TSTP Solution File: LCL301-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:51:26 EDT 2022
% Result : Unsatisfiable 1.23s 1.40s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of clauses : 135 ( 75 unt; 0 nHn; 65 RR)
% Number of literals : 214 ( 70 equ; 81 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 224 ( 28 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(not(implies(not(p),not(q))),and(not(p),q))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_4,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_6,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_7,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_8,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_11,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_11]) ).
cnf(refute_0_13,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_14,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
not(implies(not(p),not(q))) = and(not(p),q),
inference(subst,[],[refute_0_14:[bind(P,$fot(not(p))),bind(Q,$fot(q))]]) ).
cnf(refute_0_16,plain,
equivalent(not(implies(not(p),not(q))),and(not(p),q)) = equivalent(not(implies(not(p),not(q))),and(not(p),q)),
introduced(tautology,[refl,[$fot(equivalent(not(implies(not(p),not(q))),and(not(p),q)))]]) ).
cnf(refute_0_17,plain,
( equivalent(not(implies(not(p),not(q))),and(not(p),q)) != equivalent(not(implies(not(p),not(q))),and(not(p),q))
| not(implies(not(p),not(q))) != and(not(p),q)
| equivalent(not(implies(not(p),not(q))),and(not(p),q)) = equivalent(and(not(p),q),and(not(p),q)) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(not(implies(not(p),not(q))),and(not(p),q)),equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),[1,0],$fot(and(not(p),q))]]) ).
cnf(refute_0_18,plain,
( not(implies(not(p),not(q))) != and(not(p),q)
| equivalent(not(implies(not(p),not(q))),and(not(p),q)) = equivalent(and(not(p),q),and(not(p),q)) ),
inference(resolve,[$cnf( $equal(equivalent(not(implies(not(p),not(q))),and(not(p),q)),equivalent(not(implies(not(p),not(q))),and(not(p),q))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
equivalent(not(implies(not(p),not(q))),and(not(p),q)) = equivalent(and(not(p),q),and(not(p),q)),
inference(resolve,[$cnf( $equal(not(implies(not(p),not(q))),and(not(p),q)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( equivalent(not(implies(not(p),not(q))),and(not(p),q)) != equivalent(and(not(p),q),and(not(p),q))
| ~ theorem(equivalent(and(not(p),q),and(not(p),q)))
| theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),[0],$fot(equivalent(and(not(p),q),and(not(p),q)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(equivalent(and(not(p),q),and(not(p),q)))
| theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),
inference(resolve,[$cnf( $equal(equivalent(not(implies(not(p),not(q))),and(not(p),q)),equivalent(and(not(p),q),and(not(p),q))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
~ theorem(equivalent(and(not(p),q),and(not(p),q))),
inference(resolve,[$cnf( theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) )],[refute_0_21,prove_this]) ).
cnf(refute_0_23,plain,
( ~ theorem(X_89)
| ~ theorem(implies(X_89,and(X_89,X_89)))
| theorem(and(X_89,X_89)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_89,X_89))),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_24,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_25,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(implies(or(not(X_7),not(X_7)),not(X_7))),
inference(subst,[],[refute_0_25:[bind(A,$fot(not(X_7)))]]) ).
cnf(refute_0_27,plain,
implies(X_7,not(X_7)) = or(not(X_7),not(X_7)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(not(X_7)))]]) ).
cnf(refute_0_28,plain,
( implies(X_7,not(X_7)) != or(not(X_7),not(X_7))
| or(not(X_7),not(X_7)) = implies(X_7,not(X_7)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_7,not(X_7)))),bind(Y0,$fot(or(not(X_7),not(X_7))))]]) ).
cnf(refute_0_29,plain,
or(not(X_7),not(X_7)) = implies(X_7,not(X_7)),
inference(resolve,[$cnf( $equal(implies(X_7,not(X_7)),or(not(X_7),not(X_7))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( or(not(X_7),not(X_7)) != implies(X_7,not(X_7))
| ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) ),[0,0],$fot(implies(X_7,not(X_7)))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),not(X_7)),implies(X_7,not(X_7))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
theorem(implies(implies(X_7,not(X_7)),not(X_7))),
inference(resolve,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(implies(X_21,not(X_22)),Y) = or(not(implies(X_21,not(X_22))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_21,not(X_22))))]]) ).
