TSTP Solution File: LCL271-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL271-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:51:17 EDT 2022
% Result : Unsatisfiable 63.09s 63.33s
% Output : CNFRefutation 63.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 60
% Syntax : Number of clauses : 313 ( 163 unt; 0 nHn; 142 RR)
% Number of literals : 518 ( 202 equ; 206 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 606 ( 26 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(equivalent_defn,axiom,
equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ).
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(p,and(p,p))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(and(X_12089,X_12089),X_12089))
| ~ theorem(implies(implies(and(X_12089,X_12089),X_12089),equivalent(and(X_12089,X_12089),X_12089)))
| theorem(equivalent(and(X_12089,X_12089),X_12089)) ),
inference(subst,[],[rule_2:[bind(X,$fot(equivalent(and(X_12089,X_12089),X_12089))),bind(Y,$fot(implies(and(X_12089,X_12089),X_12089)))]]) ).
cnf(refute_0_1,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,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(X_13,X_14),or(X_14,X_13))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_13,X_14),or(X_14,X_13))),
inference(resolve,[$cnf( axiom(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
theorem(implies(or(X_17,not(X)),or(not(X),X_17))),
inference(subst,[],[refute_0_3:[bind(X_13,$fot(X_17)),bind(X_14,$fot(not(X)))]]) ).
cnf(refute_0_5,plain,
implies(X,X_17) = or(not(X),X_17),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_17))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( implies(X,X_17) != or(not(X),X_17)
| or(not(X),X_17) = implies(X,X_17) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_17))),bind(Y0,$fot(or(not(X),X_17)))]]) ).
cnf(refute_0_10,plain,
or(not(X),X_17) = implies(X,X_17),
inference(resolve,[$cnf( $equal(implies(X,X_17),or(not(X),X_17)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( or(not(X),X_17) != implies(X,X_17)
| ~ theorem(implies(or(X_17,not(X)),or(not(X),X_17)))
| theorem(implies(or(X_17,not(X)),implies(X,X_17))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_17,not(X)),or(not(X),X_17))) ),[0,1],$fot(implies(X,X_17))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(implies(or(X_17,not(X)),or(not(X),X_17)))
| theorem(implies(or(X_17,not(X)),implies(X,X_17))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_17),implies(X,X_17)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
theorem(implies(or(X_17,not(X)),implies(X,X_17))),
inference(resolve,[$cnf( theorem(implies(or(X_17,not(X)),or(not(X),X_17))) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ theorem(implies(or(X_17,not(X)),implies(X,X_17)))
| ~ theorem(or(X_17,not(X)))
| theorem(implies(X,X_17)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,X_17))),bind(Y,$fot(or(X_17,not(X))))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(X_17,not(X)))
| theorem(implies(X,X_17)) ),
inference(resolve,[$cnf( theorem(implies(or(X_17,not(X)),implies(X,X_17))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(not(X),not(X_98)))
| theorem(implies(X_98,not(X))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_98)),bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_17,plain,
implies(X,not(X_98)) = or(not(X),not(X_98)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_98)))]]) ).
cnf(refute_0_18,plain,
( implies(X,not(X_98)) != or(not(X),not(X_98))
| or(not(X),not(X_98)) = implies(X,not(X_98)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,not(X_98)))),bind(Y0,$fot(or(not(X),not(X_98))))]]) ).
cnf(refute_0_19,plain,
or(not(X),not(X_98)) = implies(X,not(X_98)),
inference(resolve,[$cnf( $equal(implies(X,not(X_98)),or(not(X),not(X_98))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( or(not(X),not(X_98)) != implies(X,not(X_98))
| ~ theorem(implies(X,not(X_98)))
| theorem(or(not(X),not(X_98))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),not(X_98))) ),[0],$fot(implies(X,not(X_98)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(X,not(X_98)))
| theorem(or(not(X),not(X_98))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_98)),implies(X,not(X_98))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(X,not(X_98)))
| theorem(implies(X_98,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),not(X_98))) )],[refute_0_21,refute_0_16]) ).
cnf(refute_0_23,plain,
( ~ theorem(implies(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))),not(X_98)))
| theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))]]) ).
cnf(refute_0_24,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_25,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(implies(or(not(X_5),not(X_5)),not(X_5))),
inference(subst,[],[refute_0_25:[bind(A,$fot(not(X_5)))]]) ).
cnf(refute_0_27,plain,
implies(X_5,not(X_5)) = or(not(X_5),not(X_5)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_5)),bind(Y,$fot(not(X_5)))]]) ).
cnf(refute_0_28,plain,
( implies(X_5,not(X_5)) != or(not(X_5),not(X_5))
| or(not(X_5),not(X_5)) = implies(X_5,not(X_5)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X_5,not(X_5)))),bind(Y0,$fot(or(not(X_5),not(X_5))))]]) ).
cnf(refute_0_29,plain,
or(not(X_5),not(X_5)) = implies(X_5,not(X_5)),
inference(resolve,[$cnf( $equal(implies(X_5,not(X_5)),or(not(X_5),not(X_5))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( or(not(X_5),not(X_5)) != implies(X_5,not(X_5))
| ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) ),[0,0],$fot(implies(X_5,not(X_5)))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),not(X_5)),implies(X_5,not(X_5))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
theorem(implies(implies(X_5,not(X_5)),not(X_5))),
inference(resolve,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(implies(X_19,not(X_20)),Y) = or(not(implies(X_19,not(X_20))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_19,not(X_20))))]]) ).
cnf(refute_0_34,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_35,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_34]) ).
cnf(refute_0_36,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_35:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_37,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_38,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_39,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_42,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_42]) ).
cnf(refute_0_44,plain,
and(X_19,X_20) = not(implies(X_19,not(X_20))),
inference(subst,[],[refute_0_43:[bind(P,$fot(X_19)),bind(Q,$fot(X_20))]]) ).
cnf(refute_0_45,plain,
( and(X_19,X_20) != not(implies(X_19,not(X_20)))
| not(implies(X_19,not(X_20))) = and(X_19,X_20) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(and(X_19,X_20))),bind(Y0,$fot(not(implies(X_19,not(X_20)))))]]) ).
cnf(refute_0_46,plain,
not(implies(X_19,not(X_20))) = and(X_19,X_20),
inference(resolve,[$cnf( $equal(and(X_19,X_20),not(implies(X_19,not(X_20)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( implies(implies(X_19,not(X_20)),Y) != or(not(implies(X_19,not(X_20))),Y)
| not(implies(X_19,not(X_20))) != and(X_19,X_20)
| implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_19,not(X_20)),Y),or(not(implies(X_19,not(X_20))),Y)) ),[1,0],$fot(and(X_19,X_20))]]) ).
cnf(refute_0_48,plain,
( implies(implies(X_19,not(X_20)),Y) != or(not(implies(X_19,not(X_20))),Y)
| implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_19,not(X_20))),and(X_19,X_20)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_19,not(X_20)),Y),or(not(implies(X_19,not(X_20))),Y)) )],[refute_0_33,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(implies(X_5,not(X_5)),not(X_5)) = or(and(X_5,X_5),not(X_5)),
inference(subst,[],[refute_0_49:[bind(Y,$fot(not(X_5))),bind(X_19,$fot(X_5)),bind(X_20,$fot(X_5))]]) ).
cnf(refute_0_51,plain,
( implies(implies(X_5,not(X_5)),not(X_5)) != or(and(X_5,X_5),not(X_5))
| ~ theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| theorem(or(and(X_5,X_5),not(X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),[0],$fot(or(and(X_5,X_5),not(X_5)))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| theorem(or(and(X_5,X_5),not(X_5))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_5,not(X_5)),not(X_5)),or(and(X_5,X_5),not(X_5))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(or(and(X_5,X_5),not(X_5))),
inference(resolve,[$cnf( theorem(implies(implies(X_5,not(X_5)),not(X_5))) )],[refute_0_32,refute_0_52]) ).
cnf(refute_0_54,plain,
theorem(or(and(X_98,X_98),not(X_98))),
inference(subst,[],[refute_0_53:[bind(X_5,$fot(X_98))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(or(and(X_98,X_98),not(X_98)))
| theorem(implies(X_98,and(X_98,X_98))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_98)),bind(X_17,$fot(and(X_98,X_98)))]]) ).
