TSTP Solution File: LCL239-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:51:01 EDT 2022
% Result : Unsatisfiable 0.61s 0.81s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 34
% Syntax : Number of clauses : 163 ( 87 unt; 0 nHn; 74 RR)
% Number of literals : 266 ( 107 equ; 104 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 309 ( 16 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(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
~ theorem(not(and(p,not(p)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
theorem(implies(or(not(X),X_14),or(X_14,not(X)))),
inference(subst,[],[refute_0_2:[bind(X_7,$fot(not(X))),bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_4,plain,
implies(X,X_14) = or(not(X),X_14),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_14))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X,X_14) != or(not(X),X_14)
| or(not(X),X_14) = implies(X,X_14) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_14))),bind(Y0,$fot(or(not(X),X_14)))]]) ).
cnf(refute_0_9,plain,
or(not(X),X_14) = implies(X,X_14),
inference(resolve,[$cnf( $equal(implies(X,X_14),or(not(X),X_14)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X),X_14) != implies(X,X_14)
| ~ theorem(implies(or(not(X),X_14),or(X_14,not(X))))
| theorem(implies(implies(X,X_14),or(X_14,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_14),or(X_14,not(X)))) ),[0,0],$fot(implies(X,X_14))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(or(not(X),X_14),or(X_14,not(X))))
| theorem(implies(implies(X,X_14),or(X_14,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_14),implies(X,X_14)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(implies(X,X_14),or(X_14,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_14),or(X_14,not(X)))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ theorem(implies(X,X_14))
| ~ theorem(implies(implies(X,X_14),or(X_14,not(X))))
| theorem(or(X_14,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_14,not(X)))),bind(Y,$fot(implies(X,X_14)))]]) ).
cnf(refute_0_14,plain,
( ~ theorem(implies(X,X_14))
| theorem(or(X_14,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_14),or(X_14,not(X)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ theorem(implies(X_471,X_471))
| theorem(or(X_471,not(X_471))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_471)),bind(X_14,$fot(X_471))]]) ).
cnf(refute_0_16,plain,
( ~ theorem(X_162)
| ~ theorem(implies(X_162,and(X_162,X_162)))
| theorem(and(X_162,X_162)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_162,X_162))),bind(Y,$fot(X_162))]]) ).
cnf(refute_0_17,plain,
( ~ axiom(or(and(X_22,X_22),not(X_22)))
| theorem(or(and(X_22,X_22),not(X_22))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(and(X_22,X_22),not(X_22))))]]) ).
cnf(refute_0_18,plain,
axiom(implies(or(not(X_9),not(X_9)),not(X_9))),
inference(subst,[],[axiom_1_2:[bind(A,$fot(not(X_9)))]]) ).
cnf(refute_0_19,plain,
implies(X_9,not(X_9)) = or(not(X_9),not(X_9)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_9)),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_20,plain,
( implies(X_9,not(X_9)) != or(not(X_9),not(X_9))
| or(not(X_9),not(X_9)) = implies(X_9,not(X_9)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_9,not(X_9)))),bind(Y0,$fot(or(not(X_9),not(X_9))))]]) ).
cnf(refute_0_21,plain,
or(not(X_9),not(X_9)) = implies(X_9,not(X_9)),
inference(resolve,[$cnf( $equal(implies(X_9,not(X_9)),or(not(X_9),not(X_9))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( or(not(X_9),not(X_9)) != implies(X_9,not(X_9))
| ~ axiom(implies(or(not(X_9),not(X_9)),not(X_9)))
| axiom(implies(implies(X_9,not(X_9)),not(X_9))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X_9),not(X_9)),not(X_9))) ),[0,0],$fot(implies(X_9,not(X_9)))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(or(not(X_9),not(X_9)),not(X_9)))
| axiom(implies(implies(X_9,not(X_9)),not(X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),not(X_9)),implies(X_9,not(X_9))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
axiom(implies(implies(X_9,not(X_9)),not(X_9))),
inference(resolve,[$cnf( axiom(implies(or(not(X_9),not(X_9)),not(X_9))) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
implies(implies(X_20,not(X_21)),Y) = or(not(implies(X_20,not(X_21))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_20,not(X_21))))]]) ).
cnf(refute_0_26,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_27,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_26]) ).
