TSTP Solution File: LCL238-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL238-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:51:00 EDT 2022
% Result : Unsatisfiable 13.65s 13.80s
% Output : CNFRefutation 13.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 51
% Syntax : Number of clauses : 225 ( 119 unt; 0 nHn; 102 RR)
% Number of literals : 371 ( 171 equ; 147 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; 2 con; 0-2 aty)
% Number of variables : 496 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_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(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(and(p,q),and(q,p))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(and(X_16298,X_16299),not(and(X_16299,X_16298))))
| theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(and(X_16298,X_16299))),bind(X_8,$fot(not(and(X_16299,X_16298))))]]) ).
cnf(refute_0_6,plain,
theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))),
inference(subst,[],[refute_0_2:[bind(X_8,$fot(not(X_11)))]]) ).
cnf(refute_0_7,plain,
implies(X_11,X_7) = or(not(X_11),X_7),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(X_11,X_7) != or(not(X_11),X_7)
| or(not(X_11),X_7) = implies(X_11,X_7) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X_11,X_7))),bind(Y0,$fot(or(not(X_11),X_7)))]]) ).
cnf(refute_0_12,plain,
or(not(X_11),X_7) = implies(X_11,X_7),
inference(resolve,[$cnf( $equal(implies(X_11,X_7),or(not(X_11),X_7)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( or(not(X_11),X_7) != implies(X_11,X_7)
| ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) ),[0,1],$fot(implies(X_11,X_7))]]) ).
cnf(refute_0_14,plain,
( ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_7),implies(X_11,X_7)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(implies(X_4406,X_4407))
| ~ theorem(implies(implies(X_4406,X_4407),implies(X_4406,not(not(X_4407)))))
| theorem(implies(X_4406,not(not(X_4407)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_4406,not(not(X_4407))))),bind(Y,$fot(implies(X_4406,X_4407)))]]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(not(X),X_100))
| theorem(or(X_100,not(X))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(not(X))),bind(X_8,$fot(X_100))]]) ).
cnf(refute_0_18,plain,
implies(X,X_100) = or(not(X),X_100),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_100))]]) ).
cnf(refute_0_19,plain,
( implies(X,X_100) != or(not(X),X_100)
| or(not(X),X_100) = implies(X,X_100) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,X_100))),bind(Y0,$fot(or(not(X),X_100)))]]) ).
cnf(refute_0_20,plain,
or(not(X),X_100) = implies(X,X_100),
inference(resolve,[$cnf( $equal(implies(X,X_100),or(not(X),X_100)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( or(not(X),X_100) != implies(X,X_100)
| ~ theorem(implies(X,X_100))
| theorem(or(not(X),X_100)) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),X_100)) ),[0],$fot(implies(X,X_100))]]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(X,X_100))
| theorem(or(not(X),X_100)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_100),implies(X,X_100)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ theorem(implies(X,X_100))
| theorem(or(X_100,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),X_100)) )],[refute_0_22,refute_0_17]) ).
cnf(refute_0_24,plain,
( ~ theorem(implies(X_947,X_947))
| theorem(or(X_947,not(X_947))) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_947)),bind(X_100,$fot(X_947))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(X_101)
| ~ theorem(implies(X_101,and(X_101,X_101)))
| theorem(and(X_101,X_101)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_101,X_101))),bind(Y,$fot(X_101))]]) ).
cnf(refute_0_26,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_27,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_26]) ).
cnf(refute_0_28,plain,
theorem(implies(or(not(X_11),not(X_11)),not(X_11))),
inference(subst,[],[refute_0_27:[bind(A,$fot(not(X_11)))]]) ).
cnf(refute_0_29,plain,
implies(X_11,not(X_11)) = or(not(X_11),not(X_11)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(not(X_11)))]]) ).
cnf(refute_0_30,plain,
( implies(X_11,not(X_11)) != or(not(X_11),not(X_11))
| or(not(X_11),not(X_11)) = implies(X_11,not(X_11)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X_11,not(X_11)))),bind(Y0,$fot(or(not(X_11),not(X_11))))]]) ).
cnf(refute_0_31,plain,
or(not(X_11),not(X_11)) = implies(X_11,not(X_11)),
inference(resolve,[$cnf( $equal(implies(X_11,not(X_11)),or(not(X_11),not(X_11))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( or(not(X_11),not(X_11)) != implies(X_11,not(X_11))
| ~ theorem(implies(or(not(X_11),not(X_11)),not(X_11)))
| theorem(implies(implies(X_11,not(X_11)),not(X_11))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),not(X_11)),not(X_11))) ),[0,0],$fot(implies(X_11,not(X_11)))]]) ).