cnf(refute_0_34,plain,
and(X_21,X_22) = not(implies(X_21,not(X_22))),
inference(subst,[],[refute_0_12:[bind(P,$fot(X_21)),bind(Q,$fot(X_22))]]) ).
cnf(refute_0_35,plain,
( and(X_21,X_22) != not(implies(X_21,not(X_22)))
| not(implies(X_21,not(X_22))) = and(X_21,X_22) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_21,X_22))),bind(Y0,$fot(not(implies(X_21,not(X_22)))))]]) ).
cnf(refute_0_36,plain,
not(implies(X_21,not(X_22))) = and(X_21,X_22),
inference(resolve,[$cnf( $equal(and(X_21,X_22),not(implies(X_21,not(X_22)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( implies(implies(X_21,not(X_22)),Y) != or(not(implies(X_21,not(X_22))),Y)
| not(implies(X_21,not(X_22))) != and(X_21,X_22)
| implies(implies(X_21,not(X_22)),Y) = or(and(X_21,X_22),Y) ),
introduced(tautology,[equality,[$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_38,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( $equal(not(implies(X_21,not(X_22))),and(X_21,X_22)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(implies(X_21,not(X_22)),Y) = or(and(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_21,not(X_22)),Y),or(not(implies(X_21,not(X_22))),Y)) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(X_7,not(X_7)),not(X_7)) = or(and(X_7,X_7),not(X_7)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(not(X_7))),bind(X_21,$fot(X_7)),bind(X_22,$fot(X_7))]]) ).
cnf(refute_0_41,plain,
( implies(implies(X_7,not(X_7)),not(X_7)) != or(and(X_7,X_7),not(X_7))
| ~ theorem(implies(implies(X_7,not(X_7)),not(X_7)))
| theorem(or(and(X_7,X_7),not(X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),[0],$fot(or(and(X_7,X_7),not(X_7)))]]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(implies(X_7,not(X_7)),not(X_7)))
| theorem(or(and(X_7,X_7),not(X_7))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,not(X_7)),not(X_7)),or(and(X_7,X_7),not(X_7))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
theorem(or(and(X_7,X_7),not(X_7))),
inference(resolve,[$cnf( theorem(implies(implies(X_7,not(X_7)),not(X_7))) )],[refute_0_32,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ axiom(implies(or(X_5,X_6),or(X_6,X_5)))
| theorem(implies(or(X_5,X_6),or(X_6,X_5))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_45,plain,
axiom(implies(or(X_5,X_6),or(X_6,X_5))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_5)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_46,plain,
theorem(implies(or(X_5,X_6),or(X_6,X_5))),
inference(resolve,[$cnf( axiom(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(or(X_5,X_6),or(X_6,X_5)))
| ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_6,X_5))),bind(Y,$fot(or(X_5,X_6)))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(and(X_7,X_7),not(X_7)))
| theorem(or(not(X_7),and(X_7,X_7))) ),
inference(subst,[],[refute_0_48:[bind(X_5,$fot(and(X_7,X_7))),bind(X_6,$fot(not(X_7)))]]) ).
cnf(refute_0_50,plain,
theorem(or(not(X_7),and(X_7,X_7))),
inference(resolve,[$cnf( theorem(or(and(X_7,X_7),not(X_7))) )],[refute_0_43,refute_0_49]) ).
cnf(refute_0_51,plain,
or(not(X_7),and(X_7,X_7)) = implies(X_7,and(X_7,X_7)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_7)),bind(Y,$fot(and(X_7,X_7)))]]) ).
cnf(refute_0_52,plain,
( or(not(X_7),and(X_7,X_7)) != implies(X_7,and(X_7,X_7))
| ~ theorem(or(not(X_7),and(X_7,X_7)))
| theorem(implies(X_7,and(X_7,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_7),and(X_7,X_7))) ),[0],$fot(implies(X_7,and(X_7,X_7)))]]) ).