cnf(refute_0_28,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_27:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_29,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_30,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_31,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_34,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_34]) ).
cnf(refute_0_36,plain,
and(X_20,X_21) = not(implies(X_20,not(X_21))),
inference(subst,[],[refute_0_35:[bind(P,$fot(X_20)),bind(Q,$fot(X_21))]]) ).
cnf(refute_0_37,plain,
( and(X_20,X_21) != not(implies(X_20,not(X_21)))
| not(implies(X_20,not(X_21))) = and(X_20,X_21) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(and(X_20,X_21))),bind(Y0,$fot(not(implies(X_20,not(X_21)))))]]) ).
cnf(refute_0_38,plain,
not(implies(X_20,not(X_21))) = and(X_20,X_21),
inference(resolve,[$cnf( $equal(and(X_20,X_21),not(implies(X_20,not(X_21)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( implies(implies(X_20,not(X_21)),Y) != or(not(implies(X_20,not(X_21))),Y)
| not(implies(X_20,not(X_21))) != and(X_20,X_21)
| implies(implies(X_20,not(X_21)),Y) = or(and(X_20,X_21),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_20,not(X_21)),Y),or(not(implies(X_20,not(X_21))),Y)) ),[1,0],$fot(and(X_20,X_21))]]) ).
cnf(refute_0_40,plain,
( implies(implies(X_20,not(X_21)),Y) != or(not(implies(X_20,not(X_21))),Y)
| implies(implies(X_20,not(X_21)),Y) = or(and(X_20,X_21),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_20,not(X_21))),and(X_20,X_21)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(implies(X_20,not(X_21)),Y) = or(and(X_20,X_21),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_20,not(X_21)),Y),or(not(implies(X_20,not(X_21))),Y)) )],[refute_0_25,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(implies(X_9,not(X_9)),not(X_9)) = or(and(X_9,X_9),not(X_9)),
inference(subst,[],[refute_0_41:[bind(Y,$fot(not(X_9))),bind(X_20,$fot(X_9)),bind(X_21,$fot(X_9))]]) ).
cnf(refute_0_43,plain,
( implies(implies(X_9,not(X_9)),not(X_9)) != or(and(X_9,X_9),not(X_9))
| ~ axiom(implies(implies(X_9,not(X_9)),not(X_9)))
| axiom(or(and(X_9,X_9),not(X_9))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_9,not(X_9)),not(X_9))) ),[0],$fot(or(and(X_9,X_9),not(X_9)))]]) ).
cnf(refute_0_44,plain,
( ~ axiom(implies(implies(X_9,not(X_9)),not(X_9)))
| axiom(or(and(X_9,X_9),not(X_9))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,not(X_9)),not(X_9)),or(and(X_9,X_9),not(X_9))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
axiom(or(and(X_9,X_9),not(X_9))),
inference(resolve,[$cnf( axiom(implies(implies(X_9,not(X_9)),not(X_9))) )],[refute_0_24,refute_0_44]) ).
cnf(refute_0_46,plain,
axiom(or(and(X_22,X_22),not(X_22))),
inference(subst,[],[refute_0_45:[bind(X_9,$fot(X_22))]]) ).
cnf(refute_0_47,plain,
theorem(or(and(X_22,X_22),not(X_22))),
inference(resolve,[$cnf( axiom(or(and(X_22,X_22),not(X_22))) )],[refute_0_46,refute_0_17]) ).
cnf(refute_0_48,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_2,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(and(X_22,X_22),not(X_22)))
| theorem(or(not(X_22),and(X_22,X_22))) ),
inference(subst,[],[refute_0_49:[bind(X_7,$fot(and(X_22,X_22))),bind(X_8,$fot(not(X_22)))]]) ).
cnf(refute_0_51,plain,
theorem(or(not(X_22),and(X_22,X_22))),
inference(resolve,[$cnf( theorem(or(and(X_22,X_22),not(X_22))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
or(not(X_22),and(X_22,X_22)) = implies(X_22,and(X_22,X_22)),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_22)),bind(Y,$fot(and(X_22,X_22)))]]) ).
