TSTP Solution File: LCL259-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 12:51:13 EDT 2022
% Result : Unsatisfiable 167.33s 167.51s
% Output : CNFRefutation 167.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 36
% Syntax : Number of clauses : 224 ( 124 unt; 0 nHn; 91 RR)
% Number of literals : 356 ( 98 equ; 133 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 562 ( 46 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(p,implies(p,q)),implies(p,q))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_1,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_0]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_40,X_40),X_40)),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_40))]]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_40,X_40),X_40))
| ~ theorem(or(X_40,X_40))
| theorem(X_40) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_40)),bind(Y,$fot(or(X_40,X_40)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_40,X_40))
| theorem(X_40) ),
inference(resolve,[$cnf( theorem(implies(or(X_40,X_40),X_40)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271)),implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271))))
| theorem(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271))) ),
inference(subst,[],[refute_0_4:[bind(X_40,$fot(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271))))]]) ).
cnf(refute_0_6,plain,
( ~ theorem(implies(or(X_433,X_432),or(X_433,implies(X_431,X_432))))
| ~ theorem(or(X_433,X_432))
| theorem(or(X_433,implies(X_431,X_432))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_433,implies(X_431,X_432)))),bind(Y,$fot(or(X_433,X_432)))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_8,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_9,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
theorem(implies(X_7,or(not(X),X_7))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(X_7)),bind(X_4,$fot(not(X)))]]) ).
cnf(refute_0_11,plain,
implies(X,X_7) = or(not(X),X_7),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_7))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(X,X_7) != or(not(X),X_7)
| or(not(X),X_7) = implies(X,X_7) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,X_7))),bind(Y0,$fot(or(not(X),X_7)))]]) ).
cnf(refute_0_16,plain,
or(not(X),X_7) = implies(X,X_7),
inference(resolve,[$cnf( $equal(implies(X,X_7),or(not(X),X_7)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( or(not(X),X_7) != implies(X,X_7)
| ~ theorem(implies(X_7,or(not(X),X_7)))
| theorem(implies(X_7,implies(X,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_7,or(not(X),X_7))) ),[0,1],$fot(implies(X,X_7))]]) ).
cnf(refute_0_18,plain,
( ~ theorem(implies(X_7,or(not(X),X_7)))
| theorem(implies(X_7,implies(X,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_7),implies(X,X_7)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
theorem(implies(X_7,implies(X,X_7))),
inference(resolve,[$cnf( theorem(implies(X_7,or(not(X),X_7))) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
theorem(implies(X_401,implies(X,X_401))),
inference(subst,[],[refute_0_19:[bind(X_7,$fot(X_401))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(X_50,X_51))
| ~ theorem(implies(implies(X_50,X_51),implies(or(X_52,X_50),or(X_52,X_51))))
| theorem(implies(or(X_52,X_50),or(X_52,X_51))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_52,X_50),or(X_52,X_51)))),bind(Y,$fot(implies(X_50,X_51)))]]) ).
cnf(refute_0_22,plain,
( ~ axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31))))
| theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))))]]) ).
cnf(refute_0_23,plain,
axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_30)),bind(B,$fot(X_31)),bind(C,$fot(X_32))]]) ).
cnf(refute_0_24,plain,
theorem(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))),
inference(resolve,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(X_32,X_30),or(X_32,X_31)))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
theorem(implies(implies(X_50,X_51),implies(or(X_52,X_50),or(X_52,X_51)))),
inference(subst,[],[refute_0_24:[bind(X_30,$fot(X_50)),bind(X_31,$fot(X_51)),bind(X_32,$fot(X_52))]]) ).
cnf(refute_0_26,plain,
( ~ theorem(implies(X_50,X_51))
| theorem(implies(or(X_52,X_50),or(X_52,X_51))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_50,X_51),implies(or(X_52,X_50),or(X_52,X_51)))) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
( ~ theorem(implies(X_401,implies(X,X_401)))
| theorem(implies(or(X_403,X_401),or(X_403,implies(X,X_401)))) ),
inference(subst,[],[refute_0_26:[bind(X_50,$fot(X_401)),bind(X_51,$fot(implies(X,X_401))),bind(X_52,$fot(X_403))]]) ).
cnf(refute_0_28,plain,
theorem(implies(or(X_403,X_401),or(X_403,implies(X,X_401)))),
inference(resolve,[$cnf( theorem(implies(X_401,implies(X,X_401))) )],[refute_0_20,refute_0_27]) ).
cnf(refute_0_29,plain,
theorem(implies(or(X_433,X_432),or(X_433,implies(X_431,X_432)))),
inference(subst,[],[refute_0_28:[bind(X,$fot(X_431)),bind(X_401,$fot(X_432)),bind(X_403,$fot(X_433))]]) ).
cnf(refute_0_30,plain,
( ~ theorem(or(X_433,X_432))
| theorem(or(X_433,implies(X_431,X_432))) ),
inference(resolve,[$cnf( theorem(implies(or(X_433,X_432),or(X_433,implies(X_431,X_432)))) )],[refute_0_29,refute_0_6]) ).
cnf(refute_0_31,plain,
( ~ theorem(or(implies(implies(X_66268,X_66266),X_66266),implies(X_66268,X_66267)))
| theorem(or(implies(implies(X_66268,X_66266),X_66266),implies(X_431,implies(X_66268,X_66267)))) ),
inference(subst,[],[refute_0_30:[bind(X_432,$fot(implies(X_66268,X_66267))),bind(X_433,$fot(implies(implies(X_66268,X_66266),X_66266)))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(X_75,or(X_76,X_77)))
| ~ theorem(implies(implies(X_75,or(X_76,X_77)),or(X_76,implies(X_75,X_77))))
| theorem(or(X_76,implies(X_75,X_77))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_76,implies(X_75,X_77)))),bind(Y,$fot(implies(X_75,or(X_76,X_77))))]]) ).
