,not(X_7))))),
inference(resolve,[$cnf( theorem(implies(implies(X_7,not(X_7)),not(X_7))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
or(not(X_7),not(implies(X_7,not(X_7)))) = implies(X_7,not(implies(X_7,not(X_7)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_7)),bind(Y,$fot(not(implies(X_7,not(X_7)))))]]) ).
cnf(refute_0_103,plain,
( or(not(X_7),not(implies(X_7,not(X_7)))) != implies(X_7,not(implies(X_7,not(X_7))))
| ~ theorem(or(not(X_7),not(implies(X_7,not(X_7)))))
| theorem(implies(X_7,not(implies(X_7,not(X_7))))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_7),not(implies(X_7,not(X_7))))) ),[0],$fot(implies(X_7,not(implies(X_7,not(X_7)))))]]) ).
cnf(refute_0_104,plain,
( ~ theorem(or(not(X_7),not(implies(X_7,not(X_7)))))
| theorem(implies(X_7,not(implies(X_7,not(X_7))))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),not(implies(X_7,not(X_7)))),implies(X_7,not(implies(X_7,not(X_7))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
theorem(implies(X_7,not(implies(X_7,not(X_7))))),
inference(resolve,[$cnf( theorem(or(not(X_7),not(implies(X_7,not(X_7))))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
theorem(implies(X_235,not(implies(X_235,not(X_235))))),
inference(subst,[],[refute_0_105:[bind(X_7,$fot(X_235))]]) ).
cnf(refute_0_107,plain,
( ~ theorem(X_235)
| theorem(not(implies(X_235,not(X_235)))) ),
inference(resolve,[$cnf( theorem(implies(X_235,not(implies(X_235,not(X_235))))) )],[refute_0_106,refute_0_90]) ).
cnf(refute_0_108,plain,
( ~ theorem(implies(or(A,A),A))
| theorem(not(implies(implies(or(A,A),A),not(implies(or(A,A),A))))) ),
inference(subst,[],[refute_0_107:[bind(X_235,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_109,plain,
theorem(not(implies(implies(or(A,A),A),not(implies(or(A,A),A))))),
inference(resolve,[$cnf( theorem(implies(or(A,A),A)) )],[refute_0_46,refute_0_108]) ).
cnf(refute_0_110,plain,
theorem(not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490))))),
inference(subst,[],[refute_0_109:[bind(A,$fot(X_490))]]) ).
cnf(refute_0_111,plain,
theorem(or(B,not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490)))))),
inference(resolve,[$cnf( theorem(not(implies(implies(or(X_490,X_490),X_490),not(implies(or(X_490,X_490),X_490))))) )],[refute_0_110,refute_0_89]) ).
cnf(refute_0_112,plain,
theorem(or(X_951,not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))))),
inference(subst,[],[refute_0_111:[bind(B,$fot(X_951)),bind(X_490,$fot(X_952))]]) ).
cnf(refute_0_113,plain,
theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951)),
inference(resolve,[$cnf( theorem(or(X_951,not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))))) )],[refute_0_112,refute_0_83]) ).
cnf(refute_0_114,plain,
or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951) = implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951),
inference(subst,[],[refute_0_14:[bind(X,$fot(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))))),bind(Y,$fot(X_951))]]) ).
cnf(refute_0_115,plain,
( or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951) != implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)
| ~ theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951))
| theorem(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951)) ),[0],$fot(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951))]]) ).
cnf(refute_0_116,plain,
( ~ theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951))
| theorem(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)) ),
inference(resolve,[$cnf( $equal(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951),implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
theorem(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)),
inference(resolve,[$cnf( theorem(or(not(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952)))),X_951)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( ~ theorem(X_1378)
| ~ theorem(implies(X_1378,implies(X_1379,X_1379)))
| theorem(implies(X_1379,X_1379)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1379,X_1379))),bind(Y,$fot(X_1378))]]) ).
cnf(refute_0_119,plain,
theorem(implies(A,or(not(X_7),A))),
inference(subst,[],[refute_0_85:[bind(B,$fot(not(X_7)))]]) ).
cnf(refute_0_120,plain,
implies(X_7,A) = or(not(X_7),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(A))]]) ).
cnf(refute_0_121,plain,
( implies(X_7,A) != or(not(X_7),A)
| or(not(X_7),A) = implies(X_7,A) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_7,A))),bind(Y0,$fot(or(not(X_7),A)))]]) ).