cnf(refute_0_53,plain,
( or(not(X_22),and(X_22,X_22)) != implies(X_22,and(X_22,X_22))
| ~ theorem(or(not(X_22),and(X_22,X_22)))
| theorem(implies(X_22,and(X_22,X_22))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_22),and(X_22,X_22))) ),[0],$fot(implies(X_22,and(X_22,X_22)))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(or(not(X_22),and(X_22,X_22)))
| theorem(implies(X_22,and(X_22,X_22))) ),
inference(resolve,[$cnf( $equal(or(not(X_22),and(X_22,X_22)),implies(X_22,and(X_22,X_22))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(implies(X_22,and(X_22,X_22))),
inference(resolve,[$cnf( theorem(or(not(X_22),and(X_22,X_22))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
theorem(implies(X_162,and(X_162,X_162))),
inference(subst,[],[refute_0_55:[bind(X_22,$fot(X_162))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(X_162)
| theorem(and(X_162,X_162)) ),
inference(resolve,[$cnf( theorem(implies(X_162,and(X_162,X_162))) )],[refute_0_56,refute_0_16]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(or(X_441,X_441),implies(X_440,X_441)))
| theorem(and(implies(or(X_441,X_441),implies(X_440,X_441)),implies(or(X_441,X_441),implies(X_440,X_441)))) ),
inference(subst,[],[refute_0_57:[bind(X_162,$fot(implies(or(X_441,X_441),implies(X_440,X_441))))]]) ).
cnf(refute_0_59,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_60,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ axiom(implies(X_11,implies(X_12,X_11)))
| theorem(implies(X_11,implies(X_12,X_11))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_11,implies(X_12,X_11))))]]) ).
cnf(refute_0_62,plain,
axiom(implies(A,or(not(X_9),A))),
inference(subst,[],[axiom_1_3:[bind(B,$fot(not(X_9)))]]) ).
cnf(refute_0_63,plain,
implies(X_9,A) = or(not(X_9),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_9)),bind(Y,$fot(A))]]) ).
cnf(refute_0_64,plain,
( implies(X_9,A) != or(not(X_9),A)
| or(not(X_9),A) = implies(X_9,A) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_9,A))),bind(Y0,$fot(or(not(X_9),A)))]]) ).
cnf(refute_0_65,plain,
or(not(X_9),A) = implies(X_9,A),
inference(resolve,[$cnf( $equal(implies(X_9,A),or(not(X_9),A)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( or(not(X_9),A) != implies(X_9,A)
| ~ axiom(implies(A,or(not(X_9),A)))
| axiom(implies(A,implies(X_9,A))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(A,or(not(X_9),A))) ),[0,1],$fot(implies(X_9,A))]]) ).
cnf(refute_0_67,plain,
( ~ axiom(implies(A,or(not(X_9),A)))
| axiom(implies(A,implies(X_9,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),A),implies(X_9,A)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
axiom(implies(A,implies(X_9,A))),
inference(resolve,[$cnf( axiom(implies(A,or(not(X_9),A))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
axiom(implies(X_11,implies(X_12,X_11))),
inference(subst,[],[refute_0_68:[bind(A,$fot(X_11)),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_70,plain,
theorem(implies(X_11,implies(X_12,X_11))),
inference(resolve,[$cnf( axiom(implies(X_11,implies(X_12,X_11))) )],[refute_0_69,refute_0_61]) ).
cnf(refute_0_71,plain,
theorem(implies(X_87,implies(X_12,X_87))),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(X_87))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(X_87)
| ~ theorem(implies(X_87,implies(X_12,X_87)))
| theorem(implies(X_12,X_87)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_12,X_87))),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(X_87)
| theorem(implies(X_12,X_87)) ),
inference(resolve,[$cnf( theorem(implies(X_87,implies(X_12,X_87))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ theorem(implies(or(A,A),A))
| theorem(implies(X_97,implies(or(A,A),A))) ),
inference(subst,[],[refute_0_73:[bind(X_12,$fot(X_97)),bind(X_87,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_75,plain,
theorem(implies(X_97,implies(or(A,A),A))),
inference(resolve,[$cnf( theorem(implies(or(A,A),A)) )],[refute_0_60,refute_0_74]) ).
cnf(refute_0_76,plain,
theorem(implies(X_436,implies(or(X_437,X_437),X_437))),
inference(subst,[],[refute_0_75:[bind(A,$fot(X_437)),bind(X_97,$fot(X_436))]]) ).
cnf(refute_0_77,plain,
( ~ axiom(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75))))
| theorem(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))))]]) ).