cnf(refute_0_33,plain,
( ~ axiom(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46))))
| theorem(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46)))))]]) ).
cnf(refute_0_34,plain,
axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_28)),bind(C,$fot(X_29))]]) ).
cnf(refute_0_35,plain,
implies(X,X_29) = or(not(X),X_29),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_36,plain,
( implies(X,X_29) != or(not(X),X_29)
| or(not(X),X_29) = implies(X,X_29) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,X_29))),bind(Y0,$fot(or(not(X),X_29)))]]) ).
cnf(refute_0_37,plain,
or(not(X),X_29) = implies(X,X_29),
inference(resolve,[$cnf( $equal(implies(X,X_29),or(not(X),X_29)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( or(not(X),X_29) != implies(X,X_29)
| ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29))))
| axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))) ),[0,1,1],$fot(implies(X,X_29))]]) ).
cnf(refute_0_39,plain,
( ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29))))
| axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,or(not(X),X_29)))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_42,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_41]) ).
cnf(refute_0_43,plain,
or(not(X),or(X_28,X_29)) = implies(X,or(X_28,X_29)),
inference(subst,[],[refute_0_42:[bind(Y,$fot(or(X_28,X_29)))]]) ).
cnf(refute_0_44,plain,
implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))]]) ).
cnf(refute_0_45,plain,
( implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) != implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))
| or(not(X),or(X_28,X_29)) != implies(X,or(X_28,X_29))
| implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),[1,0],$fot(implies(X,or(X_28,X_29)))]]) ).
cnf(refute_0_46,plain,
( or(not(X),or(X_28,X_29)) != implies(X,or(X_28,X_29))
| implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) = implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_28,X_29)),implies(X,or(X_28,X_29))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))) != implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))
| ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))
| axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),[0],$fot(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29))))]]) ).
cnf(refute_0_49,plain,
( ~ axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))))
| axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29))),implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
axiom(implies(implies(X,or(X_28,X_29)),or(X_28,implies(X,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_28,X_29)),or(X_28,implies(X,X_29)))) )],[refute_0_40,refute_0_49]) ).
cnf(refute_0_51,plain,
axiom(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46)))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_44)),bind(X_28,$fot(X_45)),bind(X_29,$fot(X_46))]]) ).
cnf(refute_0_52,plain,
theorem(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46)))),
inference(resolve,[$cnf( axiom(implies(implies(X_44,or(X_45,X_46)),or(X_45,implies(X_44,X_46)))) )],[refute_0_51,refute_0_33]) ).
cnf(refute_0_53,plain,
theorem(implies(implies(X_75,or(X_76,X_77)),or(X_76,implies(X_75,X_77)))),
inference(subst,[],[refute_0_52:[bind(X_44,$fot(X_75)),bind(X_45,$fot(X_76)),bind(X_46,$fot(X_77))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(X_75,or(X_76,X_77)))
| theorem(or(X_76,implies(X_75,X_77))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_75,or(X_76,X_77)),or(X_76,implies(X_75,X_77)))) )],[refute_0_53,refute_0_32]) ).
cnf(refute_0_55,plain,
( ~ theorem(implies(X_57925,or(implies(implies(X_57925,X_57923),X_57923),X_57924)))
| theorem(or(implies(implies(X_57925,X_57923),X_57923),implies(X_57925,X_57924))) ),
inference(subst,[],[refute_0_54:[bind(X_75,$fot(X_57925)),bind(X_76,$fot(implies(implies(X_57925,X_57923),X_57923))),bind(X_77,$fot(X_57924))]]) ).
cnf(refute_0_56,plain,
theorem(implies(X_41,or(X_4,X_41))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(X_41))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(X_41)
| ~ theorem(implies(X_41,or(X_4,X_41)))
| theorem(or(X_4,X_41)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_41))),bind(Y,$fot(X_41))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(X_41)
| theorem(or(X_4,X_41)) ),
inference(resolve,[$cnf( theorem(implies(X_41,or(X_4,X_41))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(implies(X_2193,implies(implies(X_2193,X_2194),X_2194)))
| theorem(or(X_4,implies(X_2193,implies(implies(X_2193,X_2194),X_2194)))) ),
inference(subst,[],[refute_0_58:[bind(X_41,$fot(implies(X_2193,implies(implies(X_2193,X_2194),X_2194))))]]) ).
cnf(refute_0_60,plain,
( ~ axiom(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(or(X_15,X_16),or(X_16,X_15))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_15,X_16),or(X_16,X_15))))]]) ).
cnf(refute_0_61,plain,
axiom(implies(or(X_15,X_16),or(X_16,X_15))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_15)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_62,plain,
theorem(implies(or(X_15,X_16),or(X_16,X_15))),
inference(resolve,[$cnf( axiom(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_16,X_15))),bind(Y,$fot(or(X_15,X_16)))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ theorem(or(X_1111,not(X_1111)))
| theorem(or(not(X_1111),X_1111)) ),
inference(subst,[],[refute_0_64:[bind(X_15,$fot(X_1111)),bind(X_16,$fot(not(X_1111)))]]) ).
