TSTP Solution File: LCL268-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL268-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:51:16 EDT 2022
% Result : Unsatisfiable 1.29s 1.50s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of clauses : 99 ( 54 unt; 0 nHn; 48 RR)
% Number of literals : 160 ( 65 equ; 62 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 176 ( 4 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(equivalent_defn,axiom,
equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ).
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(p,p)) ).
cnf(refute_0_0,plain,
( ~ theorem(X_129)
| ~ theorem(implies(X_129,and(X_129,X_129)))
| theorem(and(X_129,X_129)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_129,X_129))),bind(Y,$fot(X_129))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_1]) ).
cnf(refute_0_3,plain,
theorem(implies(or(not(X_9),not(X_9)),not(X_9))),
inference(subst,[],[refute_0_2:[bind(A,$fot(not(X_9)))]]) ).
cnf(refute_0_4,plain,
implies(X_9,not(X_9)) = or(not(X_9),not(X_9)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_9)),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X_9,not(X_9)) != or(not(X_9),not(X_9))
| or(not(X_9),not(X_9)) = implies(X_9,not(X_9)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_9,not(X_9)))),bind(Y0,$fot(or(not(X_9),not(X_9))))]]) ).
cnf(refute_0_9,plain,
or(not(X_9),not(X_9)) = implies(X_9,not(X_9)),
inference(resolve,[$cnf( $equal(implies(X_9,not(X_9)),or(not(X_9),not(X_9))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X_9),not(X_9)) != implies(X_9,not(X_9))
| ~ theorem(implies(or(not(X_9),not(X_9)),not(X_9)))
| theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_9),not(X_9)),not(X_9))) ),[0,0],$fot(implies(X_9,not(X_9)))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(or(not(X_9),not(X_9)),not(X_9)))
| theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),not(X_9)),implies(X_9,not(X_9))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(implies(X_9,not(X_9)),not(X_9))),
inference(resolve,[$cnf( theorem(implies(or(not(X_9),not(X_9)),not(X_9))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(implies(X_21,not(X_22)),Y) = or(not(implies(X_21,not(X_22))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_21,not(X_22))))]]) ).
cnf(refute_0_14,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_15,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_14]) ).
cnf(refute_0_16,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_15:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_17,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_18,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_19,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_22,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_22]) ).
cnf(refute_0_24,plain,
and(X_21,X_22) = not(implies(X_21,not(X_22))),
inference(subst,[],[refute_0_23:[bind(P,$fot(X_21)),bind(Q,$fot(X_22))]]) ).
cnf(refute_0_25,plain,
( and(X_21,X_22) != not(implies(X_21,not(X_22)))
| not(implies(X_21,not(X_22))) = and(X_21,X_22) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(and(X_21,X_22))),bind(Y0,$fot(not(implies(X_21,not(X_22)))))]]) ).
cnf(refute_0_26,plain,
not(implies(X_21,not(X_22))) = and(X_21,X_22),
inference(resolve,[$cnf( $equal(and(X_21,X_22),not(implies(X_21,not(X_22)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( implies(implies(X_21,not(X_22)),Y) != or(not(implies(X_21,not(X_22))),Y)
| not(implies(X_21,not(X_22))) != and(X_21,X_22)
| implies(implies(X_21,not(X_22)),Y) = or(and(X_21,X_22),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_21,not(X_22)),Y),or(not(implies(X_21,not(X_22))),Y)) ),[1,0],$fot(and(X_21,X_22))]]) ).
cnf(refute_0_28,plain,
( implies(implies(X_21,not(X_22)),Y) != or(not(implies(X_21,not(X_22))),Y)
| implies(implies(X_21,not(X_22)),Y) = or(and(X_21,X_22),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_21,not(X_22))),and(X_21,X_22)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(implies(X_21,not(X_22)),Y) = or(and(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_21,not(X_22)),Y),or(not(implies(X_21,not(X_22))),Y)) )],[refute_0_13,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(implies(X_9,not(X_9)),not(X_9)) = or(and(X_9,X_9),not(X_9)),
inference(subst,[],[refute_0_29:[bind(Y,$fot(not(X_9))),bind(X_21,$fot(X_9)),bind(X_22,$fot(X_9))]]) ).
cnf(refute_0_31,plain,
( implies(implies(X_9,not(X_9)),not(X_9)) != or(and(X_9,X_9),not(X_9))
| ~ theorem(implies(implies(X_9,not(X_9)),not(X_9)))
| theorem(or(and(X_9,X_9),not(X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),[0],$fot(or(and(X_9,X_9),not(X_9)))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(implies(X_9,not(X_9)),not(X_9)))
| theorem(or(and(X_9,X_9),not(X_9))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,not(X_9)),not(X_9)),or(and(X_9,X_9),not(X_9))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
theorem(or(and(X_9,X_9),not(X_9))),
inference(resolve,[$cnf( theorem(implies(implies(X_9,not(X_9)),not(X_9))) )],[refute_0_12,refute_0_32]) ).