cnf(refute_0_33,plain,
( ~ theorem(implies(or(not(X_11),not(X_11)),not(X_11)))
| theorem(implies(implies(X_11,not(X_11)),not(X_11))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(X_11)),implies(X_11,not(X_11))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
theorem(implies(implies(X_11,not(X_11)),not(X_11))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),not(X_11)),not(X_11))) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(X_23,not(X_24)),Y) = or(not(implies(X_23,not(X_24))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_23,not(X_24))))]]) ).
cnf(refute_0_36,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_37,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_36]) ).
cnf(refute_0_38,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_37:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_39,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_40,plain,
( not(or(not(P),not(Q))) != not(or(not(P),not(Q)))
| or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) ),[1,0],$fot(implies(P,not(Q)))]]) ).
cnf(refute_0_41,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_44,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_44]) ).
cnf(refute_0_46,plain,
and(X_23,X_24) = not(implies(X_23,not(X_24))),
inference(subst,[],[refute_0_45:[bind(P,$fot(X_23)),bind(Q,$fot(X_24))]]) ).
cnf(refute_0_47,plain,
( and(X_23,X_24) != not(implies(X_23,not(X_24)))
| not(implies(X_23,not(X_24))) = and(X_23,X_24) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(and(X_23,X_24))),bind(Y0,$fot(not(implies(X_23,not(X_24)))))]]) ).
cnf(refute_0_48,plain,
not(implies(X_23,not(X_24))) = and(X_23,X_24),
inference(resolve,[$cnf( $equal(and(X_23,X_24),not(implies(X_23,not(X_24)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( implies(implies(X_23,not(X_24)),Y) != or(not(implies(X_23,not(X_24))),Y)
| not(implies(X_23,not(X_24))) != and(X_23,X_24)
| implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_23,not(X_24)),Y),or(not(implies(X_23,not(X_24))),Y)) ),[1,0],$fot(and(X_23,X_24))]]) ).
cnf(refute_0_50,plain,
( implies(implies(X_23,not(X_24)),Y) != or(not(implies(X_23,not(X_24))),Y)
| implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_23,not(X_24))),and(X_23,X_24)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_23,not(X_24)),Y),or(not(implies(X_23,not(X_24))),Y)) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(implies(X_11,not(X_11)),not(X_11)) = or(and(X_11,X_11),not(X_11)),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(X_11))),bind(X_23,$fot(X_11)),bind(X_24,$fot(X_11))]]) ).
cnf(refute_0_53,plain,
( implies(implies(X_11,not(X_11)),not(X_11)) != or(and(X_11,X_11),not(X_11))
| ~ theorem(implies(implies(X_11,not(X_11)),not(X_11)))
| theorem(or(and(X_11,X_11),not(X_11))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_11,not(X_11)),not(X_11))) ),[0],$fot(or(and(X_11,X_11),not(X_11)))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(implies(X_11,not(X_11)),not(X_11)))
| theorem(or(and(X_11,X_11),not(X_11))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_11,not(X_11)),not(X_11)),or(and(X_11,X_11),not(X_11))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(or(and(X_11,X_11),not(X_11))),
inference(resolve,[$cnf( theorem(implies(implies(X_11,not(X_11)),not(X_11))) )],[refute_0_34,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ theorem(or(and(X_11,X_11),not(X_11)))
| theorem(or(not(X_11),and(X_11,X_11))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(and(X_11,X_11))),bind(X_8,$fot(not(X_11)))]]) ).
cnf(refute_0_57,plain,
theorem(or(not(X_11),and(X_11,X_11))),
inference(resolve,[$cnf( theorem(or(and(X_11,X_11),not(X_11))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
or(not(X_11),and(X_11,X_11)) = implies(X_11,and(X_11,X_11)),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_11)),bind(Y,$fot(and(X_11,X_11)))]]) ).
cnf(refute_0_59,plain,
( or(not(X_11),and(X_11,X_11)) != implies(X_11,and(X_11,X_11))
| ~ theorem(or(not(X_11),and(X_11,X_11)))
| theorem(implies(X_11,and(X_11,X_11))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_11),and(X_11,X_11))) ),[0],$fot(implies(X_11,and(X_11,X_11)))]]) ).
cnf(refute_0_60,plain,
( ~ theorem(or(not(X_11),and(X_11,X_11)))
| theorem(implies(X_11,and(X_11,X_11))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),and(X_11,X_11)),implies(X_11,and(X_11,X_11))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
theorem(implies(X_11,and(X_11,X_11))),
inference(resolve,[$cnf( theorem(or(not(X_11),and(X_11,X_11))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
theorem(implies(X_101,and(X_101,X_101))),
inference(subst,[],[refute_0_61:[bind(X_11,$fot(X_101))]]) ).
cnf(refute_0_63,plain,
( ~ theorem(X_101)
| theorem(and(X_101,X_101)) ),
inference(resolve,[$cnf( theorem(implies(X_101,and(X_101,X_101))) )],[refute_0_62,refute_0_25]) ).