cnf(refute_0_66,plain,
( ~ theorem(or(or(X_1109,not(X_1109)),or(X_1109,not(X_1109))))
| theorem(or(X_1109,not(X_1109))) ),
inference(subst,[],[refute_0_4:[bind(X_40,$fot(or(X_1109,not(X_1109))))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(implies(or(X_67,or(X_68,X_69)),or(X_68,or(X_67,X_69))))
| ~ theorem(or(X_67,or(X_68,X_69)))
| theorem(or(X_68,or(X_67,X_69))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_68,or(X_67,X_69)))),bind(Y,$fot(or(X_67,or(X_68,X_69))))]]) ).
cnf(refute_0_68,plain,
( ~ axiom(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29))))
| theorem(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29)))))]]) ).
cnf(refute_0_69,plain,
axiom(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_27)),bind(B,$fot(X_28)),bind(C,$fot(X_29))]]) ).
cnf(refute_0_70,plain,
theorem(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(X_27,or(X_28,X_29)),or(X_28,or(X_27,X_29)))) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
theorem(implies(or(X_67,or(X_68,X_69)),or(X_68,or(X_67,X_69)))),
inference(subst,[],[refute_0_70:[bind(X_27,$fot(X_67)),bind(X_28,$fot(X_68)),bind(X_29,$fot(X_69))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(or(X_67,or(X_68,X_69)))
| theorem(or(X_68,or(X_67,X_69))) ),
inference(resolve,[$cnf( theorem(implies(or(X_67,or(X_68,X_69)),or(X_68,or(X_67,X_69)))) )],[refute_0_71,refute_0_67]) ).
cnf(refute_0_73,plain,
( ~ theorem(or(X_1107,or(X_1108,not(X_1107))))
| theorem(or(X_1108,or(X_1107,not(X_1107)))) ),
inference(subst,[],[refute_0_72:[bind(X_67,$fot(X_1107)),bind(X_68,$fot(X_1108)),bind(X_69,$fot(not(X_1107)))]]) ).
cnf(refute_0_74,plain,
( ~ theorem(or(or(X_1104,not(X_1103)),X_1103))
| theorem(or(X_1103,or(X_1104,not(X_1103)))) ),
inference(subst,[],[refute_0_64:[bind(X_15,$fot(or(X_1104,not(X_1103)))),bind(X_16,$fot(X_1103))]]) ).
cnf(refute_0_75,plain,
( ~ theorem(or(or(or(X_1102,not(X_1100)),X_1100),or(or(X_1102,not(X_1100)),X_1100)))
| theorem(or(or(X_1102,not(X_1100)),X_1100)) ),
inference(subst,[],[refute_0_4:[bind(X_40,$fot(or(or(X_1102,not(X_1100)),X_1100)))]]) ).
cnf(refute_0_76,plain,
( ~ theorem(or(or(X_751,not(X_749)),or(X_750,X_749)))
| theorem(or(X_750,or(or(X_751,not(X_749)),X_749))) ),
inference(subst,[],[refute_0_72:[bind(X_67,$fot(or(X_751,not(X_749)))),bind(X_68,$fot(X_750)),bind(X_69,$fot(X_749))]]) ).
cnf(refute_0_77,plain,
( ~ theorem(or(or(X_687,X_686),or(X_688,not(X_686))))
| theorem(or(or(X_688,not(X_686)),or(X_687,X_686))) ),
inference(subst,[],[refute_0_64:[bind(X_15,$fot(or(X_687,X_686))),bind(X_16,$fot(or(X_688,not(X_686))))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(or(or(X_158,X_157),not(X_157)))
| theorem(or(X_4,or(or(X_158,X_157),not(X_157)))) ),
inference(subst,[],[refute_0_58:[bind(X_41,$fot(or(or(X_158,X_157),not(X_157))))]]) ).
cnf(refute_0_79,plain,
theorem(implies(X_143,or(X_4,X_143))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(X_143))]]) ).
cnf(refute_0_80,plain,
( ~ axiom(implies(implies(X_17,X_18),or(X_18,not(X_17))))
| theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_17,X_18),or(X_18,not(X_17)))))]]) ).
cnf(refute_0_81,plain,
axiom(implies(or(not(X),X_16),or(X_16,not(X)))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(not(X))),bind(B,$fot(X_16))]]) ).
cnf(refute_0_82,plain,
implies(X,X_16) = or(not(X),X_16),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_16))]]) ).
cnf(refute_0_83,plain,
( implies(X,X_16) != or(not(X),X_16)
| or(not(X),X_16) = implies(X,X_16) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,X_16))),bind(Y0,$fot(or(not(X),X_16)))]]) ).
cnf(refute_0_84,plain,
or(not(X),X_16) = implies(X,X_16),
inference(resolve,[$cnf( $equal(implies(X,X_16),or(not(X),X_16)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( or(not(X),X_16) != implies(X,X_16)
| ~ axiom(implies(or(not(X),X_16),or(X_16,not(X))))
| axiom(implies(implies(X,X_16),or(X_16,not(X)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),X_16),or(X_16,not(X)))) ),[0,0],$fot(implies(X,X_16))]]) ).
cnf(refute_0_86,plain,
( ~ axiom(implies(or(not(X),X_16),or(X_16,not(X))))
| axiom(implies(implies(X,X_16),or(X_16,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_16),implies(X,X_16)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
axiom(implies(implies(X,X_16),or(X_16,not(X)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),X_16),or(X_16,not(X)))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
inference(subst,[],[refute_0_87:[bind(X,$fot(X_17)),bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_89,plain,
theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
inference(resolve,[$cnf( axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_88,refute_0_80]) ).