cnf(refute_0_34,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,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_35,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_36,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,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_38,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ theorem(or(and(X_9,X_9),not(X_9)))
| theorem(or(not(X_9),and(X_9,X_9))) ),
inference(subst,[],[refute_0_38:[bind(X_7,$fot(and(X_9,X_9))),bind(X_8,$fot(not(X_9)))]]) ).
cnf(refute_0_40,plain,
theorem(or(not(X_9),and(X_9,X_9))),
inference(resolve,[$cnf( theorem(or(and(X_9,X_9),not(X_9))) )],[refute_0_33,refute_0_39]) ).
cnf(refute_0_41,plain,
or(not(X_9),and(X_9,X_9)) = implies(X_9,and(X_9,X_9)),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_9)),bind(Y,$fot(and(X_9,X_9)))]]) ).
cnf(refute_0_42,plain,
( or(not(X_9),and(X_9,X_9)) != implies(X_9,and(X_9,X_9))
| ~ theorem(or(not(X_9),and(X_9,X_9)))
| theorem(implies(X_9,and(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_9),and(X_9,X_9))) ),[0],$fot(implies(X_9,and(X_9,X_9)))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(or(not(X_9),and(X_9,X_9)))
| theorem(implies(X_9,and(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),and(X_9,X_9)),implies(X_9,and(X_9,X_9))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
theorem(implies(X_9,and(X_9,X_9))),
inference(resolve,[$cnf( theorem(or(not(X_9),and(X_9,X_9))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
theorem(implies(X_129,and(X_129,X_129))),
inference(subst,[],[refute_0_44:[bind(X_9,$fot(X_129))]]) ).
cnf(refute_0_46,plain,
( ~ theorem(X_129)
| theorem(and(X_129,X_129)) ),
inference(resolve,[$cnf( theorem(implies(X_129,and(X_129,X_129))) )],[refute_0_45,refute_0_0]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(X_1436,X_1436))
| theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436))) ),
inference(subst,[],[refute_0_46:[bind(X_129,$fot(implies(X_1436,X_1436)))]]) ).
cnf(refute_0_48,plain,
theorem(implies(or(X_95,X_95),X_95)),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_95))]]) ).
cnf(refute_0_49,plain,
( ~ theorem(implies(or(X_95,X_95),X_95))
| ~ theorem(or(X_95,X_95))
| theorem(X_95) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_95)),bind(Y,$fot(or(X_95,X_95)))]]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(X_95,X_95))
| theorem(X_95) ),
inference(resolve,[$cnf( theorem(implies(or(X_95,X_95),X_95)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ theorem(or(implies(X_1435,X_1435),implies(X_1435,X_1435)))
| theorem(implies(X_1435,X_1435)) ),
inference(subst,[],[refute_0_50:[bind(X_95,$fot(implies(X_1435,X_1435)))]]) ).
cnf(refute_0_52,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_53,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_52]) ).
cnf(refute_0_54,plain,
theorem(implies(X_1433,or(X_1432,X_1433))),
inference(subst,[],[refute_0_53:[bind(A,$fot(X_1433)),bind(B,$fot(X_1432))]]) ).
cnf(refute_0_55,plain,
( ~ axiom(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50))))
| theorem(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))))]]) ).
cnf(refute_0_56,plain,
axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,or(not(X),X_47)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_46)),bind(C,$fot(X_47))]]) ).
cnf(refute_0_57,plain,
implies(X,X_47) = or(not(X),X_47),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_47))]]) ).
cnf(refute_0_58,plain,
( implies(X,X_47) != or(not(X),X_47)
| or(not(X),X_47) = implies(X,X_47) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_47))),bind(Y0,$fot(or(not(X),X_47)))]]) ).
cnf(refute_0_59,plain,
or(not(X),X_47) = implies(X,X_47),
inference(resolve,[$cnf( $equal(implies(X,X_47),or(not(X),X_47)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( or(not(X),X_47) != implies(X,X_47)
| ~ axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,or(not(X),X_47))))
| axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,or(not(X),X_47)))) ),[0,1,1],$fot(implies(X,X_47))]]) ).
cnf(refute_0_61,plain,
( ~ axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,or(not(X),X_47))))
| axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_47),implies(X,X_47)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,or(not(X),X_47)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
or(not(X),or(X_46,X_47)) = implies(X,or(X_46,X_47)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(or(X_46,X_47)))]]) ).
cnf(refute_0_64,plain,
implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) = implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))))]]) ).
cnf(refute_0_65,plain,
( implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) != implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))
| or(not(X),or(X_46,X_47)) != implies(X,or(X_46,X_47))
| implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) = implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))),implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),[1,0],$fot(implies(X,or(X_46,X_47)))]]) ).