cnf(refute_0_64,plain,
( ~ theorem(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))))
| theorem(and(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))),implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))))) ),
inference(subst,[],[refute_0_63:[bind(X_101,$fot(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153)))))]]) ).
cnf(refute_0_65,plain,
( ~ axiom(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43))))
| theorem(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43)))))]]) ).
cnf(refute_0_66,plain,
axiom(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_41)),bind(B,$fot(X_42)),bind(C,$fot(X_43))]]) ).
cnf(refute_0_67,plain,
theorem(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43)))),
inference(resolve,[$cnf( axiom(implies(or(X_41,or(X_42,X_43)),or(X_42,or(X_41,X_43)))) )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
theorem(implies(or(X_47,or(not(X),X_49)),or(not(X),or(X_47,X_49)))),
inference(subst,[],[refute_0_67:[bind(X_41,$fot(X_47)),bind(X_42,$fot(not(X))),bind(X_43,$fot(X_49))]]) ).
cnf(refute_0_69,plain,
implies(X,or(X_47,X_49)) = or(not(X),or(X_47,X_49)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_47,X_49)))]]) ).
cnf(refute_0_70,plain,
( implies(X,or(X_47,X_49)) != or(not(X),or(X_47,X_49))
| or(not(X),or(X_47,X_49)) = implies(X,or(X_47,X_49)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,or(X_47,X_49)))),bind(Y0,$fot(or(not(X),or(X_47,X_49))))]]) ).
cnf(refute_0_71,plain,
or(not(X),or(X_47,X_49)) = implies(X,or(X_47,X_49)),
inference(resolve,[$cnf( $equal(implies(X,or(X_47,X_49)),or(not(X),or(X_47,X_49))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( or(not(X),or(X_47,X_49)) != implies(X,or(X_47,X_49))
| ~ theorem(implies(or(X_47,or(not(X),X_49)),or(not(X),or(X_47,X_49))))
| theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_47,or(not(X),X_49)),or(not(X),or(X_47,X_49)))) ),[0,1],$fot(implies(X,or(X_47,X_49)))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(implies(or(X_47,or(not(X),X_49)),or(not(X),or(X_47,X_49))))
| theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_47,X_49)),implies(X,or(X_47,X_49))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))),
inference(resolve,[$cnf( theorem(implies(or(X_47,or(not(X),X_49)),or(not(X),or(X_47,X_49)))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
or(not(X),X_49) = implies(X,X_49),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_49))]]) ).
cnf(refute_0_76,plain,
or(X_47,or(not(X),X_49)) = or(X_47,or(not(X),X_49)),
introduced(tautology,[refl,[$fot(or(X_47,or(not(X),X_49)))]]) ).
cnf(refute_0_77,plain,
( or(X_47,or(not(X),X_49)) != or(X_47,or(not(X),X_49))
| or(not(X),X_49) != implies(X,X_49)
| or(X_47,or(not(X),X_49)) = or(X_47,implies(X,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_47,or(not(X),X_49)),or(X_47,or(not(X),X_49))) ),[1,1],$fot(implies(X,X_49))]]) ).
cnf(refute_0_78,plain,
( or(not(X),X_49) != implies(X,X_49)
| or(X_47,or(not(X),X_49)) = or(X_47,implies(X,X_49)) ),
inference(resolve,[$cnf( $equal(or(X_47,or(not(X),X_49)),or(X_47,or(not(X),X_49))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
or(X_47,or(not(X),X_49)) = or(X_47,implies(X,X_49)),
inference(resolve,[$cnf( $equal(or(not(X),X_49),implies(X,X_49)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) = implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))),
introduced(tautology,[refl,[$fot(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))))]]) ).
cnf(refute_0_81,plain,
( implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) != implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))
| or(X_47,or(not(X),X_49)) != or(X_47,implies(X,X_49))
| implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) = implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))),implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) ),[1,0],$fot(or(X_47,implies(X,X_49)))]]) ).
cnf(refute_0_82,plain,
( or(X_47,or(not(X),X_49)) != or(X_47,implies(X,X_49))
| implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) = implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49))) ),
inference(resolve,[$cnf( $equal(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))),implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) = implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49))),
inference(resolve,[$cnf( $equal(or(X_47,or(not(X),X_49)),or(X_47,implies(X,X_49))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))) != implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49)))
| ~ theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))))
| theorem(implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) ),[0],$fot(implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49))))]]) ).
cnf(refute_0_85,plain,
( ~ theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))))
| theorem(implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49))),implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(implies(or(X_47,implies(X,X_49)),implies(X,or(X_47,X_49)))),
inference(resolve,[$cnf( theorem(implies(or(X_47,or(not(X),X_49)),implies(X,or(X_47,X_49)))) )],[refute_0_74,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153)))),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_151)),bind(X_47,$fot(X_152)),bind(X_49,$fot(X_153))]]) ).