cnf(refute_0_90,plain,
( ~ theorem(implies(X_17,X_18))
| ~ theorem(implies(implies(X_17,X_18),or(X_18,not(X_17))))
| theorem(or(X_18,not(X_17))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X_17)))),bind(Y,$fot(implies(X_17,X_18)))]]) ).
cnf(refute_0_91,plain,
( ~ theorem(implies(X_17,X_18))
| theorem(or(X_18,not(X_17))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ theorem(implies(X_143,or(X_4,X_143)))
| theorem(or(or(X_4,X_143),not(X_143))) ),
inference(subst,[],[refute_0_91:[bind(X_17,$fot(X_143)),bind(X_18,$fot(or(X_4,X_143)))]]) ).
cnf(refute_0_93,plain,
theorem(or(or(X_4,X_143),not(X_143))),
inference(resolve,[$cnf( theorem(implies(X_143,or(X_4,X_143))) )],[refute_0_79,refute_0_92]) ).
cnf(refute_0_94,plain,
theorem(or(or(X_158,X_157),not(X_157))),
inference(subst,[],[refute_0_93:[bind(X_143,$fot(X_157)),bind(X_4,$fot(X_158))]]) ).
cnf(refute_0_95,plain,
theorem(or(X_4,or(or(X_158,X_157),not(X_157)))),
inference(resolve,[$cnf( theorem(or(or(X_158,X_157),not(X_157))) )],[refute_0_94,refute_0_78]) ).
cnf(refute_0_96,plain,
theorem(or(X_671,or(or(X_158,X_157),not(X_157)))),
inference(subst,[],[refute_0_95:[bind(X_4,$fot(X_671))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(or(X_671,or(or(X_158,X_157),not(X_157))))
| theorem(or(or(X_158,X_157),or(X_671,not(X_157)))) ),
inference(subst,[],[refute_0_72:[bind(X_67,$fot(X_671)),bind(X_68,$fot(or(X_158,X_157))),bind(X_69,$fot(not(X_157)))]]) ).
cnf(refute_0_98,plain,
theorem(or(or(X_158,X_157),or(X_671,not(X_157)))),
inference(resolve,[$cnf( theorem(or(X_671,or(or(X_158,X_157),not(X_157)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
theorem(or(or(X_687,X_686),or(X_688,not(X_686)))),
inference(subst,[],[refute_0_98:[bind(X_157,$fot(X_686)),bind(X_158,$fot(X_687)),bind(X_671,$fot(X_688))]]) ).
cnf(refute_0_100,plain,
theorem(or(or(X_688,not(X_686)),or(X_687,X_686))),
inference(resolve,[$cnf( theorem(or(or(X_687,X_686),or(X_688,not(X_686)))) )],[refute_0_99,refute_0_77]) ).
cnf(refute_0_101,plain,
theorem(or(or(X_751,not(X_749)),or(X_750,X_749))),
inference(subst,[],[refute_0_100:[bind(X_686,$fot(X_749)),bind(X_687,$fot(X_750)),bind(X_688,$fot(X_751))]]) ).
cnf(refute_0_102,plain,
theorem(or(X_750,or(or(X_751,not(X_749)),X_749))),
inference(resolve,[$cnf( theorem(or(or(X_751,not(X_749)),or(X_750,X_749))) )],[refute_0_101,refute_0_76]) ).
cnf(refute_0_103,plain,
theorem(or(or(or(X_1102,not(X_1100)),X_1100),or(or(X_1102,not(X_1100)),X_1100))),
inference(subst,[],[refute_0_102:[bind(X_749,$fot(X_1100)),bind(X_750,$fot(or(or(X_1102,not(X_1100)),X_1100))),bind(X_751,$fot(X_1102))]]) ).
cnf(refute_0_104,plain,
theorem(or(or(X_1102,not(X_1100)),X_1100)),
inference(resolve,[$cnf( theorem(or(or(or(X_1102,not(X_1100)),X_1100),or(or(X_1102,not(X_1100)),X_1100))) )],[refute_0_103,refute_0_75]) ).
cnf(refute_0_105,plain,
theorem(or(or(X_1104,not(X_1103)),X_1103)),
inference(subst,[],[refute_0_104:[bind(X_1100,$fot(X_1103)),bind(X_1102,$fot(X_1104))]]) ).
cnf(refute_0_106,plain,
theorem(or(X_1103,or(X_1104,not(X_1103)))),
inference(resolve,[$cnf( theorem(or(or(X_1104,not(X_1103)),X_1103)) )],[refute_0_105,refute_0_74]) ).
cnf(refute_0_107,plain,
theorem(or(X_1107,or(X_1108,not(X_1107)))),
inference(subst,[],[refute_0_106:[bind(X_1103,$fot(X_1107)),bind(X_1104,$fot(X_1108))]]) ).
cnf(refute_0_108,plain,
theorem(or(X_1108,or(X_1107,not(X_1107)))),
inference(resolve,[$cnf( theorem(or(X_1107,or(X_1108,not(X_1107)))) )],[refute_0_107,refute_0_73]) ).
cnf(refute_0_109,plain,
theorem(or(or(X_1109,not(X_1109)),or(X_1109,not(X_1109)))),
inference(subst,[],[refute_0_108:[bind(X_1107,$fot(X_1109)),bind(X_1108,$fot(or(X_1109,not(X_1109))))]]) ).
cnf(refute_0_110,plain,
theorem(or(X_1109,not(X_1109))),
inference(resolve,[$cnf( theorem(or(or(X_1109,not(X_1109)),or(X_1109,not(X_1109)))) )],[refute_0_109,refute_0_66]) ).
cnf(refute_0_111,plain,
theorem(or(X_1111,not(X_1111))),
inference(subst,[],[refute_0_110:[bind(X_1109,$fot(X_1111))]]) ).
