TSTP Solution File: LCL208-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL208-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:37 EDT 2022
% Result : Unsatisfiable 3.77s 3.97s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of clauses : 170 ( 92 unt; 0 nHn; 76 RR)
% Number of literals : 272 ( 73 equ; 103 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 : 380 ( 27 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(or(p,q),implies(not(p),q))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_43,or(not(X),X_45)),or(not(X),or(X_43,X_45)))),
inference(subst,[],[refute_0_2:[bind(X_31,$fot(X_43)),bind(X_32,$fot(not(X))),bind(X_33,$fot(X_45))]]) ).
cnf(refute_0_4,plain,
implies(X,or(X_43,X_45)) = or(not(X),or(X_43,X_45)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_43,X_45)))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X,or(X_43,X_45)) != or(not(X),or(X_43,X_45))
| or(not(X),or(X_43,X_45)) = implies(X,or(X_43,X_45)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,or(X_43,X_45)))),bind(Y0,$fot(or(not(X),or(X_43,X_45))))]]) ).
cnf(refute_0_9,plain,
or(not(X),or(X_43,X_45)) = implies(X,or(X_43,X_45)),
inference(resolve,[$cnf( $equal(implies(X,or(X_43,X_45)),or(not(X),or(X_43,X_45))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X),or(X_43,X_45)) != implies(X,or(X_43,X_45))
| ~ theorem(implies(or(X_43,or(not(X),X_45)),or(not(X),or(X_43,X_45))))
| theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_43,or(not(X),X_45)),or(not(X),or(X_43,X_45)))) ),[0,1],$fot(implies(X,or(X_43,X_45)))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(or(X_43,or(not(X),X_45)),or(not(X),or(X_43,X_45))))
| theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_43,X_45)),implies(X,or(X_43,X_45))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))),
inference(resolve,[$cnf( theorem(implies(or(X_43,or(not(X),X_45)),or(not(X),or(X_43,X_45)))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_14,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_13]) ).
cnf(refute_0_15,plain,
or(not(X),X_45) = implies(X,X_45),
inference(subst,[],[refute_0_14:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_16,plain,
or(X_43,or(not(X),X_45)) = or(X_43,or(not(X),X_45)),
introduced(tautology,[refl,[$fot(or(X_43,or(not(X),X_45)))]]) ).
cnf(refute_0_17,plain,
( or(X_43,or(not(X),X_45)) != or(X_43,or(not(X),X_45))
| or(not(X),X_45) != implies(X,X_45)
| or(X_43,or(not(X),X_45)) = or(X_43,implies(X,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_43,or(not(X),X_45)),or(X_43,or(not(X),X_45))) ),[1,1],$fot(implies(X,X_45))]]) ).
cnf(refute_0_18,plain,
( or(not(X),X_45) != implies(X,X_45)
| or(X_43,or(not(X),X_45)) = or(X_43,implies(X,X_45)) ),
inference(resolve,[$cnf( $equal(or(X_43,or(not(X),X_45)),or(X_43,or(not(X),X_45))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
or(X_43,or(not(X),X_45)) = or(X_43,implies(X,X_45)),
inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) = implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))),
introduced(tautology,[refl,[$fot(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))))]]) ).
cnf(refute_0_21,plain,
( implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) != implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))
| or(X_43,or(not(X),X_45)) != or(X_43,implies(X,X_45))
| implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) = implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))),implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) ),[1,0],$fot(or(X_43,implies(X,X_45)))]]) ).
cnf(refute_0_22,plain,
( or(X_43,or(not(X),X_45)) != or(X_43,implies(X,X_45))
| implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) = implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45))) ),
inference(resolve,[$cnf( $equal(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))),implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) = implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45))),
inference(resolve,[$cnf( $equal(or(X_43,or(not(X),X_45)),or(X_43,implies(X,X_45))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))) != implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45)))
| ~ theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))))
| theorem(implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) ),[0],$fot(implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45))))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))))
| theorem(implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45))),implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(implies(or(X_43,implies(X,X_45)),implies(X,or(X_43,X_45)))),
inference(resolve,[$cnf( theorem(implies(or(X_43,or(not(X),X_45)),implies(X,or(X_43,X_45)))) )],[refute_0_12,refute_0_25]) ).