cnf(refute_0_78,plain,
axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,or(not(X),X_35)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_34)),bind(C,$fot(X_35))]]) ).
cnf(refute_0_79,plain,
implies(X,X_35) = or(not(X),X_35),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_80,plain,
( implies(X,X_35) != or(not(X),X_35)
| or(not(X),X_35) = implies(X,X_35) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_35))),bind(Y0,$fot(or(not(X),X_35)))]]) ).
cnf(refute_0_81,plain,
or(not(X),X_35) = implies(X,X_35),
inference(resolve,[$cnf( $equal(implies(X,X_35),or(not(X),X_35)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( or(not(X),X_35) != implies(X,X_35)
| ~ axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,or(not(X),X_35))))
| axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,or(not(X),X_35)))) ),[0,1,1],$fot(implies(X,X_35))]]) ).
cnf(refute_0_83,plain,
( ~ axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,or(not(X),X_35))))
| axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_35),implies(X,X_35)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,or(not(X),X_35)))) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
or(not(X),or(X_34,X_35)) = implies(X,or(X_34,X_35)),
inference(subst,[],[refute_0_27:[bind(Y,$fot(or(X_34,X_35)))]]) ).
cnf(refute_0_86,plain,
implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) = implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))))]]) ).
cnf(refute_0_87,plain,
( implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) != implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))
| or(not(X),or(X_34,X_35)) != implies(X,or(X_34,X_35))
| implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) = implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))),implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),[1,0],$fot(implies(X,or(X_34,X_35)))]]) ).
cnf(refute_0_88,plain,
( or(not(X),or(X_34,X_35)) != implies(X,or(X_34,X_35))
| implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) = implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))),implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) = implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_34,X_35)),implies(X,or(X_34,X_35))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))) != implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35)))
| ~ axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))))
| axiom(implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),[0],$fot(implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35))))]]) ).
cnf(refute_0_91,plain,
( ~ axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))))
| axiom(implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35))),implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
axiom(implies(implies(X,or(X_34,X_35)),or(X_34,implies(X,X_35)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_34,X_35)),or(X_34,implies(X,X_35)))) )],[refute_0_84,refute_0_91]) ).
cnf(refute_0_93,plain,
axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_52)),bind(X_34,$fot(not(X))),bind(X_35,$fot(X_54))]]) ).
cnf(refute_0_94,plain,
implies(X,implies(X_52,X_54)) = or(not(X),implies(X_52,X_54)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_52,X_54)))]]) ).
cnf(refute_0_95,plain,
( implies(X,implies(X_52,X_54)) != or(not(X),implies(X_52,X_54))
| or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,implies(X_52,X_54)))),bind(Y0,$fot(or(not(X),implies(X_52,X_54))))]]) ).
cnf(refute_0_96,plain,
or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_52,X_54)),or(not(X),implies(X_52,X_54))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( or(not(X),implies(X_52,X_54)) != implies(X,implies(X_52,X_54))
| ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
| axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) ),[0,1],$fot(implies(X,implies(X_52,X_54)))]]) ).
cnf(refute_0_98,plain,
( ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
| axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_52,X_54)),implies(X,implies(X_52,X_54))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))),
inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
or(not(X),X_54) = implies(X,X_54),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_54))]]) ).
cnf(refute_0_101,plain,
implies(X_52,or(not(X),X_54)) = implies(X_52,or(not(X),X_54)),
introduced(tautology,[refl,[$fot(implies(X_52,or(not(X),X_54)))]]) ).
cnf(refute_0_102,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,or(not(X),X_54))
| or(not(X),X_54) != implies(X,X_54)
| implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) ),[1,1],$fot(implies(X,X_54))]]) ).
cnf(refute_0_103,plain,
( or(not(X),X_54) != implies(X,X_54)
| implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)),
inference(resolve,[$cnf( $equal(or(not(X),X_54),implies(X,X_54)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),
introduced(tautology,[refl,[$fot(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))]]) ).
cnf(refute_0_106,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[1,0],$fot(implies(X_52,implies(X,X_54)))]]) ).
cnf(refute_0_107,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))),
inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,implies(X,X_54))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))
| ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
| axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[0],$fot(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))))]]) ).