cnf(refute_0_66,plain,
( or(not(X),or(X_46,X_47)) != implies(X,or(X_46,X_47))
| implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) = implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))),implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) = implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_46,X_47)),implies(X,or(X_46,X_47))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))) != implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47)))
| ~ axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))))
| axiom(implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),[0],$fot(implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47))))]]) ).
cnf(refute_0_69,plain,
( ~ axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))))
| axiom(implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47))),implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
axiom(implies(implies(X,or(X_46,X_47)),or(X_46,implies(X,X_47)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_46,X_47)),or(X_46,implies(X,X_47)))) )],[refute_0_62,refute_0_69]) ).
cnf(refute_0_71,plain,
axiom(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))),
inference(subst,[],[refute_0_70:[bind(X,$fot(X_48)),bind(X_46,$fot(X_49)),bind(X_47,$fot(X_50))]]) ).
cnf(refute_0_72,plain,
theorem(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))),
inference(resolve,[$cnf( axiom(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))) )],[refute_0_71,refute_0_55]) ).
cnf(refute_0_73,plain,
( ~ theorem(implies(X_48,or(X_49,X_50)))
| ~ theorem(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50))))
| theorem(or(X_49,implies(X_48,X_50))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_49,implies(X_48,X_50)))),bind(Y,$fot(implies(X_48,or(X_49,X_50))))]]) ).
cnf(refute_0_74,plain,
( ~ theorem(implies(X_48,or(X_49,X_50)))
| theorem(or(X_49,implies(X_48,X_50))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_48,or(X_49,X_50)),or(X_49,implies(X_48,X_50)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(X_1433,or(X_1432,X_1433)))
| theorem(or(X_1432,implies(X_1433,X_1433))) ),
inference(subst,[],[refute_0_74:[bind(X_48,$fot(X_1433)),bind(X_49,$fot(X_1432)),bind(X_50,$fot(X_1433))]]) ).
cnf(refute_0_76,plain,
theorem(or(X_1432,implies(X_1433,X_1433))),
inference(resolve,[$cnf( theorem(implies(X_1433,or(X_1432,X_1433))) )],[refute_0_54,refute_0_75]) ).
cnf(refute_0_77,plain,
theorem(or(implies(X_1435,X_1435),implies(X_1435,X_1435))),
inference(subst,[],[refute_0_76:[bind(X_1432,$fot(implies(X_1435,X_1435))),bind(X_1433,$fot(X_1435))]]) ).
cnf(refute_0_78,plain,
theorem(implies(X_1435,X_1435)),
inference(resolve,[$cnf( theorem(or(implies(X_1435,X_1435),implies(X_1435,X_1435))) )],[refute_0_77,refute_0_51]) ).
cnf(refute_0_79,plain,
theorem(implies(X_1436,X_1436)),
inference(subst,[],[refute_0_78:[bind(X_1435,$fot(X_1436))]]) ).
cnf(refute_0_80,plain,
theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436))),
inference(resolve,[$cnf( theorem(implies(X_1436,X_1436)) )],[refute_0_79,refute_0_47]) ).
cnf(refute_0_81,plain,
( equivalent(P,Q) != and(implies(P,Q),implies(Q,P))
| and(implies(P,Q),implies(Q,P)) = equivalent(P,Q) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(equivalent(P,Q))),bind(Y0,$fot(and(implies(P,Q),implies(Q,P))))]]) ).
cnf(refute_0_82,plain,
and(implies(P,Q),implies(Q,P)) = equivalent(P,Q),
inference(resolve,[$cnf( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_81]) ).
cnf(refute_0_83,plain,
and(implies(X_1436,X_1436),implies(X_1436,X_1436)) = equivalent(X_1436,X_1436),
inference(subst,[],[refute_0_82:[bind(P,$fot(X_1436)),bind(Q,$fot(X_1436))]]) ).
cnf(refute_0_84,plain,
( and(implies(X_1436,X_1436),implies(X_1436,X_1436)) != equivalent(X_1436,X_1436)
| ~ theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436)))
| theorem(equivalent(X_1436,X_1436)) ),
introduced(tautology,[equality,[$cnf( theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436))) ),[0],$fot(equivalent(X_1436,X_1436))]]) ).
cnf(refute_0_85,plain,
( ~ theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436)))
| theorem(equivalent(X_1436,X_1436)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1436,X_1436),implies(X_1436,X_1436)),equivalent(X_1436,X_1436)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(equivalent(X_1436,X_1436)),
inference(resolve,[$cnf( theorem(and(implies(X_1436,X_1436),implies(X_1436,X_1436))) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(equivalent(p,p)),
inference(subst,[],[refute_0_86:[bind(X_1436,$fot(p))]]) ).
cnf(refute_0_88,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(p,p)) )],[refute_0_87,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL268-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.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 : Sun Jul 3 21:02:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.29/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.50
% 1.29/1.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.29/1.51
%------------------------------------------------------------------------------