cnf(refute_0_27,plain,
theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,or(not(X),X_48)))),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_46)),bind(X_43,$fot(not(X))),bind(X_45,$fot(X_48))]]) ).
cnf(refute_0_28,plain,
implies(X,X_48) = or(not(X),X_48),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_48))]]) ).
cnf(refute_0_29,plain,
( implies(X,X_48) != or(not(X),X_48)
| or(not(X),X_48) = implies(X,X_48) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_48))),bind(Y0,$fot(or(not(X),X_48)))]]) ).
cnf(refute_0_30,plain,
or(not(X),X_48) = implies(X,X_48),
inference(resolve,[$cnf( $equal(implies(X,X_48),or(not(X),X_48)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( or(not(X),X_48) != implies(X,X_48)
| ~ theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,or(not(X),X_48))))
| theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,or(not(X),X_48)))) ),[0,1,1],$fot(implies(X,X_48))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,or(not(X),X_48))))
| theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_48),implies(X,X_48)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,or(not(X),X_48)))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
or(not(X),implies(X_46,X_48)) = implies(X,implies(X_46,X_48)),
inference(subst,[],[refute_0_14:[bind(Y,$fot(implies(X_46,X_48)))]]) ).
cnf(refute_0_35,plain,
implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) = implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))))]]) ).
cnf(refute_0_36,plain,
( implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) != implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))
| or(not(X),implies(X_46,X_48)) != implies(X,implies(X_46,X_48))
| implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) = implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))),implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),[1,0],$fot(implies(X,implies(X_46,X_48)))]]) ).
cnf(refute_0_37,plain,
( or(not(X),implies(X_46,X_48)) != implies(X,implies(X_46,X_48))
| implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) = implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))),implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) = implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_46,X_48)),implies(X,implies(X_46,X_48))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))) != implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))
| ~ theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))))
| theorem(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),[0],$fot(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48))))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))))
| theorem(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48))),implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X,implies(X_46,X_48)))
| ~ theorem(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48))))
| theorem(implies(X_46,implies(X,X_48))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_46,implies(X,X_48)))),bind(Y,$fot(implies(X,implies(X_46,X_48))))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X,implies(X_46,X_48)))
| theorem(implies(X_46,implies(X,X_48))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_46,X_48)),implies(X_46,implies(X,X_48)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(not(X_8372),implies(or(X_8372,X_8371),X_8371)))
| theorem(implies(or(X_8372,X_8371),implies(not(X_8372),X_8371))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(not(X_8372))),bind(X_46,$fot(or(X_8372,X_8371))),bind(X_48,$fot(X_8371))]]) ).
cnf(refute_0_45,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,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_46,plain,
axiom(implies(or(X_13,X_14),or(X_14,X_13))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_47,plain,
theorem(implies(or(X_13,X_14),or(X_14,X_13))),
inference(resolve,[$cnf( axiom(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_46,refute_0_45]) ).
cnf(refute_0_48,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_49,plain,
( ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(implies(or(X_8334,X_8333),X_8333),not(not(X_8334))))
| theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333))) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(implies(or(X_8334,X_8333),X_8333))),bind(X_14,$fot(not(not(X_8334))))]]) ).
cnf(refute_0_51,plain,
( ~ theorem(or(X_1641,implies(or(X_1641,X_1642),X_1642)))
| theorem(or(implies(or(X_1641,X_1642),X_1642),X_1641)) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(X_1641)),bind(X_14,$fot(implies(or(X_1641,X_1642),X_1642)))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(or(X_831,not(X_831)))
| theorem(or(not(X_831),X_831)) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(X_831)),bind(X_14,$fot(not(X_831)))]]) ).
cnf(refute_0_53,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_54,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(implies(or(X_64,X_64),X_64)),
inference(subst,[],[refute_0_54:[bind(A,$fot(X_64))]]) ).