cnf(refute_0_110,plain,
( ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
| axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))),
inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_99,refute_0_110]) ).
cnf(refute_0_112,plain,
axiom(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_73)),bind(X_52,$fot(X_74)),bind(X_54,$fot(X_75))]]) ).
cnf(refute_0_113,plain,
theorem(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))),
inference(resolve,[$cnf( axiom(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))) )],[refute_0_112,refute_0_77]) ).
cnf(refute_0_114,plain,
( ~ theorem(implies(X_74,implies(X_73,X_75)))
| ~ theorem(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75))))
| theorem(implies(X_73,implies(X_74,X_75))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_73,implies(X_74,X_75)))),bind(Y,$fot(implies(X_74,implies(X_73,X_75))))]]) ).
cnf(refute_0_115,plain,
( ~ theorem(implies(X_74,implies(X_73,X_75)))
| theorem(implies(X_73,implies(X_74,X_75))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_74,implies(X_73,X_75)),implies(X_73,implies(X_74,X_75)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( ~ theorem(implies(X_436,implies(or(X_437,X_437),X_437)))
| theorem(implies(or(X_437,X_437),implies(X_436,X_437))) ),
inference(subst,[],[refute_0_115:[bind(X_73,$fot(or(X_437,X_437))),bind(X_74,$fot(X_436)),bind(X_75,$fot(X_437))]]) ).
cnf(refute_0_117,plain,
theorem(implies(or(X_437,X_437),implies(X_436,X_437))),
inference(resolve,[$cnf( theorem(implies(X_436,implies(or(X_437,X_437),X_437))) )],[refute_0_76,refute_0_116]) ).
cnf(refute_0_118,plain,
theorem(implies(or(X_441,X_441),implies(X_440,X_441))),
inference(subst,[],[refute_0_117:[bind(X_436,$fot(X_440)),bind(X_437,$fot(X_441))]]) ).
cnf(refute_0_119,plain,
theorem(and(implies(or(X_441,X_441),implies(X_440,X_441)),implies(or(X_441,X_441),implies(X_440,X_441)))),
inference(resolve,[$cnf( theorem(implies(or(X_441,X_441),implies(X_440,X_441))) )],[refute_0_118,refute_0_58]) ).
cnf(refute_0_120,plain,
( ~ theorem(X_438)
| ~ theorem(implies(X_438,implies(X_439,X_439)))
| theorem(implies(X_439,X_439)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_439,X_439))),bind(Y,$fot(X_438))]]) ).
cnf(refute_0_121,plain,
theorem(implies(X_437,implies(X_435,X_437))),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(X_437)),bind(X_12,$fot(X_435))]]) ).
cnf(refute_0_122,plain,
( ~ theorem(implies(X_437,implies(X_435,X_437)))
| theorem(implies(X_435,implies(X_437,X_437))) ),
inference(subst,[],[refute_0_115:[bind(X_73,$fot(X_435)),bind(X_74,$fot(X_437)),bind(X_75,$fot(X_437))]]) ).
cnf(refute_0_123,plain,
theorem(implies(X_435,implies(X_437,X_437))),
inference(resolve,[$cnf( theorem(implies(X_437,implies(X_435,X_437))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
theorem(implies(X_438,implies(X_439,X_439))),
inference(subst,[],[refute_0_123:[bind(X_435,$fot(X_438)),bind(X_437,$fot(X_439))]]) ).
cnf(refute_0_125,plain,
( ~ theorem(X_438)
| theorem(implies(X_439,X_439)) ),
inference(resolve,[$cnf( theorem(implies(X_438,implies(X_439,X_439))) )],[refute_0_124,refute_0_120]) ).
cnf(refute_0_126,plain,
( ~ theorem(and(implies(or(X_441,X_441),implies(X_440,X_441)),implies(or(X_441,X_441),implies(X_440,X_441))))
| theorem(implies(X_470,X_470)) ),
inference(subst,[],[refute_0_125:[bind(X_438,$fot(and(implies(or(X_441,X_441),implies(X_440,X_441)),implies(or(X_441,X_441),implies(X_440,X_441))))),bind(X_439,$fot(X_470))]]) ).