cnf(refute_0_56,plain,
theorem(implies(X_98,and(X_98,X_98))),
inference(resolve,[$cnf( theorem(or(and(X_98,X_98),not(X_98))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ theorem(X_1037)
| ~ theorem(implies(X_1037,implies(or(X_1038,not(X_1037)),X_1038)))
| theorem(implies(or(X_1038,not(X_1037)),X_1038)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_1038,not(X_1037)),X_1038))),bind(Y,$fot(X_1037))]]) ).
cnf(refute_0_58,plain,
theorem(implies(or(X_1015,not(X_1014)),implies(X_1014,X_1015))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_1014)),bind(X_17,$fot(X_1015))]]) ).
cnf(refute_0_59,plain,
( ~ axiom(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57))))
| theorem(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))))]]) ).
cnf(refute_0_60,plain,
axiom(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_55)),bind(B,$fot(X_56)),bind(C,$fot(X_57))]]) ).
cnf(refute_0_61,plain,
theorem(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))),
inference(resolve,[$cnf( axiom(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
theorem(implies(or(X_77,or(not(X),X_79)),or(not(X),or(X_77,X_79)))),
inference(subst,[],[refute_0_61:[bind(X_55,$fot(X_77)),bind(X_56,$fot(not(X))),bind(X_57,$fot(X_79))]]) ).
cnf(refute_0_63,plain,
implies(X,or(X_77,X_79)) = or(not(X),or(X_77,X_79)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_77,X_79)))]]) ).
cnf(refute_0_64,plain,
( implies(X,or(X_77,X_79)) != or(not(X),or(X_77,X_79))
| or(not(X),or(X_77,X_79)) = implies(X,or(X_77,X_79)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,or(X_77,X_79)))),bind(Y0,$fot(or(not(X),or(X_77,X_79))))]]) ).
cnf(refute_0_65,plain,
or(not(X),or(X_77,X_79)) = implies(X,or(X_77,X_79)),
inference(resolve,[$cnf( $equal(implies(X,or(X_77,X_79)),or(not(X),or(X_77,X_79))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( or(not(X),or(X_77,X_79)) != implies(X,or(X_77,X_79))
| ~ theorem(implies(or(X_77,or(not(X),X_79)),or(not(X),or(X_77,X_79))))
| theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_77,or(not(X),X_79)),or(not(X),or(X_77,X_79)))) ),[0,1],$fot(implies(X,or(X_77,X_79)))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(implies(or(X_77,or(not(X),X_79)),or(not(X),or(X_77,X_79))))
| theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_77,X_79)),implies(X,or(X_77,X_79))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))),
inference(resolve,[$cnf( theorem(implies(or(X_77,or(not(X),X_79)),or(not(X),or(X_77,X_79)))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
or(not(X),X_79) = implies(X,X_79),
inference(subst,[],[refute_0_35:[bind(Y,$fot(X_79))]]) ).
cnf(refute_0_70,plain,
or(X_77,or(not(X),X_79)) = or(X_77,or(not(X),X_79)),
introduced(tautology,[refl,[$fot(or(X_77,or(not(X),X_79)))]]) ).
cnf(refute_0_71,plain,
( or(X_77,or(not(X),X_79)) != or(X_77,or(not(X),X_79))
| or(not(X),X_79) != implies(X,X_79)
| or(X_77,or(not(X),X_79)) = or(X_77,implies(X,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_77,or(not(X),X_79)),or(X_77,or(not(X),X_79))) ),[1,1],$fot(implies(X,X_79))]]) ).
cnf(refute_0_72,plain,
( or(not(X),X_79) != implies(X,X_79)
| or(X_77,or(not(X),X_79)) = or(X_77,implies(X,X_79)) ),
inference(resolve,[$cnf( $equal(or(X_77,or(not(X),X_79)),or(X_77,or(not(X),X_79))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
or(X_77,or(not(X),X_79)) = or(X_77,implies(X,X_79)),
inference(resolve,[$cnf( $equal(or(not(X),X_79),implies(X,X_79)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) = implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))),
introduced(tautology,[refl,[$fot(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))))]]) ).
cnf(refute_0_75,plain,
( implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) != implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))
| or(X_77,or(not(X),X_79)) != or(X_77,implies(X,X_79))
| implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) = implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))),implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) ),[1,0],$fot(or(X_77,implies(X,X_79)))]]) ).
cnf(refute_0_76,plain,
( or(X_77,or(not(X),X_79)) != or(X_77,implies(X,X_79))
| implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) = implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79))) ),
inference(resolve,[$cnf( $equal(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))),implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) = implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79))),
inference(resolve,[$cnf( $equal(or(X_77,or(not(X),X_79)),or(X_77,implies(X,X_79))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))) != implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79)))
| ~ theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))))
| theorem(implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) ),[0],$fot(implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79))))]]) ).
cnf(refute_0_79,plain,
( ~ theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))))
| theorem(implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79))),implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
theorem(implies(or(X_77,implies(X,X_79)),implies(X,or(X_77,X_79)))),
inference(resolve,[$cnf( theorem(implies(or(X_77,or(not(X),X_79)),implies(X,or(X_77,X_79)))) )],[refute_0_68,refute_0_79]) ).
cnf(refute_0_81,plain,
theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,or(not(X),X_85)))),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_83)),bind(X_77,$fot(not(X))),bind(X_79,$fot(X_85))]]) ).
cnf(refute_0_82,plain,
implies(X,X_85) = or(not(X),X_85),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_85))]]) ).
cnf(refute_0_83,plain,
( implies(X,X_85) != or(not(X),X_85)
| or(not(X),X_85) = implies(X,X_85) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_85))),bind(Y0,$fot(or(not(X),X_85)))]]) ).
cnf(refute_0_84,plain,
or(not(X),X_85) = implies(X,X_85),
inference(resolve,[$cnf( $equal(implies(X,X_85),or(not(X),X_85)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( or(not(X),X_85) != implies(X,X_85)
| ~ theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,or(not(X),X_85))))
| theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,or(not(X),X_85)))) ),[0,1,1],$fot(implies(X,X_85))]]) ).
cnf(refute_0_86,plain,
( ~ theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,or(not(X),X_85))))
| theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_85),implies(X,X_85)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,or(not(X),X_85)))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
or(not(X),implies(X_83,X_85)) = implies(X,implies(X_83,X_85)),
inference(subst,[],[refute_0_35:[bind(Y,$fot(implies(X_83,X_85)))]]) ).
cnf(refute_0_89,plain,
implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) = implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))))]]) ).
cnf(refute_0_90,plain,
( implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) != implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))
| or(not(X),implies(X_83,X_85)) != implies(X,implies(X_83,X_85))
| implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) = implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))),implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),[1,0],$fot(implies(X,implies(X_83,X_85)))]]) ).
cnf(refute_0_91,plain,
( or(not(X),implies(X_83,X_85)) != implies(X,implies(X_83,X_85))
| implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) = implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))),implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) = implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_83,X_85)),implies(X,implies(X_83,X_85))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))) != implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))
| ~ theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))))
| theorem(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),[0],$fot(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85))))]]) ).
cnf(refute_0_94,plain,
( ~ theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))))
| theorem(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85))),implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) )],[refute_0_87,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ theorem(implies(X,implies(X_83,X_85)))
| ~ theorem(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85))))
| theorem(implies(X_83,implies(X,X_85))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_83,implies(X,X_85)))),bind(Y,$fot(implies(X,implies(X_83,X_85))))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(implies(X,implies(X_83,X_85)))
| theorem(implies(X_83,implies(X,X_85))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_83,X_85)),implies(X_83,implies(X,X_85)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ theorem(implies(or(X_1015,not(X_1014)),implies(X_1014,X_1015)))
| theorem(implies(X_1014,implies(or(X_1015,not(X_1014)),X_1015))) ),
inference(subst,[],[refute_0_97:[bind(X,$fot(or(X_1015,not(X_1014)))),bind(X_83,$fot(X_1014)),bind(X_85,$fot(X_1015))]]) ).
cnf(refute_0_99,plain,
theorem(implies(X_1014,implies(or(X_1015,not(X_1014)),X_1015))),
inference(resolve,[$cnf( theorem(implies(or(X_1015,not(X_1014)),implies(X_1014,X_1015))) )],[refute_0_58,refute_0_98]) ).