cnf(refute_0_88,plain,
theorem(and(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))),implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))))),
inference(resolve,[$cnf( theorem(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153)))) )],[refute_0_87,refute_0_64]) ).
cnf(refute_0_89,plain,
( ~ theorem(X_627)
| ~ theorem(implies(X_627,implies(X_628,X_628)))
| theorem(implies(X_628,X_628)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_628,X_628))),bind(Y,$fot(X_627))]]) ).
cnf(refute_0_90,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,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_91,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_92,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_91,refute_0_90]) ).
cnf(refute_0_93,plain,
theorem(implies(X_3,or(not(X_11),X_3))),
inference(subst,[],[refute_0_92:[bind(X_4,$fot(not(X_11)))]]) ).
cnf(refute_0_94,plain,
implies(X_11,X_3) = or(not(X_11),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_95,plain,
( implies(X_11,X_3) != or(not(X_11),X_3)
| or(not(X_11),X_3) = implies(X_11,X_3) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X_11,X_3))),bind(Y0,$fot(or(not(X_11),X_3)))]]) ).
cnf(refute_0_96,plain,
or(not(X_11),X_3) = implies(X_11,X_3),
inference(resolve,[$cnf( $equal(implies(X_11,X_3),or(not(X_11),X_3)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( or(not(X_11),X_3) != implies(X_11,X_3)
| ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) ),[0,1],$fot(implies(X_11,X_3))]]) ).
cnf(refute_0_98,plain,
( ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_3),implies(X_11,X_3)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
theorem(implies(X_3,implies(X_11,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
theorem(implies(X_626,implies(X_624,X_626))),
inference(subst,[],[refute_0_99:[bind(X_11,$fot(X_624)),bind(X_3,$fot(X_626))]]) ).
cnf(refute_0_101,plain,
( ~ axiom(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55))))
| theorem(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))))]]) ).
cnf(refute_0_102,plain,
axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,or(not(X),X_43)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_42)),bind(C,$fot(X_43))]]) ).
cnf(refute_0_103,plain,
implies(X,X_43) = or(not(X),X_43),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_104,plain,
( implies(X,X_43) != or(not(X),X_43)
| or(not(X),X_43) = implies(X,X_43) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,X_43))),bind(Y0,$fot(or(not(X),X_43)))]]) ).
cnf(refute_0_105,plain,
or(not(X),X_43) = implies(X,X_43),
inference(resolve,[$cnf( $equal(implies(X,X_43),or(not(X),X_43)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( or(not(X),X_43) != implies(X,X_43)
| ~ axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,or(not(X),X_43))))
| axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,or(not(X),X_43)))) ),[0,1,1],$fot(implies(X,X_43))]]) ).
cnf(refute_0_107,plain,
( ~ axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,or(not(X),X_43))))
| axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_43),implies(X,X_43)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,or(not(X),X_43)))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
or(not(X),or(X_42,X_43)) = implies(X,or(X_42,X_43)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(or(X_42,X_43)))]]) ).
cnf(refute_0_110,plain,
implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) = implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))))]]) ).
cnf(refute_0_111,plain,
( implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) != implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))
| or(not(X),or(X_42,X_43)) != implies(X,or(X_42,X_43))
| implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) = implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))),implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),[1,0],$fot(implies(X,or(X_42,X_43)))]]) ).
cnf(refute_0_112,plain,
( or(not(X),or(X_42,X_43)) != implies(X,or(X_42,X_43))
| implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) = implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))),implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) = implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_42,X_43)),implies(X,or(X_42,X_43))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))) != implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43)))
| ~ axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))))
| axiom(implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),[0],$fot(implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43))))]]) ).
cnf(refute_0_115,plain,
( ~ axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))))
| axiom(implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43))),implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
axiom(implies(implies(X,or(X_42,X_43)),or(X_42,implies(X,X_43)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_42,X_43)),or(X_42,implies(X,X_43)))) )],[refute_0_108,refute_0_115]) ).
cnf(refute_0_117,plain,
axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))),
inference(subst,[],[refute_0_116:[bind(X,$fot(X_44)),bind(X_42,$fot(not(X))),bind(X_43,$fot(X_46))]]) ).
cnf(refute_0_118,plain,
implies(X,implies(X_44,X_46)) = or(not(X),implies(X_44,X_46)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_44,X_46)))]]) ).
cnf(refute_0_119,plain,
( implies(X,implies(X_44,X_46)) != or(not(X),implies(X_44,X_46))
| or(not(X),implies(X_44,X_46)) = implies(X,implies(X_44,X_46)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,implies(X_44,X_46)))),bind(Y0,$fot(or(not(X),implies(X_44,X_46))))]]) ).