cnf(refute_0_122,plain,
or(not(X_7),A) = implies(X_7,A),
inference(resolve,[$cnf( $equal(implies(X_7,A),or(not(X_7),A)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( or(not(X_7),A) != implies(X_7,A)
| ~ theorem(implies(A,or(not(X_7),A)))
| theorem(implies(A,implies(X_7,A))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(A,or(not(X_7),A))) ),[0,1],$fot(implies(X_7,A))]]) ).
cnf(refute_0_124,plain,
( ~ theorem(implies(A,or(not(X_7),A)))
| theorem(implies(A,implies(X_7,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),A),implies(X_7,A)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
theorem(implies(A,implies(X_7,A))),
inference(resolve,[$cnf( theorem(implies(A,or(not(X_7),A))) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
theorem(implies(X_1375,implies(X_1373,X_1375))),
inference(subst,[],[refute_0_125:[bind(A,$fot(X_1375)),bind(X_7,$fot(X_1373))]]) ).
cnf(refute_0_127,plain,
( ~ theorem(implies(X_1375,implies(X_1373,X_1375)))
| theorem(implies(X_1373,implies(X_1375,X_1375))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_1373)),bind(X_58,$fot(X_1375)),bind(X_60,$fot(X_1375))]]) ).
cnf(refute_0_128,plain,
theorem(implies(X_1373,implies(X_1375,X_1375))),
inference(resolve,[$cnf( theorem(implies(X_1375,implies(X_1373,X_1375))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
theorem(implies(X_1378,implies(X_1379,X_1379))),
inference(subst,[],[refute_0_128:[bind(X_1373,$fot(X_1378)),bind(X_1375,$fot(X_1379))]]) ).
cnf(refute_0_130,plain,
( ~ theorem(X_1378)
| theorem(implies(X_1379,X_1379)) ),
inference(resolve,[$cnf( theorem(implies(X_1378,implies(X_1379,X_1379))) )],[refute_0_129,refute_0_118]) ).
cnf(refute_0_131,plain,
( ~ theorem(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951))
| theorem(implies(X_1647,X_1647)) ),
inference(subst,[],[refute_0_130:[bind(X_1378,$fot(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951))),bind(X_1379,$fot(X_1647))]]) ).
cnf(refute_0_132,plain,
theorem(implies(X_1647,X_1647)),
inference(resolve,[$cnf( theorem(implies(implies(implies(or(X_952,X_952),X_952),not(implies(or(X_952,X_952),X_952))),X_951)) )],[refute_0_117,refute_0_131]) ).
cnf(refute_0_133,plain,
theorem(implies(not(X),not(X))),
inference(subst,[],[refute_0_132:[bind(X_1647,$fot(not(X)))]]) ).
cnf(refute_0_134,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(implies(not(X),not(X))) )],[refute_0_133,refute_0_82]) ).
cnf(refute_0_135,plain,
theorem(implies(X_7274,not(not(X_7274)))),
inference(subst,[],[refute_0_134:[bind(X,$fot(X_7274))]]) ).
cnf(refute_0_136,plain,
( ~ axiom(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36))))
| theorem(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))))]]) ).
cnf(refute_0_137,plain,
axiom(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_35)),bind(B,$fot(X_36)),bind(C,$fot(X_37))]]) ).
cnf(refute_0_138,plain,
theorem(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))) )],[refute_0_137,refute_0_136]) ).
cnf(refute_0_139,plain,
( ~ theorem(implies(X_35,X_36))
| ~ theorem(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36))))
| theorem(implies(or(X_37,X_35),or(X_37,X_36))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_37,X_35),or(X_37,X_36)))),bind(Y,$fot(implies(X_35,X_36)))]]) ).
cnf(refute_0_140,plain,
( ~ theorem(implies(X_35,X_36))
| theorem(implies(or(X_37,X_35),or(X_37,X_36))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_35,X_36),implies(or(X_37,X_35),or(X_37,X_36)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( ~ theorem(implies(X_7274,not(not(X_7274))))
| theorem(implies(or(X_7276,X_7274),or(X_7276,not(not(X_7274))))) ),
inference(subst,[],[refute_0_140:[bind(X_35,$fot(X_7274)),bind(X_36,$fot(not(not(X_7274)))),bind(X_37,$fot(X_7276))]]) ).
cnf(refute_0_142,plain,
theorem(implies(or(X_7276,X_7274),or(X_7276,not(not(X_7274))))),
inference(resolve,[$cnf( theorem(implies(X_7274,not(not(X_7274)))) )],[refute_0_135,refute_0_141]) ).