cnf(refute_0_100,plain,
theorem(implies(X_1037,implies(or(X_1038,not(X_1037)),X_1038))),
inference(subst,[],[refute_0_99:[bind(X_1014,$fot(X_1037)),bind(X_1015,$fot(X_1038))]]) ).
cnf(refute_0_101,plain,
( ~ theorem(X_1037)
| theorem(implies(or(X_1038,not(X_1037)),X_1038)) ),
inference(resolve,[$cnf( theorem(implies(X_1037,implies(or(X_1038,not(X_1037)),X_1038))) )],[refute_0_100,refute_0_57]) ).
cnf(refute_0_102,plain,
( ~ theorem(implies(X_98,and(X_98,X_98)))
| theorem(implies(or(X_11988,not(implies(X_98,and(X_98,X_98)))),X_11988)) ),
inference(subst,[],[refute_0_101:[bind(X_1037,$fot(implies(X_98,and(X_98,X_98)))),bind(X_1038,$fot(X_11988))]]) ).
cnf(refute_0_103,plain,
theorem(implies(or(X_11988,not(implies(X_98,and(X_98,X_98)))),X_11988)),
inference(resolve,[$cnf( theorem(implies(X_98,and(X_98,X_98))) )],[refute_0_56,refute_0_102]) ).
cnf(refute_0_104,plain,
theorem(implies(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))),not(X_98))),
inference(subst,[],[refute_0_103:[bind(X_11988,$fot(not(X_98))),bind(X_98,$fot(X_12048))]]) ).
cnf(refute_0_105,plain,
theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))),
inference(resolve,[$cnf( theorem(implies(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))),not(X_98))) )],[refute_0_104,refute_0_23]) ).
cnf(refute_0_106,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_107,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_43,refute_0_106]) ).
cnf(refute_0_108,plain,
not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) = and(X_98,implies(X_12048,and(X_12048,X_12048))),
inference(subst,[],[refute_0_107:[bind(P,$fot(X_98)),bind(Q,$fot(implies(X_12048,and(X_12048,X_12048))))]]) ).
cnf(refute_0_109,plain,
or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))) = implies(X_98,not(implies(X_12048,and(X_12048,X_12048)))),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_98)),bind(Y,$fot(not(implies(X_12048,and(X_12048,X_12048)))))]]) ).
cnf(refute_0_110,plain,
not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))),
introduced(tautology,[refl,[$fot(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))]]) ).
cnf(refute_0_111,plain,
( not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) != not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))
| or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))) != implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))),not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) ),[1,0],$fot(implies(X_98,not(implies(X_12048,and(X_12048,X_12048)))))]]) ).
cnf(refute_0_112,plain,
( or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))) != implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))),not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))),
inference(resolve,[$cnf( $equal(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))),implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_115,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_8,refute_0_114]) ).
cnf(refute_0_116,plain,
( not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) != and(X_98,implies(X_12048,and(X_12048,X_12048)))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) != not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048)))))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = and(X_98,implies(X_12048,and(X_12048,X_12048))) ),
inference(subst,[],[refute_0_115:[bind(X0,$fot(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))),bind(Y0,$fot(not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))))),bind(Z,$fot(and(X_98,implies(X_12048,and(X_12048,X_12048)))))]]) ).
cnf(refute_0_117,plain,
( not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))) != and(X_98,implies(X_12048,and(X_12048,X_12048)))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = and(X_98,implies(X_12048,and(X_12048,X_12048))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))),not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048)))))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) = and(X_98,implies(X_12048,and(X_12048,X_12048))),
inference(resolve,[$cnf( $equal(not(implies(X_98,not(implies(X_12048,and(X_12048,X_12048))))),and(X_98,implies(X_12048,and(X_12048,X_12048)))) )],[refute_0_108,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) = implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))),
introduced(tautology,[refl,[$fot(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))))]]) ).
cnf(refute_0_120,plain,
( implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) != implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))
| not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) != and(X_98,implies(X_12048,and(X_12048,X_12048)))
| implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) = implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))),implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))) ),[1,1],$fot(and(X_98,implies(X_12048,and(X_12048,X_12048))))]]) ).
cnf(refute_0_121,plain,
( not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))) != and(X_98,implies(X_12048,and(X_12048,X_12048)))
| implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) = implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048)))) ),
inference(resolve,[$cnf( $equal(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))),implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) = implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048)))),
inference(resolve,[$cnf( $equal(not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))),and(X_98,implies(X_12048,and(X_12048,X_12048)))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))) != implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048))))
| ~ theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))))
| theorem(implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048))))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))) ),[0],$fot(implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048)))))]]) ).
cnf(refute_0_124,plain,
( ~ theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))))
| theorem(implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048))))) ),
inference(resolve,[$cnf( $equal(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048)))))),implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
theorem(implies(X_98,and(X_98,implies(X_12048,and(X_12048,X_12048))))),
inference(resolve,[$cnf( theorem(implies(X_98,not(or(not(X_98),not(implies(X_12048,and(X_12048,X_12048))))))) )],[refute_0_105,refute_0_124]) ).
cnf(refute_0_126,plain,
theorem(implies(implies(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))))),
inference(subst,[],[refute_0_125:[bind(X_12048,$fot(X_12087)),bind(X_98,$fot(implies(and(X_12087,X_12087),X_12087)))]]) ).
cnf(refute_0_127,plain,
equivalent(and(X_12087,X_12087),X_12087) = and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))),
inference(subst,[],[equivalent_defn:[bind(P,$fot(and(X_12087,X_12087))),bind(Q,$fot(X_12087))]]) ).
cnf(refute_0_128,plain,
( equivalent(and(X_12087,X_12087),X_12087) != and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087)))
| and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))) = equivalent(and(X_12087,X_12087),X_12087) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(equivalent(and(X_12087,X_12087),X_12087))),bind(Y0,$fot(and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087)))))]]) ).
cnf(refute_0_129,plain,
and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))) = equivalent(and(X_12087,X_12087),X_12087),
inference(resolve,[$cnf( $equal(equivalent(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))) != equivalent(and(X_12087,X_12087),X_12087)
| ~ theorem(implies(implies(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087)))))
| theorem(implies(implies(and(X_12087,X_12087),X_12087),equivalent(and(X_12087,X_12087),X_12087))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))))) ),[0,1],$fot(equivalent(and(X_12087,X_12087),X_12087))]]) ).
cnf(refute_0_131,plain,
( ~ theorem(implies(implies(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087)))))
| theorem(implies(implies(and(X_12087,X_12087),X_12087),equivalent(and(X_12087,X_12087),X_12087))) ),
inference(resolve,[$cnf( $equal(and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))),equivalent(and(X_12087,X_12087),X_12087)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
theorem(implies(implies(and(X_12087,X_12087),X_12087),equivalent(and(X_12087,X_12087),X_12087))),
inference(resolve,[$cnf( theorem(implies(implies(and(X_12087,X_12087),X_12087),and(implies(and(X_12087,X_12087),X_12087),implies(X_12087,and(X_12087,X_12087))))) )],[refute_0_126,refute_0_131]) ).
cnf(refute_0_133,plain,
theorem(implies(implies(and(X_12089,X_12089),X_12089),equivalent(and(X_12089,X_12089),X_12089))),
inference(subst,[],[refute_0_132:[bind(X_12087,$fot(X_12089))]]) ).
cnf(refute_0_134,plain,
( ~ theorem(implies(and(X_12089,X_12089),X_12089))
| theorem(equivalent(and(X_12089,X_12089),X_12089)) ),
inference(resolve,[$cnf( theorem(implies(implies(and(X_12089,X_12089),X_12089),equivalent(and(X_12089,X_12089),X_12089))) )],[refute_0_133,refute_0_0]) ).
cnf(refute_0_135,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_136,plain,
( ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_3,refute_0_135]) ).
cnf(refute_0_137,plain,
( ~ theorem(or(X_10858,not(and(X_10857,X_10858))))
| theorem(or(not(and(X_10857,X_10858)),X_10858)) ),
inference(subst,[],[refute_0_136:[bind(X_13,$fot(X_10858)),bind(X_14,$fot(not(and(X_10857,X_10858))))]]) ).
cnf(refute_0_138,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_139,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_138]) ).