cnf(refute_0_120,plain,
or(not(X),implies(X_44,X_46)) = implies(X,implies(X_44,X_46)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_44,X_46)),or(not(X),implies(X_44,X_46))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( or(not(X),implies(X_44,X_46)) != implies(X,implies(X_44,X_46))
| ~ axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46))))
| axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))) ),[0,1],$fot(implies(X,implies(X_44,X_46)))]]) ).
cnf(refute_0_122,plain,
( ~ axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46))))
| axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_44,X_46)),implies(X,implies(X_44,X_46))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))),
inference(resolve,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
or(not(X),X_46) = implies(X,X_46),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_125,plain,
implies(X_44,or(not(X),X_46)) = implies(X_44,or(not(X),X_46)),
introduced(tautology,[refl,[$fot(implies(X_44,or(not(X),X_46)))]]) ).
cnf(refute_0_126,plain,
( implies(X_44,or(not(X),X_46)) != implies(X_44,or(not(X),X_46))
| or(not(X),X_46) != implies(X,X_46)
| implies(X_44,or(not(X),X_46)) = implies(X_44,implies(X,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_44,or(not(X),X_46)),implies(X_44,or(not(X),X_46))) ),[1,1],$fot(implies(X,X_46))]]) ).
cnf(refute_0_127,plain,
( or(not(X),X_46) != implies(X,X_46)
| implies(X_44,or(not(X),X_46)) = implies(X_44,implies(X,X_46)) ),
inference(resolve,[$cnf( $equal(implies(X_44,or(not(X),X_46)),implies(X_44,or(not(X),X_46))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(X_44,or(not(X),X_46)) = implies(X_44,implies(X,X_46)),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),
introduced(tautology,[refl,[$fot(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))]]) ).
cnf(refute_0_130,plain,
( implies(X_44,or(not(X),X_46)) != implies(X_44,implies(X,X_46))
| implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) != implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))
| implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),[1,0],$fot(implies(X_44,implies(X,X_46)))]]) ).
cnf(refute_0_131,plain,
( implies(X_44,or(not(X),X_46)) != implies(X_44,implies(X,X_46))
| implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))),
inference(resolve,[$cnf( $equal(implies(X_44,or(not(X),X_46)),implies(X_44,implies(X,X_46))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) != implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))
| ~ axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))
| axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),[0],$fot(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))))]]) ).
cnf(refute_0_134,plain,
( ~ axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))
| axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))),
inference(resolve,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_123,refute_0_134]) ).
cnf(refute_0_136,plain,
axiom(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))),
inference(subst,[],[refute_0_135:[bind(X,$fot(X_53)),bind(X_44,$fot(X_54)),bind(X_46,$fot(X_55))]]) ).
cnf(refute_0_137,plain,
theorem(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))),
inference(resolve,[$cnf( axiom(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))) )],[refute_0_136,refute_0_101]) ).
cnf(refute_0_138,plain,
( ~ theorem(implies(X_54,implies(X_53,X_55)))
| ~ theorem(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55))))
| theorem(implies(X_53,implies(X_54,X_55))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_53,implies(X_54,X_55)))),bind(Y,$fot(implies(X_54,implies(X_53,X_55))))]]) ).
cnf(refute_0_139,plain,
( ~ theorem(implies(X_54,implies(X_53,X_55)))
| theorem(implies(X_53,implies(X_54,X_55))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_54,implies(X_53,X_55)),implies(X_53,implies(X_54,X_55)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ theorem(implies(X_626,implies(X_624,X_626)))
| theorem(implies(X_624,implies(X_626,X_626))) ),
inference(subst,[],[refute_0_139:[bind(X_53,$fot(X_624)),bind(X_54,$fot(X_626)),bind(X_55,$fot(X_626))]]) ).
cnf(refute_0_141,plain,
theorem(implies(X_624,implies(X_626,X_626))),
inference(resolve,[$cnf( theorem(implies(X_626,implies(X_624,X_626))) )],[refute_0_100,refute_0_140]) ).
cnf(refute_0_142,plain,
theorem(implies(X_627,implies(X_628,X_628))),
inference(subst,[],[refute_0_141:[bind(X_624,$fot(X_627)),bind(X_626,$fot(X_628))]]) ).
cnf(refute_0_143,plain,
( ~ theorem(X_627)
| theorem(implies(X_628,X_628)) ),
inference(resolve,[$cnf( theorem(implies(X_627,implies(X_628,X_628))) )],[refute_0_142,refute_0_89]) ).
cnf(refute_0_144,plain,
( ~ theorem(and(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))),implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153)))))
| theorem(implies(X_946,X_946)) ),
inference(subst,[],[refute_0_143:[bind(X_627,$fot(and(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))),implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153)))))),bind(X_628,$fot(X_946))]]) ).
cnf(refute_0_145,plain,
theorem(implies(X_946,X_946)),
inference(resolve,[$cnf( theorem(and(implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))),implies(or(X_152,implies(X_151,X_153)),implies(X_151,or(X_152,X_153))))) )],[refute_0_88,refute_0_144]) ).