cnf(refute_0_112,plain,
theorem(or(not(X_1111),X_1111)),
inference(resolve,[$cnf( theorem(or(X_1111,not(X_1111))) )],[refute_0_111,refute_0_65]) ).
cnf(refute_0_113,plain,
or(not(X_1111),X_1111) = implies(X_1111,X_1111),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_1111)),bind(Y,$fot(X_1111))]]) ).
cnf(refute_0_114,plain,
( or(not(X_1111),X_1111) != implies(X_1111,X_1111)
| ~ theorem(or(not(X_1111),X_1111))
| theorem(implies(X_1111,X_1111)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_1111),X_1111)) ),[0],$fot(implies(X_1111,X_1111))]]) ).
cnf(refute_0_115,plain,
( ~ theorem(or(not(X_1111),X_1111))
| theorem(implies(X_1111,X_1111)) ),
inference(resolve,[$cnf( $equal(or(not(X_1111),X_1111),implies(X_1111,X_1111)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
theorem(implies(X_1111,X_1111)),
inference(resolve,[$cnf( theorem(or(not(X_1111),X_1111)) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
theorem(implies(implies(X_2178,X_2180),implies(X_2178,X_2180))),
inference(subst,[],[refute_0_116:[bind(X_1111,$fot(implies(X_2178,X_2180)))]]) ).
cnf(refute_0_118,plain,
( ~ theorem(implies(X_82,implies(X_81,X_83)))
| ~ theorem(implies(implies(X_82,implies(X_81,X_83)),implies(X_81,implies(X_82,X_83))))
| theorem(implies(X_81,implies(X_82,X_83))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_81,implies(X_82,X_83)))),bind(Y,$fot(implies(X_82,implies(X_81,X_83))))]]) ).
cnf(refute_0_119,plain,
( ~ axiom(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58))))
| theorem(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58)))))]]) ).
cnf(refute_0_120,plain,
axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_44)),bind(X_28,$fot(not(X))),bind(X_29,$fot(X_46))]]) ).
cnf(refute_0_121,plain,
implies(X,implies(X_44,X_46)) = or(not(X),implies(X_44,X_46)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_44,X_46)))]]) ).
cnf(refute_0_122,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_14:[bind(X0,$fot(implies(X,implies(X_44,X_46)))),bind(Y0,$fot(or(not(X),implies(X_44,X_46))))]]) ).
cnf(refute_0_123,plain,
or(not(X),implies(X_44,X_46)) = implies(X,implies(X_44,X_46)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_44,X_46)),or(not(X),implies(X_44,X_46))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( or(not(X),implies(X_44,X_46)) != implies(X,implies(X_44,X_46))
| ~ axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46))))
| axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))) ),[0,1],$fot(implies(X,implies(X_44,X_46)))]]) ).
cnf(refute_0_125,plain,
( ~ axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46))))
| axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_44,X_46)),implies(X,implies(X_44,X_46))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))),
inference(resolve,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),or(not(X),implies(X_44,X_46)))) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
or(not(X),X_46) = implies(X,X_46),
inference(subst,[],[refute_0_42:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_128,plain,
implies(X_44,or(not(X),X_46)) = implies(X_44,or(not(X),X_46)),
introduced(tautology,[refl,[$fot(implies(X_44,or(not(X),X_46)))]]) ).
cnf(refute_0_129,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_130,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( $equal(implies(X_44,or(not(X),X_46)),implies(X_44,or(not(X),X_46))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(X_44,or(not(X),X_46)) = implies(X_44,implies(X,X_46)),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),
introduced(tautology,[refl,[$fot(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))]]) ).
cnf(refute_0_133,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_134,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( $equal(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) = implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))),
inference(resolve,[$cnf( $equal(implies(X_44,or(not(X),X_46)),implies(X_44,implies(X,X_46))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))) != implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))
| ~ axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))
| axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) ),[0],$fot(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46))))]]) ).
cnf(refute_0_137,plain,
( ~ axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))))
| axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46))),implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
axiom(implies(implies(X_44,implies(X,X_46)),implies(X,implies(X_44,X_46)))),
inference(resolve,[$cnf( axiom(implies(implies(X_44,or(not(X),X_46)),implies(X,implies(X_44,X_46)))) )],[refute_0_126,refute_0_137]) ).
cnf(refute_0_139,plain,
axiom(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58)))),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_56)),bind(X_44,$fot(X_57)),bind(X_46,$fot(X_58))]]) ).
cnf(refute_0_140,plain,
theorem(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58)))),
inference(resolve,[$cnf( axiom(implies(implies(X_57,implies(X_56,X_58)),implies(X_56,implies(X_57,X_58)))) )],[refute_0_139,refute_0_119]) ).
cnf(refute_0_141,plain,
theorem(implies(implies(X_82,implies(X_81,X_83)),implies(X_81,implies(X_82,X_83)))),
inference(subst,[],[refute_0_140:[bind(X_56,$fot(X_81)),bind(X_57,$fot(X_82)),bind(X_58,$fot(X_83))]]) ).
cnf(refute_0_142,plain,
( ~ theorem(implies(X_82,implies(X_81,X_83)))
| theorem(implies(X_81,implies(X_82,X_83))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_82,implies(X_81,X_83)),implies(X_81,implies(X_82,X_83)))) )],[refute_0_141,refute_0_118]) ).