cnf(refute_0_140,plain,
theorem(implies(X_90,or(B,X_90))),
inference(subst,[],[refute_0_139:[bind(A,$fot(X_90))]]) ).
cnf(refute_0_141,plain,
( ~ theorem(X_90)
| ~ theorem(implies(X_90,or(B,X_90)))
| theorem(or(B,X_90)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_90))),bind(Y,$fot(X_90))]]) ).
cnf(refute_0_142,plain,
( ~ theorem(X_90)
| theorem(or(B,X_90)) ),
inference(resolve,[$cnf( theorem(implies(X_90,or(B,X_90))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( ~ theorem(or(X_1239,not(X_1239)))
| theorem(or(B,or(X_1239,not(X_1239)))) ),
inference(subst,[],[refute_0_142:[bind(X_90,$fot(or(X_1239,not(X_1239))))]]) ).
cnf(refute_0_144,plain,
theorem(implies(or(not(X),X_18),or(X_18,not(X)))),
inference(subst,[],[refute_0_3:[bind(X_13,$fot(not(X))),bind(X_14,$fot(X_18))]]) ).
cnf(refute_0_145,plain,
implies(X,X_18) = or(not(X),X_18),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_18))]]) ).
cnf(refute_0_146,plain,
( implies(X,X_18) != or(not(X),X_18)
| or(not(X),X_18) = implies(X,X_18) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_18))),bind(Y0,$fot(or(not(X),X_18)))]]) ).
cnf(refute_0_147,plain,
or(not(X),X_18) = implies(X,X_18),
inference(resolve,[$cnf( $equal(implies(X,X_18),or(not(X),X_18)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( or(not(X),X_18) != implies(X,X_18)
| ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) ),[0,0],$fot(implies(X,X_18))]]) ).
cnf(refute_0_149,plain,
( ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_18),implies(X,X_18)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
theorem(implies(implies(X,X_18),or(X_18,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) )],[refute_0_144,refute_0_149]) ).
cnf(refute_0_151,plain,
( ~ theorem(implies(X,X_18))
| ~ theorem(implies(implies(X,X_18),or(X_18,not(X))))
| theorem(or(X_18,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X)))),bind(Y,$fot(implies(X,X_18)))]]) ).
cnf(refute_0_152,plain,
( ~ theorem(implies(X,X_18))
| theorem(or(X_18,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_18),or(X_18,not(X)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( ~ theorem(implies(X_1237,X_1237))
| theorem(or(X_1237,not(X_1237))) ),
inference(subst,[],[refute_0_152:[bind(X,$fot(X_1237)),bind(X_18,$fot(X_1237))]]) ).
cnf(refute_0_154,plain,
( ~ theorem(X_100)
| ~ theorem(implies(X_100,and(X_100,X_100)))
| theorem(and(X_100,X_100)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_100,X_100))),bind(Y,$fot(X_100))]]) ).
cnf(refute_0_155,plain,
theorem(implies(X_100,and(X_100,X_100))),
inference(subst,[],[refute_0_56:[bind(X_98,$fot(X_100))]]) ).
cnf(refute_0_156,plain,
( ~ theorem(X_100)
| theorem(and(X_100,X_100)) ),
inference(resolve,[$cnf( theorem(implies(X_100,and(X_100,X_100))) )],[refute_0_155,refute_0_154]) ).
cnf(refute_0_157,plain,
( ~ theorem(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))))
| theorem(and(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))),equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))))) ),
inference(subst,[],[refute_0_156:[bind(X_100,$fot(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155)))))]]) ).
cnf(refute_0_158,plain,
theorem(implies(X_9,or(not(X),X_9))),
inference(subst,[],[refute_0_139:[bind(A,$fot(X_9)),bind(B,$fot(not(X)))]]) ).
cnf(refute_0_159,plain,
implies(X,X_9) = or(not(X),X_9),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_9))]]) ).
cnf(refute_0_160,plain,
( implies(X,X_9) != or(not(X),X_9)
| or(not(X),X_9) = implies(X,X_9) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,X_9))),bind(Y0,$fot(or(not(X),X_9)))]]) ).
cnf(refute_0_161,plain,
or(not(X),X_9) = implies(X,X_9),
inference(resolve,[$cnf( $equal(implies(X,X_9),or(not(X),X_9)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( or(not(X),X_9) != implies(X,X_9)
| ~ theorem(implies(X_9,or(not(X),X_9)))
| theorem(implies(X_9,implies(X,X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_9,or(not(X),X_9))) ),[0,1],$fot(implies(X,X_9))]]) ).
cnf(refute_0_163,plain,
( ~ theorem(implies(X_9,or(not(X),X_9)))
| theorem(implies(X_9,implies(X,X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_9),implies(X,X_9)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
theorem(implies(X_9,implies(X,X_9))),
inference(resolve,[$cnf( theorem(implies(X_9,or(not(X),X_9))) )],[refute_0_158,refute_0_163]) ).
cnf(refute_0_165,plain,
theorem(implies(X_90,implies(X,X_90))),
inference(subst,[],[refute_0_164:[bind(X_9,$fot(X_90))]]) ).
cnf(refute_0_166,plain,
( ~ theorem(X_90)
| ~ theorem(implies(X_90,implies(X,X_90)))
| theorem(implies(X,X_90)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,X_90))),bind(Y,$fot(X_90))]]) ).
cnf(refute_0_167,plain,
( ~ theorem(X_90)
| theorem(implies(X,X_90)) ),
inference(resolve,[$cnf( theorem(implies(X_90,implies(X,X_90))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( ~ theorem(implies(X_98,and(X_98,X_98)))
| theorem(implies(X_102,implies(X_98,and(X_98,X_98)))) ),
inference(subst,[],[refute_0_167:[bind(X,$fot(X_102)),bind(X_90,$fot(implies(X_98,and(X_98,X_98))))]]) ).
cnf(refute_0_169,plain,
theorem(implies(X_102,implies(X_98,and(X_98,X_98)))),
inference(resolve,[$cnf( theorem(implies(X_98,and(X_98,X_98))) )],[refute_0_56,refute_0_168]) ).
cnf(refute_0_170,plain,
theorem(implies(implies(X_98,and(X_98,X_98)),implies(X_98,and(X_98,X_98)))),
inference(subst,[],[refute_0_169:[bind(X_102,$fot(implies(X_98,and(X_98,X_98))))]]) ).
cnf(refute_0_171,plain,
( ~ theorem(implies(X_101,X_101))
| ~ theorem(implies(implies(X_101,X_101),equivalent(X_101,X_101)))
| theorem(equivalent(X_101,X_101)) ),
inference(subst,[],[rule_2:[bind(X,$fot(equivalent(X_101,X_101))),bind(Y,$fot(implies(X_101,X_101)))]]) ).
cnf(refute_0_172,plain,
theorem(or(and(implies(X_27,X_27),implies(X_27,X_27)),not(implies(X_27,X_27)))),
inference(subst,[],[refute_0_53:[bind(X_5,$fot(implies(X_27,X_27)))]]) ).
cnf(refute_0_173,plain,
equivalent(X_27,X_27) = and(implies(X_27,X_27),implies(X_27,X_27)),
inference(subst,[],[equivalent_defn:[bind(P,$fot(X_27)),bind(Q,$fot(X_27))]]) ).
cnf(refute_0_174,plain,
( equivalent(X_27,X_27) != and(implies(X_27,X_27),implies(X_27,X_27))
| and(implies(X_27,X_27),implies(X_27,X_27)) = equivalent(X_27,X_27) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(equivalent(X_27,X_27))),bind(Y0,$fot(and(implies(X_27,X_27),implies(X_27,X_27))))]]) ).
cnf(refute_0_175,plain,
and(implies(X_27,X_27),implies(X_27,X_27)) = equivalent(X_27,X_27),
inference(resolve,[$cnf( $equal(equivalent(X_27,X_27),and(implies(X_27,X_27),implies(X_27,X_27))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( and(implies(X_27,X_27),implies(X_27,X_27)) != equivalent(X_27,X_27)
| ~ theorem(or(and(implies(X_27,X_27),implies(X_27,X_27)),not(implies(X_27,X_27))))
| theorem(or(equivalent(X_27,X_27),not(implies(X_27,X_27)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(and(implies(X_27,X_27),implies(X_27,X_27)),not(implies(X_27,X_27)))) ),[0,0],$fot(equivalent(X_27,X_27))]]) ).