cnf(refute_0_146,plain,
theorem(implies(X_947,X_947)),
inference(subst,[],[refute_0_145:[bind(X_946,$fot(X_947))]]) ).
cnf(refute_0_147,plain,
theorem(or(X_947,not(X_947))),
inference(resolve,[$cnf( theorem(implies(X_947,X_947)) )],[refute_0_146,refute_0_24]) ).
cnf(refute_0_148,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_147:[bind(X_947,$fot(not(X)))]]) ).
cnf(refute_0_149,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_150,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_151,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_153,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
theorem(implies(X_4396,not(not(X_4396)))),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_4396))]]) ).
cnf(refute_0_156,plain,
( ~ axiom(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39))))
| theorem(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39)))))]]) ).
cnf(refute_0_157,plain,
axiom(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_38)),bind(B,$fot(X_39)),bind(C,$fot(X_40))]]) ).
cnf(refute_0_158,plain,
theorem(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39)))),
inference(resolve,[$cnf( axiom(implies(implies(X_38,X_39),implies(or(X_40,X_38),or(X_40,X_39)))) )],[refute_0_157,refute_0_156]) ).
cnf(refute_0_159,plain,
theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),or(not(X),X_60)))),
inference(subst,[],[refute_0_158:[bind(X_38,$fot(X_59)),bind(X_39,$fot(X_60)),bind(X_40,$fot(not(X)))]]) ).
cnf(refute_0_160,plain,
implies(X,X_60) = or(not(X),X_60),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_60))]]) ).
cnf(refute_0_161,plain,
( implies(X,X_60) != or(not(X),X_60)
| or(not(X),X_60) = implies(X,X_60) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(implies(X,X_60))),bind(Y0,$fot(or(not(X),X_60)))]]) ).
cnf(refute_0_162,plain,
or(not(X),X_60) = implies(X,X_60),
inference(resolve,[$cnf( $equal(implies(X,X_60),or(not(X),X_60)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( or(not(X),X_60) != implies(X,X_60)
| ~ theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),or(not(X),X_60))))
| theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),or(not(X),X_60)))) ),[0,1,1],$fot(implies(X,X_60))]]) ).
cnf(refute_0_164,plain,
( ~ theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),or(not(X),X_60))))
| theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_60),implies(X,X_60)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),or(not(X),X_60)))) )],[refute_0_159,refute_0_164]) ).
cnf(refute_0_166,plain,
or(not(X),X_59) = implies(X,X_59),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_59))]]) ).
cnf(refute_0_167,plain,
implies(or(not(X),X_59),implies(X,X_60)) = implies(or(not(X),X_59),implies(X,X_60)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_59),implies(X,X_60)))]]) ).
cnf(refute_0_168,plain,
( implies(or(not(X),X_59),implies(X,X_60)) != implies(or(not(X),X_59),implies(X,X_60))
| or(not(X),X_59) != implies(X,X_59)
| implies(or(not(X),X_59),implies(X,X_60)) = implies(implies(X,X_59),implies(X,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_59),implies(X,X_60)),implies(or(not(X),X_59),implies(X,X_60))) ),[1,0],$fot(implies(X,X_59))]]) ).
cnf(refute_0_169,plain,
( or(not(X),X_59) != implies(X,X_59)
| implies(or(not(X),X_59),implies(X,X_60)) = implies(implies(X,X_59),implies(X,X_60)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_59),implies(X,X_60)),implies(or(not(X),X_59),implies(X,X_60))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
implies(or(not(X),X_59),implies(X,X_60)) = implies(implies(X,X_59),implies(X,X_60)),
inference(resolve,[$cnf( $equal(or(not(X),X_59),implies(X,X_59)) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) = implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))),
introduced(tautology,[refl,[$fot(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))))]]) ).
cnf(refute_0_172,plain,
( implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) != implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))
| implies(or(not(X),X_59),implies(X,X_60)) != implies(implies(X,X_59),implies(X,X_60))
| implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) = implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))),implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) ),[1,1],$fot(implies(implies(X,X_59),implies(X,X_60)))]]) ).
cnf(refute_0_173,plain,
( implies(or(not(X),X_59),implies(X,X_60)) != implies(implies(X,X_59),implies(X,X_60))
| implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) = implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))),implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) = implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_59),implies(X,X_60)),implies(implies(X,X_59),implies(X,X_60))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))) != implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))
| ~ theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))))
| theorem(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) ),[0],$fot(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60))))]]) ).
cnf(refute_0_176,plain,
( ~ theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))))
| theorem(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60))),implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
theorem(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_59,X_60),implies(or(not(X),X_59),implies(X,X_60)))) )],[refute_0_165,refute_0_176]) ).