cnf(refute_0_56,plain,
( ~ theorem(implies(or(X_64,X_64),X_64))
| ~ theorem(or(X_64,X_64))
| theorem(X_64) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_64)),bind(Y,$fot(or(X_64,X_64)))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(or(X_64,X_64))
| theorem(X_64) ),
inference(resolve,[$cnf( theorem(implies(or(X_64,X_64),X_64)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(or(X_830,not(X_830)),or(X_830,not(X_830))))
| theorem(or(X_830,not(X_830))) ),
inference(subst,[],[refute_0_57:[bind(X_64,$fot(or(X_830,not(X_830))))]]) ).
cnf(refute_0_59,plain,
( ~ theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| ~ theorem(or(X_31,or(X_32,X_33)))
| theorem(or(X_32,or(X_31,X_33))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_32,or(X_31,X_33)))),bind(Y,$fot(or(X_31,or(X_32,X_33))))]]) ).
cnf(refute_0_60,plain,
( ~ theorem(or(X_31,or(X_32,X_33)))
| theorem(or(X_32,or(X_31,X_33))) ),
inference(resolve,[$cnf( theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_2,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ theorem(or(X_826,or(X_825,not(X_826))))
| theorem(or(X_825,or(X_826,not(X_826)))) ),
inference(subst,[],[refute_0_60:[bind(X_31,$fot(X_826)),bind(X_32,$fot(X_825)),bind(X_33,$fot(not(X_826)))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(or(or(X_816,not(X_817)),X_817))
| theorem(or(X_817,or(X_816,not(X_817)))) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(or(X_816,not(X_817)))),bind(X_14,$fot(X_817))]]) ).
cnf(refute_0_63,plain,
( ~ theorem(or(or(or(X_813,not(X_815)),X_815),or(or(X_813,not(X_815)),X_815)))
| theorem(or(or(X_813,not(X_815)),X_815)) ),
inference(subst,[],[refute_0_57:[bind(X_64,$fot(or(or(X_813,not(X_815)),X_815)))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(or(or(X_716,not(X_718)),or(X_717,X_718)))
| theorem(or(X_717,or(or(X_716,not(X_718)),X_718))) ),
inference(subst,[],[refute_0_60:[bind(X_31,$fot(or(X_716,not(X_718)))),bind(X_32,$fot(X_717)),bind(X_33,$fot(X_718))]]) ).
cnf(refute_0_65,plain,
( ~ theorem(or(or(X_701,X_702),or(X_700,not(X_702))))
| theorem(or(or(X_700,not(X_702)),or(X_701,X_702))) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(or(X_701,X_702))),bind(X_14,$fot(or(X_700,not(X_702))))]]) ).
cnf(refute_0_66,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_67,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(X_65,or(B,X_65))),
inference(subst,[],[refute_0_67:[bind(A,$fot(X_65))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(X_65)
| ~ theorem(implies(X_65,or(B,X_65)))
| theorem(or(B,X_65)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_65))),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(X_65)
| theorem(or(B,X_65)) ),
inference(resolve,[$cnf( theorem(implies(X_65,or(B,X_65))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ theorem(or(or(X_93,X_94),not(X_94)))
| theorem(or(B,or(or(X_93,X_94),not(X_94)))) ),
inference(subst,[],[refute_0_70:[bind(X_65,$fot(or(or(X_93,X_94),not(X_94))))]]) ).
cnf(refute_0_72,plain,
theorem(implies(X_87,or(B,X_87))),
inference(subst,[],[refute_0_67:[bind(A,$fot(X_87))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(or(not(X),X_78))
| theorem(or(X_78,not(X))) ),
inference(subst,[],[refute_0_49:[bind(X_13,$fot(not(X))),bind(X_14,$fot(X_78))]]) ).
cnf(refute_0_74,plain,
implies(X,X_78) = or(not(X),X_78),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_78))]]) ).
cnf(refute_0_75,plain,
( implies(X,X_78) != or(not(X),X_78)
| or(not(X),X_78) = implies(X,X_78) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_78))),bind(Y0,$fot(or(not(X),X_78)))]]) ).