cnf(refute_0_143,plain,
theorem(implies(or(X_7302,X_7301),or(X_7302,not(not(X_7301))))),
inference(subst,[],[refute_0_142:[bind(X_7274,$fot(X_7301)),bind(X_7276,$fot(X_7302))]]) ).
cnf(refute_0_144,plain,
( ~ theorem(or(X_7302,X_7301))
| theorem(or(X_7302,not(not(X_7301)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_7302,X_7301),or(X_7302,not(not(X_7301))))) )],[refute_0_143,refute_0_65]) ).
cnf(refute_0_145,plain,
( ~ theorem(or(implies(or(X_5805,X_32884),X_5805),X_32884))
| theorem(or(implies(or(X_5805,X_32884),X_5805),not(not(X_32884)))) ),
inference(subst,[],[refute_0_144:[bind(X_7301,$fot(X_32884)),bind(X_7302,$fot(implies(or(X_5805,X_32884),X_5805)))]]) ).
cnf(refute_0_146,plain,
theorem(or(implies(or(X_5805,X_32884),X_5805),not(not(X_32884)))),
inference(resolve,[$cnf( theorem(or(implies(or(X_5805,X_32884),X_5805),X_32884)) )],[refute_0_64,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ theorem(implies(or(X_725,X_726),or(X_727,or(X_726,X_725))))
| ~ theorem(or(X_725,X_726))
| theorem(or(X_727,or(X_726,X_725))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_727,or(X_726,X_725)))),bind(Y,$fot(or(X_725,X_726)))]]) ).
cnf(refute_0_148,plain,
( ~ theorem(implies(or(X_13,X_14),or(X_14,X_13)))
| theorem(or(X_77,implies(or(X_13,X_14),or(X_14,X_13)))) ),
inference(subst,[],[refute_0_88:[bind(B,$fot(X_77)),bind(X_68,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_149,plain,
theorem(or(X_77,implies(or(X_13,X_14),or(X_14,X_13)))),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_53,refute_0_148]) ).
cnf(refute_0_150,plain,
theorem(or(X_682,implies(or(X_13,X_14),or(X_14,X_13)))),
inference(subst,[],[refute_0_149:[bind(X_77,$fot(X_682))]]) ).
cnf(refute_0_151,plain,
theorem(implies(or(X_32,or(not(X),X_34)),or(not(X),or(X_32,X_34)))),
inference(subst,[],[refute_0_2:[bind(X_29,$fot(X_32)),bind(X_30,$fot(not(X))),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_152,plain,
implies(X,or(X_32,X_34)) = or(not(X),or(X_32,X_34)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_32,X_34)))]]) ).
cnf(refute_0_153,plain,
( implies(X,or(X_32,X_34)) != or(not(X),or(X_32,X_34))
| or(not(X),or(X_32,X_34)) = implies(X,or(X_32,X_34)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,or(X_32,X_34)))),bind(Y0,$fot(or(not(X),or(X_32,X_34))))]]) ).
cnf(refute_0_154,plain,
or(not(X),or(X_32,X_34)) = implies(X,or(X_32,X_34)),
inference(resolve,[$cnf( $equal(implies(X,or(X_32,X_34)),or(not(X),or(X_32,X_34))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( or(not(X),or(X_32,X_34)) != implies(X,or(X_32,X_34))
| ~ theorem(implies(or(X_32,or(not(X),X_34)),or(not(X),or(X_32,X_34))))
| theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_32,or(not(X),X_34)),or(not(X),or(X_32,X_34)))) ),[0,1],$fot(implies(X,or(X_32,X_34)))]]) ).
cnf(refute_0_156,plain,
( ~ theorem(implies(or(X_32,or(not(X),X_34)),or(not(X),or(X_32,X_34))))
| theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_34)),implies(X,or(X_32,X_34))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))),
inference(resolve,[$cnf( theorem(implies(or(X_32,or(not(X),X_34)),or(not(X),or(X_32,X_34)))) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
or(X_32,or(not(X),X_34)) = or(X_32,or(not(X),X_34)),
introduced(tautology,[refl,[$fot(or(X_32,or(not(X),X_34)))]]) ).
cnf(refute_0_159,plain,
( or(X_32,or(not(X),X_34)) != or(X_32,or(not(X),X_34))
| or(not(X),X_34) != implies(X,X_34)
| or(X_32,or(not(X),X_34)) = or(X_32,implies(X,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_32,or(not(X),X_34)),or(X_32,or(not(X),X_34))) ),[1,1],$fot(implies(X,X_34))]]) ).