cnf(refute_0_178,plain,
( ~ theorem(implies(X_59,X_60))
| ~ theorem(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60))))
| theorem(implies(implies(X,X_59),implies(X,X_60))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X,X_59),implies(X,X_60)))),bind(Y,$fot(implies(X_59,X_60)))]]) ).
cnf(refute_0_179,plain,
( ~ theorem(implies(X_59,X_60))
| theorem(implies(implies(X,X_59),implies(X,X_60))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_59,X_60),implies(implies(X,X_59),implies(X,X_60)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( ~ theorem(implies(X_4396,not(not(X_4396))))
| theorem(implies(implies(X_4395,X_4396),implies(X_4395,not(not(X_4396))))) ),
inference(subst,[],[refute_0_179:[bind(X,$fot(X_4395)),bind(X_59,$fot(X_4396)),bind(X_60,$fot(not(not(X_4396))))]]) ).
cnf(refute_0_181,plain,
theorem(implies(implies(X_4395,X_4396),implies(X_4395,not(not(X_4396))))),
inference(resolve,[$cnf( theorem(implies(X_4396,not(not(X_4396)))) )],[refute_0_155,refute_0_180]) ).
cnf(refute_0_182,plain,
theorem(implies(implies(X_4406,X_4407),implies(X_4406,not(not(X_4407))))),
inference(subst,[],[refute_0_181:[bind(X_4395,$fot(X_4406)),bind(X_4396,$fot(X_4407))]]) ).
cnf(refute_0_183,plain,
( ~ theorem(implies(X_4406,X_4407))
| theorem(implies(X_4406,not(not(X_4407)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_4406,X_4407),implies(X_4406,not(not(X_4407))))) )],[refute_0_182,refute_0_16]) ).
cnf(refute_0_184,plain,
( ~ theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7)))
| theorem(implies(or(X_7,not(X_11)),not(not(implies(X_11,X_7))))) ),
inference(subst,[],[refute_0_183:[bind(X_4406,$fot(or(X_7,not(X_11)))),bind(X_4407,$fot(implies(X_11,X_7)))]]) ).
cnf(refute_0_185,plain,
theorem(implies(or(X_7,not(X_11)),not(not(implies(X_11,X_7))))),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) )],[refute_0_15,refute_0_184]) ).
cnf(refute_0_186,plain,
theorem(implies(or(not(Q),not(X_16103)),not(not(implies(X_16103,not(Q)))))),
inference(subst,[],[refute_0_185:[bind(X_11,$fot(X_16103)),bind(X_7,$fot(not(Q)))]]) ).
cnf(refute_0_187,plain,
and(X_16103,Q) = not(implies(X_16103,not(Q))),
inference(subst,[],[refute_0_45:[bind(P,$fot(X_16103))]]) ).
cnf(refute_0_188,plain,
( and(X_16103,Q) != not(implies(X_16103,not(Q)))
| not(implies(X_16103,not(Q))) = and(X_16103,Q) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(and(X_16103,Q))),bind(Y0,$fot(not(implies(X_16103,not(Q)))))]]) ).
cnf(refute_0_189,plain,
not(implies(X_16103,not(Q))) = and(X_16103,Q),
inference(resolve,[$cnf( $equal(and(X_16103,Q),not(implies(X_16103,not(Q)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
( not(implies(X_16103,not(Q))) != and(X_16103,Q)
| ~ theorem(implies(or(not(Q),not(X_16103)),not(not(implies(X_16103,not(Q))))))
| theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(Q),not(X_16103)),not(not(implies(X_16103,not(Q)))))) ),[0,1,0],$fot(and(X_16103,Q))]]) ).
cnf(refute_0_191,plain,
( ~ theorem(implies(or(not(Q),not(X_16103)),not(not(implies(X_16103,not(Q))))))
| theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) ),
inference(resolve,[$cnf( $equal(not(implies(X_16103,not(Q))),and(X_16103,Q)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))),
inference(resolve,[$cnf( theorem(implies(or(not(Q),not(X_16103)),not(not(implies(X_16103,not(Q)))))) )],[refute_0_186,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(Q,not(X_16103)),not(and(X_16103,Q))) = or(and(Q,X_16103),not(and(X_16103,Q))),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(and(X_16103,Q)))),bind(X_23,$fot(Q)),bind(X_24,$fot(X_16103))]]) ).
cnf(refute_0_194,plain,
or(not(Q),not(X_16103)) = implies(Q,not(X_16103)),
inference(subst,[],[refute_0_37:[bind(X,$fot(Q)),bind(Y,$fot(not(X_16103)))]]) ).
cnf(refute_0_195,plain,
implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))),
introduced(tautology,[refl,[$fot(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))))]]) ).
cnf(refute_0_196,plain,
( implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) != implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))
| or(not(Q),not(X_16103)) != implies(Q,not(X_16103))
| implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = implies(implies(Q,not(X_16103)),not(and(X_16103,Q))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))),implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) ),[1,0],$fot(implies(Q,not(X_16103)))]]) ).