cnf(refute_0_76,plain,
or(not(X),X_78) = implies(X,X_78),
inference(resolve,[$cnf( $equal(implies(X,X_78),or(not(X),X_78)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( or(not(X),X_78) != implies(X,X_78)
| ~ theorem(implies(X,X_78))
| theorem(or(not(X),X_78)) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),X_78)) ),[0],$fot(implies(X,X_78))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(implies(X,X_78))
| theorem(or(not(X),X_78)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_78),implies(X,X_78)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ theorem(implies(X,X_78))
| theorem(or(X_78,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),X_78)) )],[refute_0_78,refute_0_73]) ).
cnf(refute_0_80,plain,
( ~ theorem(implies(X_87,or(B,X_87)))
| theorem(or(or(B,X_87),not(X_87))) ),
inference(subst,[],[refute_0_79:[bind(X,$fot(X_87)),bind(X_78,$fot(or(B,X_87)))]]) ).
cnf(refute_0_81,plain,
theorem(or(or(B,X_87),not(X_87))),
inference(resolve,[$cnf( theorem(implies(X_87,or(B,X_87))) )],[refute_0_72,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(or(or(X_93,X_94),not(X_94))),
inference(subst,[],[refute_0_81:[bind(B,$fot(X_93)),bind(X_87,$fot(X_94))]]) ).
cnf(refute_0_83,plain,
theorem(or(B,or(or(X_93,X_94),not(X_94)))),
inference(resolve,[$cnf( theorem(or(or(X_93,X_94),not(X_94))) )],[refute_0_82,refute_0_71]) ).
cnf(refute_0_84,plain,
theorem(or(X_672,or(or(X_93,X_94),not(X_94)))),
inference(subst,[],[refute_0_83:[bind(B,$fot(X_672))]]) ).
cnf(refute_0_85,plain,
( ~ theorem(or(X_672,or(or(X_93,X_94),not(X_94))))
| theorem(or(or(X_93,X_94),or(X_672,not(X_94)))) ),
inference(subst,[],[refute_0_60:[bind(X_31,$fot(X_672)),bind(X_32,$fot(or(X_93,X_94))),bind(X_33,$fot(not(X_94)))]]) ).
cnf(refute_0_86,plain,
theorem(or(or(X_93,X_94),or(X_672,not(X_94)))),
inference(resolve,[$cnf( theorem(or(X_672,or(or(X_93,X_94),not(X_94)))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(or(or(X_701,X_702),or(X_700,not(X_702)))),
inference(subst,[],[refute_0_86:[bind(X_672,$fot(X_700)),bind(X_93,$fot(X_701)),bind(X_94,$fot(X_702))]]) ).
cnf(refute_0_88,plain,
theorem(or(or(X_700,not(X_702)),or(X_701,X_702))),
inference(resolve,[$cnf( theorem(or(or(X_701,X_702),or(X_700,not(X_702)))) )],[refute_0_87,refute_0_65]) ).
cnf(refute_0_89,plain,
theorem(or(or(X_716,not(X_718)),or(X_717,X_718))),
inference(subst,[],[refute_0_88:[bind(X_700,$fot(X_716)),bind(X_701,$fot(X_717)),bind(X_702,$fot(X_718))]]) ).
cnf(refute_0_90,plain,
theorem(or(X_717,or(or(X_716,not(X_718)),X_718))),
inference(resolve,[$cnf( theorem(or(or(X_716,not(X_718)),or(X_717,X_718))) )],[refute_0_89,refute_0_64]) ).
cnf(refute_0_91,plain,
theorem(or(or(or(X_813,not(X_815)),X_815),or(or(X_813,not(X_815)),X_815))),
inference(subst,[],[refute_0_90:[bind(X_716,$fot(X_813)),bind(X_717,$fot(or(or(X_813,not(X_815)),X_815))),bind(X_718,$fot(X_815))]]) ).
cnf(refute_0_92,plain,
theorem(or(or(X_813,not(X_815)),X_815)),
inference(resolve,[$cnf( theorem(or(or(or(X_813,not(X_815)),X_815),or(or(X_813,not(X_815)),X_815))) )],[refute_0_91,refute_0_63]) ).