cnf(refute_0_143,plain,
( ~ theorem(implies(implies(X_2178,X_2180),implies(X_2178,X_2180)))
| theorem(implies(X_2178,implies(implies(X_2178,X_2180),X_2180))) ),
inference(subst,[],[refute_0_142:[bind(X_81,$fot(X_2178)),bind(X_82,$fot(implies(X_2178,X_2180))),bind(X_83,$fot(X_2180))]]) ).
cnf(refute_0_144,plain,
theorem(implies(X_2178,implies(implies(X_2178,X_2180),X_2180))),
inference(resolve,[$cnf( theorem(implies(implies(X_2178,X_2180),implies(X_2178,X_2180))) )],[refute_0_117,refute_0_143]) ).
cnf(refute_0_145,plain,
theorem(implies(X_2193,implies(implies(X_2193,X_2194),X_2194))),
inference(subst,[],[refute_0_144:[bind(X_2178,$fot(X_2193)),bind(X_2180,$fot(X_2194))]]) ).
cnf(refute_0_146,plain,
theorem(or(X_4,implies(X_2193,implies(implies(X_2193,X_2194),X_2194)))),
inference(resolve,[$cnf( theorem(implies(X_2193,implies(implies(X_2193,X_2194),X_2194))) )],[refute_0_145,refute_0_59]) ).
cnf(refute_0_147,plain,
theorem(or(X_4107,implies(X_4106,implies(implies(X_4106,X_2194),X_2194)))),
inference(subst,[],[refute_0_146:[bind(X_2193,$fot(X_4106)),bind(X_4,$fot(X_4107))]]) ).
cnf(refute_0_148,plain,
( ~ theorem(implies(or(X_79,implies(X_78,X_80)),implies(X_78,or(X_79,X_80))))
| ~ theorem(or(X_79,implies(X_78,X_80)))
| theorem(implies(X_78,or(X_79,X_80))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_78,or(X_79,X_80)))),bind(Y,$fot(or(X_79,implies(X_78,X_80))))]]) ).
cnf(refute_0_149,plain,
( ~ axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49))))
| theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))))]]) ).
cnf(refute_0_150,plain,
axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_27)),bind(B,$fot(not(X))),bind(C,$fot(X_29))]]) ).
cnf(refute_0_151,plain,
implies(X,or(X_27,X_29)) = or(not(X),or(X_27,X_29)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_27,X_29)))]]) ).
cnf(refute_0_152,plain,
( implies(X,or(X_27,X_29)) != or(not(X),or(X_27,X_29))
| or(not(X),or(X_27,X_29)) = implies(X,or(X_27,X_29)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,or(X_27,X_29)))),bind(Y0,$fot(or(not(X),or(X_27,X_29))))]]) ).
cnf(refute_0_153,plain,
or(not(X),or(X_27,X_29)) = implies(X,or(X_27,X_29)),
inference(resolve,[$cnf( $equal(implies(X,or(X_27,X_29)),or(not(X),or(X_27,X_29))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( or(not(X),or(X_27,X_29)) != implies(X,or(X_27,X_29))
| ~ axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29))))
| axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))) ),[0,1],$fot(implies(X,or(X_27,X_29)))]]) ).
cnf(refute_0_155,plain,
( ~ axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29))))
| axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_27,X_29)),implies(X,or(X_27,X_29))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))) )],[refute_0_150,refute_0_155]) ).
cnf(refute_0_157,plain,
or(X_27,or(not(X),X_29)) = or(X_27,or(not(X),X_29)),
introduced(tautology,[refl,[$fot(or(X_27,or(not(X),X_29)))]]) ).
cnf(refute_0_158,plain,
( or(X_27,or(not(X),X_29)) != or(X_27,or(not(X),X_29))
| or(not(X),X_29) != implies(X,X_29)
| or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,or(not(X),X_29))) ),[1,1],$fot(implies(X,X_29))]]) ).
cnf(refute_0_159,plain,
( or(not(X),X_29) != implies(X,X_29)
| or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)) ),
inference(resolve,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,or(not(X),X_29))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_37,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),
introduced(tautology,[refl,[$fot(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))]]) ).
cnf(refute_0_162,plain,
( implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) != implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))
| or(X_27,or(not(X),X_29)) != or(X_27,implies(X,X_29))
| implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),[1,0],$fot(or(X_27,implies(X,X_29)))]]) ).
cnf(refute_0_163,plain,
( or(X_27,or(not(X),X_29)) != or(X_27,implies(X,X_29))
| implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))) ),
inference(resolve,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))),
inference(resolve,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,implies(X,X_29))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) != implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))
| ~ axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))
| axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),[0],$fot(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))))]]) ).
cnf(refute_0_166,plain,
( ~ axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))
| axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_156,refute_0_166]) ).
cnf(refute_0_168,plain,
axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(subst,[],[refute_0_167:[bind(X,$fot(X_47)),bind(X_27,$fot(X_48)),bind(X_29,$fot(X_49))]]) ).
cnf(refute_0_169,plain,
theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(resolve,[$cnf( axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) )],[refute_0_168,refute_0_149]) ).
cnf(refute_0_170,plain,
theorem(implies(or(X_79,implies(X_78,X_80)),implies(X_78,or(X_79,X_80)))),
inference(subst,[],[refute_0_169:[bind(X_47,$fot(X_78)),bind(X_48,$fot(X_79)),bind(X_49,$fot(X_80))]]) ).
cnf(refute_0_171,plain,
( ~ theorem(or(X_79,implies(X_78,X_80)))
| theorem(implies(X_78,or(X_79,X_80))) ),
inference(resolve,[$cnf( theorem(implies(or(X_79,implies(X_78,X_80)),implies(X_78,or(X_79,X_80)))) )],[refute_0_170,refute_0_148]) ).