cnf(refute_0_197,plain,
( or(not(Q),not(X_16103)) != implies(Q,not(X_16103))
| implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = implies(implies(Q,not(X_16103)),not(and(X_16103,Q))) ),
inference(resolve,[$cnf( $equal(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))),implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = implies(implies(Q,not(X_16103)),not(and(X_16103,Q))),
inference(resolve,[$cnf( $equal(or(not(Q),not(X_16103)),implies(Q,not(X_16103))) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_200,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_10,refute_0_199]) ).
cnf(refute_0_201,plain,
( implies(implies(Q,not(X_16103)),not(and(X_16103,Q))) != or(and(Q,X_16103),not(and(X_16103,Q)))
| implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) != implies(implies(Q,not(X_16103)),not(and(X_16103,Q)))
| implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = or(and(Q,X_16103),not(and(X_16103,Q))) ),
inference(subst,[],[refute_0_200:[bind(X0,$fot(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))))),bind(Y0,$fot(implies(implies(Q,not(X_16103)),not(and(X_16103,Q))))),bind(Z,$fot(or(and(Q,X_16103),not(and(X_16103,Q)))))]]) ).
cnf(refute_0_202,plain,
( implies(implies(Q,not(X_16103)),not(and(X_16103,Q))) != or(and(Q,X_16103),not(and(X_16103,Q)))
| implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = or(and(Q,X_16103),not(and(X_16103,Q))) ),
inference(resolve,[$cnf( $equal(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))),implies(implies(Q,not(X_16103)),not(and(X_16103,Q)))) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) = or(and(Q,X_16103),not(and(X_16103,Q))),
inference(resolve,[$cnf( $equal(implies(implies(Q,not(X_16103)),not(and(X_16103,Q))),or(and(Q,X_16103),not(and(X_16103,Q)))) )],[refute_0_193,refute_0_202]) ).
cnf(refute_0_204,plain,
( implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))) != or(and(Q,X_16103),not(and(X_16103,Q)))
| ~ theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))))
| theorem(or(and(Q,X_16103),not(and(X_16103,Q)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) ),[0],$fot(or(and(Q,X_16103),not(and(X_16103,Q))))]]) ).
cnf(refute_0_205,plain,
( ~ theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))))
| theorem(or(and(Q,X_16103),not(and(X_16103,Q)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q))),or(and(Q,X_16103),not(and(X_16103,Q)))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
theorem(or(and(Q,X_16103),not(and(X_16103,Q)))),
inference(resolve,[$cnf( theorem(implies(or(not(Q),not(X_16103)),not(and(X_16103,Q)))) )],[refute_0_192,refute_0_205]) ).
cnf(refute_0_207,plain,
theorem(or(and(X_16298,X_16299),not(and(X_16299,X_16298)))),
inference(subst,[],[refute_0_206:[bind(Q,$fot(X_16298)),bind(X_16103,$fot(X_16299))]]) ).
cnf(refute_0_208,plain,
theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299))),
inference(resolve,[$cnf( theorem(or(and(X_16298,X_16299),not(and(X_16299,X_16298)))) )],[refute_0_207,refute_0_5]) ).
cnf(refute_0_209,plain,
or(not(and(X_16299,X_16298)),and(X_16298,X_16299)) = implies(and(X_16299,X_16298),and(X_16298,X_16299)),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(X_16299,X_16298))),bind(Y,$fot(and(X_16298,X_16299)))]]) ).
cnf(refute_0_210,plain,
( or(not(and(X_16299,X_16298)),and(X_16298,X_16299)) != implies(and(X_16299,X_16298),and(X_16298,X_16299))
| ~ theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299)))
| theorem(implies(and(X_16299,X_16298),and(X_16298,X_16299))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299))) ),[0],$fot(implies(and(X_16299,X_16298),and(X_16298,X_16299)))]]) ).
cnf(refute_0_211,plain,
( ~ theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299)))
| theorem(implies(and(X_16299,X_16298),and(X_16298,X_16299))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_16299,X_16298)),and(X_16298,X_16299)),implies(and(X_16299,X_16298),and(X_16298,X_16299))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
theorem(implies(and(X_16299,X_16298),and(X_16298,X_16299))),
inference(resolve,[$cnf( theorem(or(not(and(X_16299,X_16298)),and(X_16298,X_16299))) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
theorem(implies(and(p,q),and(q,p))),
inference(subst,[],[refute_0_212:[bind(X_16298,$fot(q)),bind(X_16299,$fot(p))]]) ).
cnf(refute_0_214,plain,
$false,
inference(resolve,[$cnf( theorem(implies(and(p,q),and(q,p))) )],[refute_0_213,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL238-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 3 15:53:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.65/13.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.65/13.80
% 13.65/13.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.65/13.82
%------------------------------------------------------------------------------