cnf(refute_0_177,plain,
( ~ theorem(or(and(implies(X_27,X_27),implies(X_27,X_27)),not(implies(X_27,X_27))))
| theorem(or(equivalent(X_27,X_27),not(implies(X_27,X_27)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_27,X_27),implies(X_27,X_27)),equivalent(X_27,X_27)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
theorem(or(equivalent(X_27,X_27),not(implies(X_27,X_27)))),
inference(resolve,[$cnf( theorem(or(and(implies(X_27,X_27),implies(X_27,X_27)),not(implies(X_27,X_27)))) )],[refute_0_172,refute_0_177]) ).
cnf(refute_0_179,plain,
( ~ theorem(or(equivalent(X_27,X_27),not(implies(X_27,X_27))))
| theorem(implies(implies(X_27,X_27),equivalent(X_27,X_27))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(implies(X_27,X_27))),bind(X_17,$fot(equivalent(X_27,X_27)))]]) ).
cnf(refute_0_180,plain,
theorem(implies(implies(X_27,X_27),equivalent(X_27,X_27))),
inference(resolve,[$cnf( theorem(or(equivalent(X_27,X_27),not(implies(X_27,X_27)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
theorem(implies(implies(X_101,X_101),equivalent(X_101,X_101))),
inference(subst,[],[refute_0_180:[bind(X_27,$fot(X_101))]]) ).
cnf(refute_0_182,plain,
( ~ theorem(implies(X_101,X_101))
| theorem(equivalent(X_101,X_101)) ),
inference(resolve,[$cnf( theorem(implies(implies(X_101,X_101),equivalent(X_101,X_101))) )],[refute_0_181,refute_0_171]) ).
cnf(refute_0_183,plain,
( ~ theorem(implies(implies(X_98,and(X_98,X_98)),implies(X_98,and(X_98,X_98))))
| theorem(equivalent(implies(X_98,and(X_98,X_98)),implies(X_98,and(X_98,X_98)))) ),
inference(subst,[],[refute_0_182:[bind(X_101,$fot(implies(X_98,and(X_98,X_98))))]]) ).
cnf(refute_0_184,plain,
theorem(equivalent(implies(X_98,and(X_98,X_98)),implies(X_98,and(X_98,X_98)))),
inference(resolve,[$cnf( theorem(implies(implies(X_98,and(X_98,X_98)),implies(X_98,and(X_98,X_98)))) )],[refute_0_170,refute_0_183]) ).
cnf(refute_0_185,plain,
theorem(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155)))),
inference(subst,[],[refute_0_184:[bind(X_98,$fot(X_155))]]) ).
cnf(refute_0_186,plain,
theorem(and(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))),equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))))),
inference(resolve,[$cnf( theorem(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155)))) )],[refute_0_185,refute_0_157]) ).
cnf(refute_0_187,plain,
( ~ theorem(X_1020)
| ~ theorem(implies(X_1020,implies(X_1021,X_1021)))
| theorem(implies(X_1021,X_1021)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1021,X_1021))),bind(Y,$fot(X_1020))]]) ).
cnf(refute_0_188,plain,
theorem(implies(X_1015,implies(X_1014,X_1015))),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_1014)),bind(X_9,$fot(X_1015))]]) ).
cnf(refute_0_189,plain,
( ~ theorem(implies(X_1015,implies(X_1014,X_1015)))
| theorem(implies(X_1014,implies(X_1015,X_1015))) ),
inference(subst,[],[refute_0_97:[bind(X,$fot(X_1015)),bind(X_83,$fot(X_1014)),bind(X_85,$fot(X_1015))]]) ).
cnf(refute_0_190,plain,
theorem(implies(X_1014,implies(X_1015,X_1015))),
inference(resolve,[$cnf( theorem(implies(X_1015,implies(X_1014,X_1015))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
theorem(implies(X_1020,implies(X_1021,X_1021))),
inference(subst,[],[refute_0_190:[bind(X_1014,$fot(X_1020)),bind(X_1015,$fot(X_1021))]]) ).
cnf(refute_0_192,plain,
( ~ theorem(X_1020)
| theorem(implies(X_1021,X_1021)) ),
inference(resolve,[$cnf( theorem(implies(X_1020,implies(X_1021,X_1021))) )],[refute_0_191,refute_0_187]) ).
cnf(refute_0_193,plain,
( ~ theorem(and(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))),equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155)))))
| theorem(implies(X_1236,X_1236)) ),
inference(subst,[],[refute_0_192:[bind(X_1020,$fot(and(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))),equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155)))))),bind(X_1021,$fot(X_1236))]]) ).
cnf(refute_0_194,plain,
theorem(implies(X_1236,X_1236)),
inference(resolve,[$cnf( theorem(and(equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))),equivalent(implies(X_155,and(X_155,X_155)),implies(X_155,and(X_155,X_155))))) )],[refute_0_186,refute_0_193]) ).
cnf(refute_0_195,plain,
theorem(implies(X_1237,X_1237)),
inference(subst,[],[refute_0_194:[bind(X_1236,$fot(X_1237))]]) ).
cnf(refute_0_196,plain,
theorem(or(X_1237,not(X_1237))),
inference(resolve,[$cnf( theorem(implies(X_1237,X_1237)) )],[refute_0_195,refute_0_153]) ).
cnf(refute_0_197,plain,
theorem(or(X_1239,not(X_1239))),
inference(subst,[],[refute_0_196:[bind(X_1237,$fot(X_1239))]]) ).
cnf(refute_0_198,plain,
theorem(or(B,or(X_1239,not(X_1239)))),
inference(resolve,[$cnf( theorem(or(X_1239,not(X_1239))) )],[refute_0_197,refute_0_143]) ).
cnf(refute_0_199,plain,
theorem(or(X_2107,or(X_2108,not(X_2108)))),
inference(subst,[],[refute_0_198:[bind(B,$fot(X_2107)),bind(X_1239,$fot(X_2108))]]) ).
cnf(refute_0_200,plain,
( ~ theorem(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57))))
| ~ theorem(or(X_55,or(X_56,X_57)))
| theorem(or(X_56,or(X_55,X_57))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_56,or(X_55,X_57)))),bind(Y,$fot(or(X_55,or(X_56,X_57))))]]) ).
cnf(refute_0_201,plain,
( ~ theorem(or(X_55,or(X_56,X_57)))
| theorem(or(X_56,or(X_55,X_57))) ),
inference(resolve,[$cnf( theorem(implies(or(X_55,or(X_56,X_57)),or(X_56,or(X_55,X_57)))) )],[refute_0_61,refute_0_200]) ).
cnf(refute_0_202,plain,
( ~ theorem(or(X_2107,or(X_2108,not(X_2108))))
| theorem(or(X_2108,or(X_2107,not(X_2108)))) ),
inference(subst,[],[refute_0_201:[bind(X_55,$fot(X_2107)),bind(X_56,$fot(X_2108)),bind(X_57,$fot(not(X_2108)))]]) ).
cnf(refute_0_203,plain,
theorem(or(X_2108,or(X_2107,not(X_2108)))),
inference(resolve,[$cnf( theorem(or(X_2107,or(X_2108,not(X_2108)))) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
theorem(or(X_2113,or(not(X),not(X_2113)))),
inference(subst,[],[refute_0_203:[bind(X_2107,$fot(not(X))),bind(X_2108,$fot(X_2113))]]) ).
cnf(refute_0_205,plain,
implies(X,not(X_2113)) = or(not(X),not(X_2113)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_2113)))]]) ).
cnf(refute_0_206,plain,
( implies(X,not(X_2113)) != or(not(X),not(X_2113))
| or(not(X),not(X_2113)) = implies(X,not(X_2113)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,not(X_2113)))),bind(Y0,$fot(or(not(X),not(X_2113))))]]) ).
cnf(refute_0_207,plain,
or(not(X),not(X_2113)) = implies(X,not(X_2113)),
inference(resolve,[$cnf( $equal(implies(X,not(X_2113)),or(not(X),not(X_2113))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
( or(not(X),not(X_2113)) != implies(X,not(X_2113))
| ~ theorem(or(X_2113,or(not(X),not(X_2113))))
| theorem(or(X_2113,implies(X,not(X_2113)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(X_2113,or(not(X),not(X_2113)))) ),[0,1],$fot(implies(X,not(X_2113)))]]) ).