cnf(refute_0_93,plain,
theorem(or(or(X_816,not(X_817)),X_817)),
inference(subst,[],[refute_0_92:[bind(X_813,$fot(X_816)),bind(X_815,$fot(X_817))]]) ).
cnf(refute_0_94,plain,
theorem(or(X_817,or(X_816,not(X_817)))),
inference(resolve,[$cnf( theorem(or(or(X_816,not(X_817)),X_817)) )],[refute_0_93,refute_0_62]) ).
cnf(refute_0_95,plain,
theorem(or(X_826,or(X_825,not(X_826)))),
inference(subst,[],[refute_0_94:[bind(X_816,$fot(X_825)),bind(X_817,$fot(X_826))]]) ).
cnf(refute_0_96,plain,
theorem(or(X_825,or(X_826,not(X_826)))),
inference(resolve,[$cnf( theorem(or(X_826,or(X_825,not(X_826)))) )],[refute_0_95,refute_0_61]) ).
cnf(refute_0_97,plain,
theorem(or(or(X_830,not(X_830)),or(X_830,not(X_830)))),
inference(subst,[],[refute_0_96:[bind(X_825,$fot(or(X_830,not(X_830)))),bind(X_826,$fot(X_830))]]) ).
cnf(refute_0_98,plain,
theorem(or(X_830,not(X_830))),
inference(resolve,[$cnf( theorem(or(or(X_830,not(X_830)),or(X_830,not(X_830)))) )],[refute_0_97,refute_0_58]) ).
cnf(refute_0_99,plain,
theorem(or(X_831,not(X_831))),
inference(subst,[],[refute_0_98:[bind(X_830,$fot(X_831))]]) ).
cnf(refute_0_100,plain,
theorem(or(not(X_831),X_831)),
inference(resolve,[$cnf( theorem(or(X_831,not(X_831))) )],[refute_0_99,refute_0_52]) ).
cnf(refute_0_101,plain,
or(not(X_831),X_831) = implies(X_831,X_831),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_831)),bind(Y,$fot(X_831))]]) ).
cnf(refute_0_102,plain,
( or(not(X_831),X_831) != implies(X_831,X_831)
| ~ theorem(or(not(X_831),X_831))
| theorem(implies(X_831,X_831)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_831),X_831)) ),[0],$fot(implies(X_831,X_831))]]) ).
cnf(refute_0_103,plain,
( ~ theorem(or(not(X_831),X_831))
| theorem(implies(X_831,X_831)) ),
inference(resolve,[$cnf( $equal(or(not(X_831),X_831),implies(X_831,X_831)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
theorem(implies(X_831,X_831)),
inference(resolve,[$cnf( theorem(or(not(X_831),X_831)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
theorem(implies(or(X_1637,X_1638),or(X_1637,X_1638))),
inference(subst,[],[refute_0_104:[bind(X_831,$fot(or(X_1637,X_1638)))]]) ).
cnf(refute_0_106,plain,
( ~ axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))))]]) ).
cnf(refute_0_107,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_108,plain,
implies(X,X_33) = or(not(X),X_33),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_109,plain,
( implies(X,X_33) != or(not(X),X_33)
| or(not(X),X_33) = implies(X,X_33) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).
cnf(refute_0_110,plain,
or(not(X),X_33) = implies(X,X_33),
inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( or(not(X),X_33) != implies(X,X_33)
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) ),[0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_112,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) )],[refute_0_107,refute_0_112]) ).
cnf(refute_0_114,plain,
or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
inference(subst,[],[refute_0_14:[bind(Y,$fot(or(X_32,X_33)))]]) ).
cnf(refute_0_115,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_116,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))
| or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[1,0],$fot(implies(X,or(X_32,X_33)))]]) ).
cnf(refute_0_117,plain,
( or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_33)),implies(X,or(X_32,X_33))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[0],$fot(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_120,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_113,refute_0_120]) ).
cnf(refute_0_122,plain,
axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).
cnf(refute_0_123,plain,
theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_122,refute_0_106]) ).