cnf(refute_0_160,plain,
( or(not(X),X_34) != implies(X,X_34)
| or(X_32,or(not(X),X_34)) = or(X_32,implies(X,X_34)) ),
inference(resolve,[$cnf( $equal(or(X_32,or(not(X),X_34)),or(X_32,or(not(X),X_34))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
or(X_32,or(not(X),X_34)) = or(X_32,implies(X,X_34)),
inference(resolve,[$cnf( $equal(or(not(X),X_34),implies(X,X_34)) )],[refute_0_9,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) = implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))),
introduced(tautology,[refl,[$fot(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))))]]) ).
cnf(refute_0_163,plain,
( implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) != implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))
| or(X_32,or(not(X),X_34)) != or(X_32,implies(X,X_34))
| implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) = implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))),implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) ),[1,0],$fot(or(X_32,implies(X,X_34)))]]) ).
cnf(refute_0_164,plain,
( or(X_32,or(not(X),X_34)) != or(X_32,implies(X,X_34))
| implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) = implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34))) ),
inference(resolve,[$cnf( $equal(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))),implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) = implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34))),
inference(resolve,[$cnf( $equal(or(X_32,or(not(X),X_34)),or(X_32,implies(X,X_34))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))) != implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))
| ~ theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))))
| theorem(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) ),[0],$fot(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34))))]]) ).
cnf(refute_0_167,plain,
( ~ theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))))
| theorem(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34))),implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
theorem(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))),
inference(resolve,[$cnf( theorem(implies(or(X_32,or(not(X),X_34)),implies(X,or(X_32,X_34)))) )],[refute_0_157,refute_0_167]) ).
cnf(refute_0_169,plain,
( ~ theorem(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34))))
| ~ theorem(or(X_32,implies(X,X_34)))
| theorem(implies(X,or(X_32,X_34))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,or(X_32,X_34)))),bind(Y,$fot(or(X_32,implies(X,X_34))))]]) ).
cnf(refute_0_170,plain,
( ~ theorem(or(X_32,implies(X,X_34)))
| theorem(implies(X,or(X_32,X_34))) ),
inference(resolve,[$cnf( theorem(implies(or(X_32,implies(X,X_34)),implies(X,or(X_32,X_34)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( ~ theorem(or(X_682,implies(or(X_13,X_14),or(X_14,X_13))))
| theorem(implies(or(X_13,X_14),or(X_682,or(X_14,X_13)))) ),
inference(subst,[],[refute_0_170:[bind(X,$fot(or(X_13,X_14))),bind(X_32,$fot(X_682)),bind(X_34,$fot(or(X_14,X_13)))]]) ).
cnf(refute_0_172,plain,
theorem(implies(or(X_13,X_14),or(X_682,or(X_14,X_13)))),
inference(resolve,[$cnf( theorem(or(X_682,implies(or(X_13,X_14),or(X_14,X_13)))) )],[refute_0_150,refute_0_171]) ).
cnf(refute_0_173,plain,
theorem(implies(or(X_725,X_726),or(X_727,or(X_726,X_725)))),
inference(subst,[],[refute_0_172:[bind(X_13,$fot(X_725)),bind(X_14,$fot(X_726)),bind(X_682,$fot(X_727))]]) ).
cnf(refute_0_174,plain,
( ~ theorem(or(X_725,X_726))
| theorem(or(X_727,or(X_726,X_725))) ),
inference(resolve,[$cnf( theorem(implies(or(X_725,X_726),or(X_727,or(X_726,X_725)))) )],[refute_0_173,refute_0_147]) ).
cnf(refute_0_175,plain,
( ~ theorem(or(implies(or(X_5805,X_32884),X_5805),not(not(X_32884))))
| theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))) ),
inference(subst,[],[refute_0_174:[bind(X_725,$fot(implies(or(X_5805,X_32884),X_5805))),bind(X_726,$fot(not(not(X_32884)))),bind(X_727,$fot(X_41518))]]) ).
cnf(refute_0_176,plain,
theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))),
inference(resolve,[$cnf( theorem(or(implies(or(X_5805,X_32884),X_5805),not(not(X_32884)))) )],[refute_0_146,refute_0_175]) ).