cnf(refute_0_209,plain,
( ~ theorem(or(X_2113,or(not(X),not(X_2113))))
| theorem(or(X_2113,implies(X,not(X_2113)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_2113)),implies(X,not(X_2113))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
theorem(or(X_2113,implies(X,not(X_2113)))),
inference(resolve,[$cnf( theorem(or(X_2113,or(not(X),not(X_2113)))) )],[refute_0_204,refute_0_209]) ).
cnf(refute_0_211,plain,
theorem(or(X_10847,implies(X,not(X_10847)))),
inference(subst,[],[refute_0_210:[bind(X_2113,$fot(X_10847))]]) ).
cnf(refute_0_212,plain,
( ~ theorem(implies(or(X_1612,X_1611),or(X_1612,not(not(X_1611)))))
| ~ theorem(or(X_1612,X_1611))
| theorem(or(X_1612,not(not(X_1611)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_1612,not(not(X_1611))))),bind(Y,$fot(or(X_1612,X_1611)))]]) ).
cnf(refute_0_213,plain,
( ~ theorem(implies(not(X_98),not(X_98)))
| theorem(implies(X_98,not(not(X_98)))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(not(X_98)))]]) ).
cnf(refute_0_214,plain,
theorem(implies(not(X_98),not(X_98))),
inference(subst,[],[refute_0_194:[bind(X_1236,$fot(not(X_98)))]]) ).
cnf(refute_0_215,plain,
theorem(implies(X_98,not(not(X_98)))),
inference(resolve,[$cnf( theorem(implies(not(X_98),not(X_98))) )],[refute_0_214,refute_0_213]) ).
cnf(refute_0_216,plain,
theorem(implies(X_1606,not(not(X_1606)))),
inference(subst,[],[refute_0_215:[bind(X_98,$fot(X_1606))]]) ).
cnf(refute_0_217,plain,
( ~ axiom(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47))))
| theorem(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))))]]) ).
cnf(refute_0_218,plain,
axiom(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_46)),bind(B,$fot(X_47)),bind(C,$fot(X_48))]]) ).
cnf(refute_0_219,plain,
theorem(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))),
inference(resolve,[$cnf( axiom(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))) )],[refute_0_218,refute_0_217]) ).
cnf(refute_0_220,plain,
( ~ theorem(implies(X_46,X_47))
| ~ theorem(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47))))
| theorem(implies(or(X_48,X_46),or(X_48,X_47))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_48,X_46),or(X_48,X_47)))),bind(Y,$fot(implies(X_46,X_47)))]]) ).
cnf(refute_0_221,plain,
( ~ theorem(implies(X_46,X_47))
| theorem(implies(or(X_48,X_46),or(X_48,X_47))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(X_48,X_46),or(X_48,X_47)))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( ~ theorem(implies(X_1606,not(not(X_1606))))
| theorem(implies(or(X_1608,X_1606),or(X_1608,not(not(X_1606))))) ),
inference(subst,[],[refute_0_221:[bind(X_46,$fot(X_1606)),bind(X_47,$fot(not(not(X_1606)))),bind(X_48,$fot(X_1608))]]) ).
cnf(refute_0_223,plain,
theorem(implies(or(X_1608,X_1606),or(X_1608,not(not(X_1606))))),
inference(resolve,[$cnf( theorem(implies(X_1606,not(not(X_1606)))) )],[refute_0_216,refute_0_222]) ).
cnf(refute_0_224,plain,
theorem(implies(or(X_1612,X_1611),or(X_1612,not(not(X_1611))))),
inference(subst,[],[refute_0_223:[bind(X_1606,$fot(X_1611)),bind(X_1608,$fot(X_1612))]]) ).
cnf(refute_0_225,plain,
( ~ theorem(or(X_1612,X_1611))
| theorem(or(X_1612,not(not(X_1611)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_1612,X_1611),or(X_1612,not(not(X_1611))))) )],[refute_0_224,refute_0_212]) ).
cnf(refute_0_226,plain,
( ~ theorem(or(X_10847,implies(X,not(X_10847))))
| theorem(or(X_10847,not(not(implies(X,not(X_10847)))))) ),
inference(subst,[],[refute_0_225:[bind(X_1611,$fot(implies(X,not(X_10847)))),bind(X_1612,$fot(X_10847))]]) ).
cnf(refute_0_227,plain,
theorem(or(X_10847,not(not(implies(X,not(X_10847)))))),
inference(resolve,[$cnf( theorem(or(X_10847,implies(X,not(X_10847)))) )],[refute_0_211,refute_0_226]) ).
cnf(refute_0_228,plain,
not(implies(X,not(X_10847))) = and(X,X_10847),
inference(subst,[],[refute_0_107:[bind(P,$fot(X)),bind(Q,$fot(X_10847))]]) ).
cnf(refute_0_229,plain,
not(not(implies(X,not(X_10847)))) = not(not(implies(X,not(X_10847)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X_10847)))))]]) ).
cnf(refute_0_230,plain,
( not(implies(X,not(X_10847))) != and(X,X_10847)
| not(not(implies(X,not(X_10847)))) != not(not(implies(X,not(X_10847))))
| not(not(implies(X,not(X_10847)))) = not(and(X,X_10847)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X_10847)))),not(not(implies(X,not(X_10847))))) ),[1,0],$fot(and(X,X_10847))]]) ).
cnf(refute_0_231,plain,
( not(implies(X,not(X_10847))) != and(X,X_10847)
| not(not(implies(X,not(X_10847)))) = not(and(X,X_10847)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_10847)))),not(not(implies(X,not(X_10847))))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
not(not(implies(X,not(X_10847)))) = not(and(X,X_10847)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_10847))),and(X,X_10847)) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
or(X_10847,not(not(implies(X,not(X_10847))))) = or(X_10847,not(not(implies(X,not(X_10847))))),
introduced(tautology,[refl,[$fot(or(X_10847,not(not(implies(X,not(X_10847))))))]]) ).
cnf(refute_0_234,plain,
( not(not(implies(X,not(X_10847)))) != not(and(X,X_10847))
| or(X_10847,not(not(implies(X,not(X_10847))))) != or(X_10847,not(not(implies(X,not(X_10847)))))
| or(X_10847,not(not(implies(X,not(X_10847))))) = or(X_10847,not(and(X,X_10847))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_10847,not(not(implies(X,not(X_10847))))),or(X_10847,not(not(implies(X,not(X_10847)))))) ),[1,1],$fot(not(and(X,X_10847)))]]) ).
cnf(refute_0_235,plain,
( not(not(implies(X,not(X_10847)))) != not(and(X,X_10847))
| or(X_10847,not(not(implies(X,not(X_10847))))) = or(X_10847,not(and(X,X_10847))) ),
inference(resolve,[$cnf( $equal(or(X_10847,not(not(implies(X,not(X_10847))))),or(X_10847,not(not(implies(X,not(X_10847)))))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
or(X_10847,not(not(implies(X,not(X_10847))))) = or(X_10847,not(and(X,X_10847))),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_10847)))),not(and(X,X_10847))) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
( or(X_10847,not(not(implies(X,not(X_10847))))) != or(X_10847,not(and(X,X_10847)))
| ~ theorem(or(X_10847,not(not(implies(X,not(X_10847))))))
| theorem(or(X_10847,not(and(X,X_10847)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(X_10847,not(not(implies(X,not(X_10847)))))) ),[0],$fot(or(X_10847,not(and(X,X_10847))))]]) ).
cnf(refute_0_238,plain,
( ~ theorem(or(X_10847,not(not(implies(X,not(X_10847))))))
| theorem(or(X_10847,not(and(X,X_10847)))) ),
inference(resolve,[$cnf( $equal(or(X_10847,not(not(implies(X,not(X_10847))))),or(X_10847,not(and(X,X_10847)))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
theorem(or(X_10847,not(and(X,X_10847)))),
inference(resolve,[$cnf( theorem(or(X_10847,not(not(implies(X,not(X_10847)))))) )],[refute_0_227,refute_0_238]) ).
cnf(refute_0_240,plain,
theorem(or(X_10858,not(and(X_10857,X_10858)))),
inference(subst,[],[refute_0_239:[bind(X,$fot(X_10857)),bind(X_10847,$fot(X_10858))]]) ).