cnf(refute_0_124,plain,
( ~ theorem(implies(X_34,or(X_35,X_36)))
| ~ theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(or(X_35,implies(X_34,X_36))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_35,implies(X_34,X_36)))),bind(Y,$fot(implies(X_34,or(X_35,X_36))))]]) ).
cnf(refute_0_125,plain,
( ~ theorem(implies(X_34,or(X_35,X_36)))
| theorem(or(X_35,implies(X_34,X_36))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ theorem(implies(or(X_1637,X_1638),or(X_1637,X_1638)))
| theorem(or(X_1637,implies(or(X_1637,X_1638),X_1638))) ),
inference(subst,[],[refute_0_125:[bind(X_34,$fot(or(X_1637,X_1638))),bind(X_35,$fot(X_1637)),bind(X_36,$fot(X_1638))]]) ).
cnf(refute_0_127,plain,
theorem(or(X_1637,implies(or(X_1637,X_1638),X_1638))),
inference(resolve,[$cnf( theorem(implies(or(X_1637,X_1638),or(X_1637,X_1638))) )],[refute_0_105,refute_0_126]) ).
cnf(refute_0_128,plain,
theorem(or(X_1641,implies(or(X_1641,X_1642),X_1642))),
inference(subst,[],[refute_0_127:[bind(X_1637,$fot(X_1641)),bind(X_1638,$fot(X_1642))]]) ).
cnf(refute_0_129,plain,
theorem(or(implies(or(X_1641,X_1642),X_1642),X_1641)),
inference(resolve,[$cnf( theorem(or(X_1641,implies(or(X_1641,X_1642),X_1642))) )],[refute_0_128,refute_0_51]) ).
cnf(refute_0_130,plain,
theorem(or(implies(or(X_8183,X_1642),X_1642),X_8183)),
inference(subst,[],[refute_0_129:[bind(X_1641,$fot(X_8183))]]) ).
cnf(refute_0_131,plain,
( ~ theorem(implies(or(X_3158,X_3157),or(X_3158,not(not(X_3157)))))
| ~ theorem(or(X_3158,X_3157))
| theorem(or(X_3158,not(not(X_3157)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_3158,not(not(X_3157))))),bind(Y,$fot(or(X_3158,X_3157)))]]) ).
cnf(refute_0_132,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_98:[bind(X_830,$fot(not(X)))]]) ).
cnf(refute_0_133,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_134,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_135,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_137,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_132,refute_0_137]) ).
cnf(refute_0_139,plain,
theorem(implies(X_3152,not(not(X_3152)))),
inference(subst,[],[refute_0_138:[bind(X,$fot(X_3152))]]) ).
cnf(refute_0_140,plain,
( ~ axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41))))
| theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))))]]) ).
cnf(refute_0_141,plain,
axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_40)),bind(B,$fot(X_41)),bind(C,$fot(X_42))]]) ).
cnf(refute_0_142,plain,
theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))),
inference(resolve,[$cnf( axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))) )],[refute_0_141,refute_0_140]) ).
cnf(refute_0_143,plain,
( ~ theorem(implies(X_40,X_41))
| ~ theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41))))
| theorem(implies(or(X_42,X_40),or(X_42,X_41))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_42,X_40),or(X_42,X_41)))),bind(Y,$fot(implies(X_40,X_41)))]]) ).
cnf(refute_0_144,plain,
( ~ theorem(implies(X_40,X_41))
| theorem(implies(or(X_42,X_40),or(X_42,X_41))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
( ~ theorem(implies(X_3152,not(not(X_3152))))
| theorem(implies(or(X_3154,X_3152),or(X_3154,not(not(X_3152))))) ),
inference(subst,[],[refute_0_144:[bind(X_40,$fot(X_3152)),bind(X_41,$fot(not(not(X_3152)))),bind(X_42,$fot(X_3154))]]) ).
cnf(refute_0_146,plain,
theorem(implies(or(X_3154,X_3152),or(X_3154,not(not(X_3152))))),
inference(resolve,[$cnf( theorem(implies(X_3152,not(not(X_3152)))) )],[refute_0_139,refute_0_145]) ).