cnf(refute_0_172,plain,
( ~ theorem(or(X_4107,implies(X_4106,implies(implies(X_4106,X_2194),X_2194))))
| theorem(implies(X_4106,or(X_4107,implies(implies(X_4106,X_2194),X_2194)))) ),
inference(subst,[],[refute_0_171:[bind(X_78,$fot(X_4106)),bind(X_79,$fot(X_4107)),bind(X_80,$fot(implies(implies(X_4106,X_2194),X_2194)))]]) ).
cnf(refute_0_173,plain,
theorem(implies(X_4106,or(X_4107,implies(implies(X_4106,X_2194),X_2194)))),
inference(resolve,[$cnf( theorem(or(X_4107,implies(X_4106,implies(implies(X_4106,X_2194),X_2194)))) )],[refute_0_147,refute_0_172]) ).
cnf(refute_0_174,plain,
theorem(implies(X_56912,or(X_56910,implies(implies(X_56912,X_2194),X_2194)))),
inference(subst,[],[refute_0_173:[bind(X_4106,$fot(X_56912)),bind(X_4107,$fot(X_56910))]]) ).
cnf(refute_0_175,plain,
( ~ theorem(implies(X_276,or(X_274,X_275)))
| ~ theorem(implies(implies(X_276,or(X_274,X_275)),implies(X_276,or(X_275,X_274))))
| theorem(implies(X_276,or(X_275,X_274))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_276,or(X_275,X_274)))),bind(Y,$fot(implies(X_276,or(X_274,X_275))))]]) ).
cnf(refute_0_176,plain,
( ~ theorem(implies(X_54,X_55))
| ~ theorem(implies(implies(X_54,X_55),implies(implies(X_53,X_54),implies(X_53,X_55))))
| theorem(implies(implies(X_53,X_54),implies(X_53,X_55))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X_53,X_54),implies(X_53,X_55)))),bind(Y,$fot(implies(X_54,X_55)))]]) ).
cnf(refute_0_177,plain,
( ~ axiom(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35))))
| theorem(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35)))))]]) ).
cnf(refute_0_178,plain,
axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),or(not(X),X_31)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_30)),bind(B,$fot(X_31)),bind(C,$fot(not(X)))]]) ).
cnf(refute_0_179,plain,
implies(X,X_31) = or(not(X),X_31),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_180,plain,
( implies(X,X_31) != or(not(X),X_31)
| or(not(X),X_31) = implies(X,X_31) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,X_31))),bind(Y0,$fot(or(not(X),X_31)))]]) ).
cnf(refute_0_181,plain,
or(not(X),X_31) = implies(X,X_31),
inference(resolve,[$cnf( $equal(implies(X,X_31),or(not(X),X_31)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
( or(not(X),X_31) != implies(X,X_31)
| ~ axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),or(not(X),X_31))))
| axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),or(not(X),X_31)))) ),[0,1,1],$fot(implies(X,X_31))]]) ).
cnf(refute_0_183,plain,
( ~ axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),or(not(X),X_31))))
| axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_31),implies(X,X_31)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))),
inference(resolve,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),or(not(X),X_31)))) )],[refute_0_178,refute_0_183]) ).
cnf(refute_0_185,plain,
or(not(X),X_30) = implies(X,X_30),
inference(subst,[],[refute_0_42:[bind(Y,$fot(X_30))]]) ).
cnf(refute_0_186,plain,
implies(or(not(X),X_30),implies(X,X_31)) = implies(or(not(X),X_30),implies(X,X_31)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_30),implies(X,X_31)))]]) ).
cnf(refute_0_187,plain,
( implies(or(not(X),X_30),implies(X,X_31)) != implies(or(not(X),X_30),implies(X,X_31))
| or(not(X),X_30) != implies(X,X_30)
| implies(or(not(X),X_30),implies(X,X_31)) = implies(implies(X,X_30),implies(X,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_30),implies(X,X_31)),implies(or(not(X),X_30),implies(X,X_31))) ),[1,0],$fot(implies(X,X_30))]]) ).
cnf(refute_0_188,plain,
( or(not(X),X_30) != implies(X,X_30)
| implies(or(not(X),X_30),implies(X,X_31)) = implies(implies(X,X_30),implies(X,X_31)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_30),implies(X,X_31)),implies(or(not(X),X_30),implies(X,X_31))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(or(not(X),X_30),implies(X,X_31)) = implies(implies(X,X_30),implies(X,X_31)),
inference(resolve,[$cnf( $equal(or(not(X),X_30),implies(X,X_30)) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) = implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))),
introduced(tautology,[refl,[$fot(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))))]]) ).
cnf(refute_0_191,plain,
( implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) != implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))
| implies(or(not(X),X_30),implies(X,X_31)) != implies(implies(X,X_30),implies(X,X_31))
| implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) = implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))),implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) ),[1,1],$fot(implies(implies(X,X_30),implies(X,X_31)))]]) ).
cnf(refute_0_192,plain,
( implies(or(not(X),X_30),implies(X,X_31)) != implies(implies(X,X_30),implies(X,X_31))
| implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) = implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))),implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) = implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_30),implies(X,X_31)),implies(implies(X,X_30),implies(X,X_31))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))) != implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31)))
| ~ axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))))
| axiom(implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) ),[0],$fot(implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31))))]]) ).