cnf(refute_0_241,plain,
theorem(or(not(and(X_10857,X_10858)),X_10858)),
inference(resolve,[$cnf( theorem(or(X_10858,not(and(X_10857,X_10858)))) )],[refute_0_240,refute_0_137]) ).
cnf(refute_0_242,plain,
or(not(and(X_10857,X_10858)),X_10858) = implies(and(X_10857,X_10858),X_10858),
inference(subst,[],[refute_0_35:[bind(X,$fot(and(X_10857,X_10858))),bind(Y,$fot(X_10858))]]) ).
cnf(refute_0_243,plain,
( or(not(and(X_10857,X_10858)),X_10858) != implies(and(X_10857,X_10858),X_10858)
| ~ theorem(or(not(and(X_10857,X_10858)),X_10858))
| theorem(implies(and(X_10857,X_10858),X_10858)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_10857,X_10858)),X_10858)) ),[0],$fot(implies(and(X_10857,X_10858),X_10858))]]) ).
cnf(refute_0_244,plain,
( ~ theorem(or(not(and(X_10857,X_10858)),X_10858))
| theorem(implies(and(X_10857,X_10858),X_10858)) ),
inference(resolve,[$cnf( $equal(or(not(and(X_10857,X_10858)),X_10858),implies(and(X_10857,X_10858),X_10858)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
theorem(implies(and(X_10857,X_10858),X_10858)),
inference(resolve,[$cnf( theorem(or(not(and(X_10857,X_10858)),X_10858)) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
theorem(implies(and(X_12089,X_12089),X_12089)),
inference(subst,[],[refute_0_245:[bind(X_10857,$fot(X_12089)),bind(X_10858,$fot(X_12089))]]) ).
cnf(refute_0_247,plain,
theorem(equivalent(and(X_12089,X_12089),X_12089)),
inference(resolve,[$cnf( theorem(implies(and(X_12089,X_12089),X_12089)) )],[refute_0_246,refute_0_134]) ).
cnf(refute_0_248,plain,
theorem(equivalent(and(X_28369,X_28369),X_28369)),
inference(subst,[],[refute_0_247:[bind(X_12089,$fot(X_28369))]]) ).
cnf(refute_0_249,plain,
( ~ theorem(equivalent(X_10917,X_10916))
| ~ theorem(implies(equivalent(X_10917,X_10916),equivalent(X_10916,X_10917)))
| theorem(equivalent(X_10916,X_10917)) ),
inference(subst,[],[rule_2:[bind(X,$fot(equivalent(X_10916,X_10917))),bind(Y,$fot(equivalent(X_10917,X_10916)))]]) ).
cnf(refute_0_250,plain,
( ~ theorem(or(and(X_10853,X_10854),not(and(X_10854,X_10853))))
| theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854))) ),
inference(subst,[],[refute_0_136:[bind(X_13,$fot(and(X_10853,X_10854))),bind(X_14,$fot(not(and(X_10854,X_10853))))]]) ).
cnf(refute_0_251,plain,
theorem(implies(or(not(X),not(X_33)),implies(X_33,not(X)))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_33)),bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_252,plain,
implies(X,not(X_33)) = or(not(X),not(X_33)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_33)))]]) ).
cnf(refute_0_253,plain,
( implies(X,not(X_33)) != or(not(X),not(X_33))
| or(not(X),not(X_33)) = implies(X,not(X_33)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(implies(X,not(X_33)))),bind(Y0,$fot(or(not(X),not(X_33))))]]) ).
cnf(refute_0_254,plain,
or(not(X),not(X_33)) = implies(X,not(X_33)),
inference(resolve,[$cnf( $equal(implies(X,not(X_33)),or(not(X),not(X_33))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
( or(not(X),not(X_33)) != implies(X,not(X_33))
| ~ theorem(implies(or(not(X),not(X_33)),implies(X_33,not(X))))
| theorem(implies(implies(X,not(X_33)),implies(X_33,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),not(X_33)),implies(X_33,not(X)))) ),[0,0],$fot(implies(X,not(X_33)))]]) ).
cnf(refute_0_256,plain,
( ~ theorem(implies(or(not(X),not(X_33)),implies(X_33,not(X))))
| theorem(implies(implies(X,not(X_33)),implies(X_33,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_33)),implies(X,not(X_33))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
theorem(implies(implies(X,not(X_33)),implies(X_33,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),not(X_33)),implies(X_33,not(X)))) )],[refute_0_251,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(implies(X,not(X_33)),implies(X_33,not(X))) = or(and(X,X_33),implies(X_33,not(X))),
inference(subst,[],[refute_0_49:[bind(Y,$fot(implies(X_33,not(X)))),bind(X_19,$fot(X)),bind(X_20,$fot(X_33))]]) ).
cnf(refute_0_259,plain,
( implies(implies(X,not(X_33)),implies(X_33,not(X))) != or(and(X,X_33),implies(X_33,not(X)))
| ~ theorem(implies(implies(X,not(X_33)),implies(X_33,not(X))))
| theorem(or(and(X,X_33),implies(X_33,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X,not(X_33)),implies(X_33,not(X)))) ),[0],$fot(or(and(X,X_33),implies(X_33,not(X))))]]) ).
cnf(refute_0_260,plain,
( ~ theorem(implies(implies(X,not(X_33)),implies(X_33,not(X))))
| theorem(or(and(X,X_33),implies(X_33,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_33)),implies(X_33,not(X))),or(and(X,X_33),implies(X_33,not(X)))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
theorem(or(and(X,X_33),implies(X_33,not(X)))),
inference(resolve,[$cnf( theorem(implies(implies(X,not(X_33)),implies(X_33,not(X)))) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
( ~ theorem(or(and(X,X_33),implies(X_33,not(X))))
| theorem(or(and(X,X_33),not(not(implies(X_33,not(X)))))) ),
inference(subst,[],[refute_0_225:[bind(X_1611,$fot(implies(X_33,not(X)))),bind(X_1612,$fot(and(X,X_33)))]]) ).
cnf(refute_0_263,plain,
theorem(or(and(X,X_33),not(not(implies(X_33,not(X)))))),
inference(resolve,[$cnf( theorem(or(and(X,X_33),implies(X_33,not(X)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
not(implies(X_33,not(X))) = and(X_33,X),
inference(subst,[],[refute_0_107:[bind(P,$fot(X_33)),bind(Q,$fot(X))]]) ).
cnf(refute_0_265,plain,
not(not(implies(X_33,not(X)))) = not(not(implies(X_33,not(X)))),
introduced(tautology,[refl,[$fot(not(not(implies(X_33,not(X)))))]]) ).
cnf(refute_0_266,plain,
( not(implies(X_33,not(X))) != and(X_33,X)
| not(not(implies(X_33,not(X)))) != not(not(implies(X_33,not(X))))
| not(not(implies(X_33,not(X)))) = not(and(X_33,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X_33,not(X)))),not(not(implies(X_33,not(X))))) ),[1,0],$fot(and(X_33,X))]]) ).
cnf(refute_0_267,plain,
( not(implies(X_33,not(X))) != and(X_33,X)
| not(not(implies(X_33,not(X)))) = not(and(X_33,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_33,not(X)))),not(not(implies(X_33,not(X))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
not(not(implies(X_33,not(X)))) = not(and(X_33,X)),
inference(resolve,[$cnf( $equal(not(implies(X_33,not(X))),and(X_33,X)) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
or(and(X,X_33),not(not(implies(X_33,not(X))))) = or(and(X,X_33),not(not(implies(X_33,not(X))))),
introduced(tautology,[refl,[$fot(or(and(X,X_33),not(not(implies(X_33,not(X))))))]]) ).
cnf(refute_0_270,plain,
( not(not(implies(X_33,not(X)))) != not(and(X_33,X))
| or(and(X,X_33),not(not(implies(X_33,not(X))))) != or(and(X,X_33),not(not(implies(X_33,not(X)))))
| or(and(X,X_33),not(not(implies(X_33,not(X))))) = or(and(X,X_33),not(and(X_33,X))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,X_33),not(not(implies(X_33,not(X))))),or(and(X,X_33),not(not(implies(X_33,not(X)))))) ),[1,1],$fot(not(and(X_33,X)))]]) ).