cnf(refute_0_127,plain,
theorem(implies(X_470,X_470)),
inference(resolve,[$cnf( theorem(and(implies(or(X_441,X_441),implies(X_440,X_441)),implies(or(X_441,X_441),implies(X_440,X_441)))) )],[refute_0_119,refute_0_126]) ).
cnf(refute_0_128,plain,
theorem(implies(X_471,X_471)),
inference(subst,[],[refute_0_127:[bind(X_470,$fot(X_471))]]) ).
cnf(refute_0_129,plain,
theorem(or(X_471,not(X_471))),
inference(resolve,[$cnf( theorem(implies(X_471,X_471)) )],[refute_0_128,refute_0_15]) ).
cnf(refute_0_130,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_129:[bind(X_471,$fot(not(X)))]]) ).
cnf(refute_0_131,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_132,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_133,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_135,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( ~ theorem(X_473)
| ~ theorem(implies(X_473,not(not(X_473))))
| theorem(not(not(X_473))) ),
inference(subst,[],[rule_2:[bind(X,$fot(not(not(X_473)))),bind(Y,$fot(X_473))]]) ).
cnf(refute_0_138,plain,
theorem(implies(X_473,not(not(X_473)))),
inference(subst,[],[refute_0_136:[bind(X,$fot(X_473))]]) ).
cnf(refute_0_139,plain,
( ~ theorem(X_473)
| theorem(not(not(X_473))) ),
inference(resolve,[$cnf( theorem(implies(X_473,not(not(X_473)))) )],[refute_0_138,refute_0_137]) ).
cnf(refute_0_140,plain,
( ~ theorem(implies(X,not(not(X))))
| theorem(not(not(implies(X,not(not(X)))))) ),
inference(subst,[],[refute_0_139:[bind(X_473,$fot(implies(X,not(not(X)))))]]) ).
cnf(refute_0_141,plain,
theorem(not(not(implies(X,not(not(X)))))),
inference(resolve,[$cnf( theorem(implies(X,not(not(X)))) )],[refute_0_136,refute_0_140]) ).
cnf(refute_0_142,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_143,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_35,refute_0_142]) ).
cnf(refute_0_144,plain,
not(implies(X,not(not(X)))) = and(X,not(X)),
inference(subst,[],[refute_0_143:[bind(P,$fot(X)),bind(Q,$fot(not(X)))]]) ).
cnf(refute_0_145,plain,
not(not(implies(X,not(not(X))))) = not(not(implies(X,not(not(X))))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(not(X))))))]]) ).
cnf(refute_0_146,plain,
( not(implies(X,not(not(X)))) != and(X,not(X))
| not(not(implies(X,not(not(X))))) != not(not(implies(X,not(not(X)))))
| not(not(implies(X,not(not(X))))) = not(and(X,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(not(X))))),not(not(implies(X,not(not(X)))))) ),[1,0],$fot(and(X,not(X)))]]) ).
cnf(refute_0_147,plain,
( not(implies(X,not(not(X)))) != and(X,not(X))
| not(not(implies(X,not(not(X))))) = not(and(X,not(X))) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(not(X))))),not(not(implies(X,not(not(X)))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
not(not(implies(X,not(not(X))))) = not(and(X,not(X))),
inference(resolve,[$cnf( $equal(not(implies(X,not(not(X)))),and(X,not(X))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
( not(not(implies(X,not(not(X))))) != not(and(X,not(X)))
| ~ theorem(not(not(implies(X,not(not(X))))))
| theorem(not(and(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(not(not(implies(X,not(not(X)))))) ),[0],$fot(not(and(X,not(X))))]]) ).
cnf(refute_0_150,plain,
( ~ theorem(not(not(implies(X,not(not(X))))))
| theorem(not(and(X,not(X)))) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(not(X))))),not(and(X,not(X)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
theorem(not(and(X,not(X)))),
inference(resolve,[$cnf( theorem(not(not(implies(X,not(not(X)))))) )],[refute_0_141,refute_0_150]) ).
cnf(refute_0_152,plain,
theorem(not(and(p,not(p)))),
inference(subst,[],[refute_0_151:[bind(X,$fot(p))]]) ).
cnf(refute_0_153,plain,
$false,
inference(resolve,[$cnf( theorem(not(and(p,not(p)))) )],[refute_0_152,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% 0.05/0.11 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 4 20:27:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.81
% 0.61/0.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.66/0.83
%------------------------------------------------------------------------------