cnf(refute_0_177,plain,
or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)) = implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)),
inference(subst,[],[refute_0_14:[bind(X,$fot(not(X_32884))),bind(Y,$fot(implies(or(X_5805,X_32884),X_5805)))]]) ).
cnf(refute_0_178,plain,
or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) = or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))),
introduced(tautology,[refl,[$fot(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))))]]) ).
cnf(refute_0_179,plain,
( or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) != or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))
| or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)) != implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))
| or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) = or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))),or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))) ),[1,1],$fot(implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))]]) ).
cnf(refute_0_180,plain,
( or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)) != implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))
| or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) = or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))) ),
inference(resolve,[$cnf( $equal(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))),or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) = or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))),
inference(resolve,[$cnf( $equal(or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)),implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
( or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))) != or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))
| ~ theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))))
| theorem(or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))) ),[0],$fot(or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805))))]]) ).
cnf(refute_0_183,plain,
( ~ theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))))
| theorem(or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))) ),
inference(resolve,[$cnf( $equal(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805))),or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
theorem(or(X_41518,implies(not(X_32884),implies(or(X_5805,X_32884),X_5805)))),
inference(resolve,[$cnf( theorem(or(X_41518,or(not(not(X_32884)),implies(or(X_5805,X_32884),X_5805)))) )],[refute_0_176,refute_0_183]) ).
cnf(refute_0_185,plain,
theorem(or(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)),implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)))),
inference(subst,[],[refute_0_184:[bind(X_32884,$fot(X_41524)),bind(X_41518,$fot(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)))),bind(X_5805,$fot(X_41526))]]) ).
cnf(refute_0_186,plain,
theorem(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526))),
inference(resolve,[$cnf( theorem(or(implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)),implies(not(X_41524),implies(or(X_41526,X_41524),X_41526)))) )],[refute_0_185,refute_0_50]) ).
cnf(refute_0_187,plain,
theorem(implies(not(X_41527),implies(or(X_41528,X_41527),X_41528))),
inference(subst,[],[refute_0_186:[bind(X_41524,$fot(X_41527)),bind(X_41526,$fot(X_41528))]]) ).
cnf(refute_0_188,plain,
theorem(implies(or(X_41528,X_41527),implies(not(X_41527),X_41528))),
inference(resolve,[$cnf( theorem(implies(not(X_41527),implies(or(X_41528,X_41527),X_41528))) )],[refute_0_187,refute_0_44]) ).
cnf(refute_0_189,plain,
theorem(implies(or(not(X),X_41602),implies(not(X_41602),not(X)))),
inference(subst,[],[refute_0_188:[bind(X_41527,$fot(X_41602)),bind(X_41528,$fot(not(X)))]]) ).
cnf(refute_0_190,plain,
implies(X,X_41602) = or(not(X),X_41602),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_41602))]]) ).
cnf(refute_0_191,plain,
( implies(X,X_41602) != or(not(X),X_41602)
| or(not(X),X_41602) = implies(X,X_41602) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_41602))),bind(Y0,$fot(or(not(X),X_41602)))]]) ).
cnf(refute_0_192,plain,
or(not(X),X_41602) = implies(X,X_41602),
inference(resolve,[$cnf( $equal(implies(X,X_41602),or(not(X),X_41602)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
( or(not(X),X_41602) != implies(X,X_41602)
| ~ theorem(implies(or(not(X),X_41602),implies(not(X_41602),not(X))))
| theorem(implies(implies(X,X_41602),implies(not(X_41602),not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_41602),implies(not(X_41602),not(X)))) ),[0,0],$fot(implies(X,X_41602))]]) ).
cnf(refute_0_194,plain,
( ~ theorem(implies(or(not(X),X_41602),implies(not(X_41602),not(X))))
| theorem(implies(implies(X,X_41602),implies(not(X_41602),not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_41602),implies(X,X_41602)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
theorem(implies(implies(X,X_41602),implies(not(X_41602),not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_41602),implies(not(X_41602),not(X)))) )],[refute_0_189,refute_0_194]) ).
cnf(refute_0_196,plain,
theorem(implies(implies(p,q),implies(not(q),not(p)))),
inference(subst,[],[refute_0_195:[bind(X,$fot(p)),bind(X_41602,$fot(q))]]) ).
cnf(refute_0_197,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(p,q),implies(not(q),not(p)))) )],[refute_0_196,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL182-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 09:26:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 34.54/34.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.54/34.75
% 34.54/34.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.54/34.77
%------------------------------------------------------------------------------