cnf(refute_0_271,plain,
( not(not(implies(X_33,not(X)))) != not(and(X_33,X))
| or(and(X,X_33),not(not(implies(X_33,not(X))))) = or(and(X,X_33),not(and(X_33,X))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_33),not(not(implies(X_33,not(X))))),or(and(X,X_33),not(not(implies(X_33,not(X)))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
or(and(X,X_33),not(not(implies(X_33,not(X))))) = or(and(X,X_33),not(and(X_33,X))),
inference(resolve,[$cnf( $equal(not(not(implies(X_33,not(X)))),not(and(X_33,X))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
( or(and(X,X_33),not(not(implies(X_33,not(X))))) != or(and(X,X_33),not(and(X_33,X)))
| ~ theorem(or(and(X,X_33),not(not(implies(X_33,not(X))))))
| theorem(or(and(X,X_33),not(and(X_33,X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(and(X,X_33),not(not(implies(X_33,not(X)))))) ),[0],$fot(or(and(X,X_33),not(and(X_33,X))))]]) ).
cnf(refute_0_274,plain,
( ~ theorem(or(and(X,X_33),not(not(implies(X_33,not(X))))))
| theorem(or(and(X,X_33),not(and(X_33,X)))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_33),not(not(implies(X_33,not(X))))),or(and(X,X_33),not(and(X_33,X)))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
theorem(or(and(X,X_33),not(and(X_33,X)))),
inference(resolve,[$cnf( theorem(or(and(X,X_33),not(not(implies(X_33,not(X)))))) )],[refute_0_263,refute_0_274]) ).
cnf(refute_0_276,plain,
theorem(or(and(X_10853,X_10854),not(and(X_10854,X_10853)))),
inference(subst,[],[refute_0_275:[bind(X,$fot(X_10853)),bind(X_33,$fot(X_10854))]]) ).
cnf(refute_0_277,plain,
theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854))),
inference(resolve,[$cnf( theorem(or(and(X_10853,X_10854),not(and(X_10854,X_10853)))) )],[refute_0_276,refute_0_250]) ).
cnf(refute_0_278,plain,
or(not(and(X_10854,X_10853)),and(X_10853,X_10854)) = implies(and(X_10854,X_10853),and(X_10853,X_10854)),
inference(subst,[],[refute_0_35:[bind(X,$fot(and(X_10854,X_10853))),bind(Y,$fot(and(X_10853,X_10854)))]]) ).
cnf(refute_0_279,plain,
( or(not(and(X_10854,X_10853)),and(X_10853,X_10854)) != implies(and(X_10854,X_10853),and(X_10853,X_10854))
| ~ theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854)))
| theorem(implies(and(X_10854,X_10853),and(X_10853,X_10854))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854))) ),[0],$fot(implies(and(X_10854,X_10853),and(X_10853,X_10854)))]]) ).
cnf(refute_0_280,plain,
( ~ theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854)))
| theorem(implies(and(X_10854,X_10853),and(X_10853,X_10854))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_10854,X_10853)),and(X_10853,X_10854)),implies(and(X_10854,X_10853),and(X_10853,X_10854))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
theorem(implies(and(X_10854,X_10853),and(X_10853,X_10854))),
inference(resolve,[$cnf( theorem(or(not(and(X_10854,X_10853)),and(X_10853,X_10854))) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
theorem(implies(and(implies(Q,P),implies(P,Q)),and(implies(P,Q),implies(Q,P)))),
inference(subst,[],[refute_0_281:[bind(X_10853,$fot(implies(P,Q))),bind(X_10854,$fot(implies(Q,P)))]]) ).
cnf(refute_0_283,plain,
( equivalent(P,Q) != and(implies(P,Q),implies(Q,P))
| and(implies(P,Q),implies(Q,P)) = equivalent(P,Q) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(equivalent(P,Q))),bind(Y0,$fot(and(implies(P,Q),implies(Q,P))))]]) ).
cnf(refute_0_284,plain,
and(implies(P,Q),implies(Q,P)) = equivalent(P,Q),
inference(resolve,[$cnf( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_283]) ).
cnf(refute_0_285,plain,
( and(implies(P,Q),implies(Q,P)) != equivalent(P,Q)
| ~ theorem(implies(and(implies(Q,P),implies(P,Q)),and(implies(P,Q),implies(Q,P))))
| theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(and(implies(Q,P),implies(P,Q)),and(implies(P,Q),implies(Q,P)))) ),[0,1],$fot(equivalent(P,Q))]]) ).
cnf(refute_0_286,plain,
( ~ theorem(implies(and(implies(Q,P),implies(P,Q)),and(implies(P,Q),implies(Q,P))))
| theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) ),
inference(resolve,[$cnf( $equal(and(implies(P,Q),implies(Q,P)),equivalent(P,Q)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))),
inference(resolve,[$cnf( theorem(implies(and(implies(Q,P),implies(P,Q)),and(implies(P,Q),implies(Q,P)))) )],[refute_0_282,refute_0_286]) ).
cnf(refute_0_288,plain,
and(implies(Q,P),implies(P,Q)) = equivalent(Q,P),
inference(subst,[],[refute_0_284:[bind(P,$fot(Q)),bind(Q,$fot(P))]]) ).
cnf(refute_0_289,plain,
implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) = implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)),
introduced(tautology,[refl,[$fot(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)))]]) ).
cnf(refute_0_290,plain,
( and(implies(Q,P),implies(P,Q)) != equivalent(Q,P)
| implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) != implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))
| implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) = implies(equivalent(Q,P),equivalent(P,Q)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)),implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) ),[1,0],$fot(equivalent(Q,P))]]) ).
cnf(refute_0_291,plain,
( and(implies(Q,P),implies(P,Q)) != equivalent(Q,P)
| implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) = implies(equivalent(Q,P),equivalent(P,Q)) ),
inference(resolve,[$cnf( $equal(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)),implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) = implies(equivalent(Q,P),equivalent(P,Q)),
inference(resolve,[$cnf( $equal(and(implies(Q,P),implies(P,Q)),equivalent(Q,P)) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)) != implies(equivalent(Q,P),equivalent(P,Q))
| ~ theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)))
| theorem(implies(equivalent(Q,P),equivalent(P,Q))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) ),[0],$fot(implies(equivalent(Q,P),equivalent(P,Q)))]]) ).
cnf(refute_0_294,plain,
( ~ theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)))
| theorem(implies(equivalent(Q,P),equivalent(P,Q))) ),
inference(resolve,[$cnf( $equal(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q)),implies(equivalent(Q,P),equivalent(P,Q))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
theorem(implies(equivalent(Q,P),equivalent(P,Q))),
inference(resolve,[$cnf( theorem(implies(and(implies(Q,P),implies(P,Q)),equivalent(P,Q))) )],[refute_0_287,refute_0_294]) ).
cnf(refute_0_296,plain,
theorem(implies(equivalent(X_10917,X_10916),equivalent(X_10916,X_10917))),
inference(subst,[],[refute_0_295:[bind(P,$fot(X_10916)),bind(Q,$fot(X_10917))]]) ).
cnf(refute_0_297,plain,
( ~ theorem(equivalent(X_10917,X_10916))
| theorem(equivalent(X_10916,X_10917)) ),
inference(resolve,[$cnf( theorem(implies(equivalent(X_10917,X_10916),equivalent(X_10916,X_10917))) )],[refute_0_296,refute_0_249]) ).
cnf(refute_0_298,plain,
( ~ theorem(equivalent(and(X_28369,X_28369),X_28369))
| theorem(equivalent(X_28369,and(X_28369,X_28369))) ),
inference(subst,[],[refute_0_297:[bind(X_10916,$fot(X_28369)),bind(X_10917,$fot(and(X_28369,X_28369)))]]) ).
cnf(refute_0_299,plain,
theorem(equivalent(X_28369,and(X_28369,X_28369))),
inference(resolve,[$cnf( theorem(equivalent(and(X_28369,X_28369),X_28369)) )],[refute_0_248,refute_0_298]) ).
cnf(refute_0_300,plain,
theorem(equivalent(p,and(p,p))),
inference(subst,[],[refute_0_299:[bind(X_28369,$fot(p))]]) ).
cnf(refute_0_301,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(p,and(p,p))) )],[refute_0_300,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL271-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 18:21:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 63.09/63.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.09/63.33
% 63.09/63.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.19/63.37
%------------------------------------------------------------------------------