cnf(refute_0_195,plain,
( ~ axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))))
| axiom(implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31))),implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
axiom(implies(implies(X_30,X_31),implies(implies(X,X_30),implies(X,X_31)))),
inference(resolve,[$cnf( axiom(implies(implies(X_30,X_31),implies(or(not(X),X_30),implies(X,X_31)))) )],[refute_0_184,refute_0_195]) ).
cnf(refute_0_197,plain,
axiom(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35)))),
inference(subst,[],[refute_0_196:[bind(X,$fot(X_33)),bind(X_30,$fot(X_34)),bind(X_31,$fot(X_35))]]) ).
cnf(refute_0_198,plain,
theorem(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,X_35),implies(implies(X_33,X_34),implies(X_33,X_35)))) )],[refute_0_197,refute_0_177]) ).
cnf(refute_0_199,plain,
theorem(implies(implies(X_54,X_55),implies(implies(X_53,X_54),implies(X_53,X_55)))),
inference(subst,[],[refute_0_198:[bind(X_33,$fot(X_53)),bind(X_34,$fot(X_54)),bind(X_35,$fot(X_55))]]) ).
cnf(refute_0_200,plain,
( ~ theorem(implies(X_54,X_55))
| theorem(implies(implies(X_53,X_54),implies(X_53,X_55))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_54,X_55),implies(implies(X_53,X_54),implies(X_53,X_55)))) )],[refute_0_199,refute_0_176]) ).
cnf(refute_0_201,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(implies(X_264,or(X_15,X_16)),implies(X_264,or(X_16,X_15)))) ),
inference(subst,[],[refute_0_200:[bind(X_53,$fot(X_264)),bind(X_54,$fot(or(X_15,X_16))),bind(X_55,$fot(or(X_16,X_15)))]]) ).
cnf(refute_0_202,plain,
theorem(implies(implies(X_264,or(X_15,X_16)),implies(X_264,or(X_16,X_15)))),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_62,refute_0_201]) ).
cnf(refute_0_203,plain,
theorem(implies(implies(X_276,or(X_274,X_275)),implies(X_276,or(X_275,X_274)))),
inference(subst,[],[refute_0_202:[bind(X_15,$fot(X_274)),bind(X_16,$fot(X_275)),bind(X_264,$fot(X_276))]]) ).
cnf(refute_0_204,plain,
( ~ theorem(implies(X_276,or(X_274,X_275)))
| theorem(implies(X_276,or(X_275,X_274))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_276,or(X_274,X_275)),implies(X_276,or(X_275,X_274)))) )],[refute_0_203,refute_0_175]) ).
cnf(refute_0_205,plain,
( ~ theorem(implies(X_56912,or(X_56910,implies(implies(X_56912,X_2194),X_2194))))
| theorem(implies(X_56912,or(implies(implies(X_56912,X_2194),X_2194),X_56910))) ),
inference(subst,[],[refute_0_204:[bind(X_274,$fot(X_56910)),bind(X_275,$fot(implies(implies(X_56912,X_2194),X_2194))),bind(X_276,$fot(X_56912))]]) ).
cnf(refute_0_206,plain,
theorem(implies(X_56912,or(implies(implies(X_56912,X_2194),X_2194),X_56910))),
inference(resolve,[$cnf( theorem(implies(X_56912,or(X_56910,implies(implies(X_56912,X_2194),X_2194)))) )],[refute_0_174,refute_0_205]) ).
cnf(refute_0_207,plain,
theorem(implies(X_57925,or(implies(implies(X_57925,X_57923),X_57923),X_57924))),
inference(subst,[],[refute_0_206:[bind(X_2194,$fot(X_57923)),bind(X_56910,$fot(X_57924)),bind(X_56912,$fot(X_57925))]]) ).
cnf(refute_0_208,plain,
theorem(or(implies(implies(X_57925,X_57923),X_57923),implies(X_57925,X_57924))),
inference(resolve,[$cnf( theorem(implies(X_57925,or(implies(implies(X_57925,X_57923),X_57923),X_57924))) )],[refute_0_207,refute_0_55]) ).
cnf(refute_0_209,plain,
theorem(or(implies(implies(X_66268,X_66266),X_66266),implies(X_66268,X_66267))),
inference(subst,[],[refute_0_208:[bind(X_57923,$fot(X_66266)),bind(X_57924,$fot(X_66267)),bind(X_57925,$fot(X_66268))]]) ).
cnf(refute_0_210,plain,
theorem(or(implies(implies(X_66268,X_66266),X_66266),implies(X_431,implies(X_66268,X_66267)))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_66268,X_66266),X_66266),implies(X_66268,X_66267))) )],[refute_0_209,refute_0_31]) ).
cnf(refute_0_211,plain,
theorem(or(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271)),implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271)))),
inference(subst,[],[refute_0_210:[bind(X_431,$fot(implies(X_66272,implies(X_66272,X_66271)))),bind(X_66266,$fot(implies(X_66272,X_66271))),bind(X_66267,$fot(X_66271)),bind(X_66268,$fot(X_66272))]]) ).
cnf(refute_0_212,plain,
theorem(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271)),implies(implies(X_66272,implies(X_66272,X_66271)),implies(X_66272,X_66271)))) )],[refute_0_211,refute_0_5]) ).
cnf(refute_0_213,plain,
theorem(implies(implies(p,implies(p,q)),implies(p,q))),
inference(subst,[],[refute_0_212:[bind(X_66271,$fot(q)),bind(X_66272,$fot(p))]]) ).
cnf(refute_0_214,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(p,implies(p,q)),implies(p,q))) )],[refute_0_213,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 22:56:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 167.33/167.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 167.33/167.51
% 167.33/167.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 167.33/167.53
%------------------------------------------------------------------------------