cnf(refute_0_147,plain,
theorem(implies(or(X_3158,X_3157),or(X_3158,not(not(X_3157))))),
inference(subst,[],[refute_0_146:[bind(X_3152,$fot(X_3157)),bind(X_3154,$fot(X_3158))]]) ).
cnf(refute_0_148,plain,
( ~ theorem(or(X_3158,X_3157))
| theorem(or(X_3158,not(not(X_3157)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_3158,X_3157),or(X_3158,not(not(X_3157))))) )],[refute_0_147,refute_0_131]) ).
cnf(refute_0_149,plain,
( ~ theorem(or(implies(or(X_8183,X_1642),X_1642),X_8183))
| theorem(or(implies(or(X_8183,X_1642),X_1642),not(not(X_8183)))) ),
inference(subst,[],[refute_0_148:[bind(X_3157,$fot(X_8183)),bind(X_3158,$fot(implies(or(X_8183,X_1642),X_1642)))]]) ).
cnf(refute_0_150,plain,
theorem(or(implies(or(X_8183,X_1642),X_1642),not(not(X_8183)))),
inference(resolve,[$cnf( theorem(or(implies(or(X_8183,X_1642),X_1642),X_8183)) )],[refute_0_130,refute_0_149]) ).
cnf(refute_0_151,plain,
theorem(or(implies(or(X_8334,X_8333),X_8333),not(not(X_8334)))),
inference(subst,[],[refute_0_150:[bind(X_1642,$fot(X_8333)),bind(X_8183,$fot(X_8334))]]) ).
cnf(refute_0_152,plain,
theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333))),
inference(resolve,[$cnf( theorem(or(implies(or(X_8334,X_8333),X_8333),not(not(X_8334)))) )],[refute_0_151,refute_0_50]) ).
cnf(refute_0_153,plain,
or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333)) = implies(not(X_8334),implies(or(X_8334,X_8333),X_8333)),
inference(subst,[],[refute_0_14:[bind(X,$fot(not(X_8334))),bind(Y,$fot(implies(or(X_8334,X_8333),X_8333)))]]) ).
cnf(refute_0_154,plain,
( or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333)) != implies(not(X_8334),implies(or(X_8334,X_8333),X_8333))
| ~ theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333)))
| theorem(implies(not(X_8334),implies(or(X_8334,X_8333),X_8333))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333))) ),[0],$fot(implies(not(X_8334),implies(or(X_8334,X_8333),X_8333)))]]) ).
cnf(refute_0_155,plain,
( ~ theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333)))
| theorem(implies(not(X_8334),implies(or(X_8334,X_8333),X_8333))) ),
inference(resolve,[$cnf( $equal(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333)),implies(not(X_8334),implies(or(X_8334,X_8333),X_8333))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
theorem(implies(not(X_8334),implies(or(X_8334,X_8333),X_8333))),
inference(resolve,[$cnf( theorem(or(not(not(X_8334)),implies(or(X_8334,X_8333),X_8333))) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
theorem(implies(not(X_8372),implies(or(X_8372,X_8371),X_8371))),
inference(subst,[],[refute_0_156:[bind(X_8333,$fot(X_8371)),bind(X_8334,$fot(X_8372))]]) ).
cnf(refute_0_158,plain,
theorem(implies(or(X_8372,X_8371),implies(not(X_8372),X_8371))),
inference(resolve,[$cnf( theorem(implies(not(X_8372),implies(or(X_8372,X_8371),X_8371))) )],[refute_0_157,refute_0_44]) ).
cnf(refute_0_159,plain,
theorem(implies(or(p,q),implies(not(p),q))),
inference(subst,[],[refute_0_158:[bind(X_8371,$fot(q)),bind(X_8372,$fot(p))]]) ).
cnf(refute_0_160,plain,
$false,
inference(resolve,[$cnf( theorem(implies(or(p,q),implies(not(p),q))) )],[refute_0_159,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL208-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 16:16:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.77/3.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.77/3.97
% 3.77/3.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.77/3.98
%------------------------------------------------------------------------------