cnf(refute_0_53,plain,
( ~ theorem(or(not(X_7),and(X_7,X_7)))
| theorem(implies(X_7,and(X_7,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),and(X_7,X_7)),implies(X_7,and(X_7,X_7))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
theorem(implies(X_7,and(X_7,X_7))),
inference(resolve,[$cnf( theorem(or(not(X_7),and(X_7,X_7))) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(implies(X_89,and(X_89,X_89))),
inference(subst,[],[refute_0_54:[bind(X_7,$fot(X_89))]]) ).
cnf(refute_0_56,plain,
( ~ theorem(X_89)
| theorem(and(X_89,X_89)) ),
inference(resolve,[$cnf( theorem(implies(X_89,and(X_89,X_89))) )],[refute_0_55,refute_0_23]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(X_1313,X_1313))
| theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313))) ),
inference(subst,[],[refute_0_56:[bind(X_89,$fot(implies(X_1313,X_1313)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_1312,not(X_1312)))
| theorem(or(not(X_1312),X_1312)) ),
inference(subst,[],[refute_0_48:[bind(X_5,$fot(X_1312)),bind(X_6,$fot(not(X_1312)))]]) ).
cnf(refute_0_59,plain,
theorem(implies(or(X_83,X_83),X_83)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_83))]]) ).
cnf(refute_0_60,plain,
( ~ theorem(implies(or(X_83,X_83),X_83))
| ~ theorem(or(X_83,X_83))
| theorem(X_83) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_83)),bind(Y,$fot(or(X_83,X_83)))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(or(X_83,X_83))
| theorem(X_83) ),
inference(resolve,[$cnf( theorem(implies(or(X_83,X_83),X_83)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ theorem(or(or(X_1310,not(X_1310)),or(X_1310,not(X_1310))))
| theorem(or(X_1310,not(X_1310))) ),
inference(subst,[],[refute_0_61:[bind(X_83,$fot(or(X_1310,not(X_1310))))]]) ).
cnf(refute_0_63,plain,
( ~ axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39))))
| theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))))]]) ).
cnf(refute_0_64,plain,
axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_37)),bind(B,$fot(X_38)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_65,plain,
theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
( ~ theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39))))
| ~ theorem(or(X_37,or(X_38,X_39)))
| theorem(or(X_38,or(X_37,X_39))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_38,or(X_37,X_39)))),bind(Y,$fot(or(X_37,or(X_38,X_39))))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(or(X_37,or(X_38,X_39)))
| theorem(or(X_38,or(X_37,X_39))) ),
inference(resolve,[$cnf( theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ theorem(or(X_1308,or(X_1309,not(X_1308))))
| theorem(or(X_1309,or(X_1308,not(X_1308)))) ),
inference(subst,[],[refute_0_67:[bind(X_37,$fot(X_1308)),bind(X_38,$fot(X_1309)),bind(X_39,$fot(not(X_1308)))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(or(or(X_1307,not(X_1306)),X_1306))
| theorem(or(X_1306,or(X_1307,not(X_1306)))) ),
inference(subst,[],[refute_0_48:[bind(X_5,$fot(or(X_1307,not(X_1306)))),bind(X_6,$fot(X_1306))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(or(or(or(X_1305,not(X_1303)),X_1303),or(or(X_1305,not(X_1303)),X_1303)))
| theorem(or(or(X_1305,not(X_1303)),X_1303)) ),
inference(subst,[],[refute_0_61:[bind(X_83,$fot(or(or(X_1305,not(X_1303)),X_1303)))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(or(or(X_1302,not(X_1300)),or(X_1301,X_1300)))
| theorem(or(X_1301,or(or(X_1302,not(X_1300)),X_1300))) ),
inference(subst,[],[refute_0_67:[bind(X_37,$fot(or(X_1302,not(X_1300)))),bind(X_38,$fot(X_1301)),bind(X_39,$fot(X_1300))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(or(or(X_966,X_965),or(X_967,not(X_965))))
| theorem(or(or(X_967,not(X_965)),or(X_966,X_965))) ),
inference(subst,[],[refute_0_48:[bind(X_5,$fot(or(X_966,X_965))),bind(X_6,$fot(or(X_967,not(X_965))))]]) ).
cnf(refute_0_73,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_74,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_75,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
theorem(implies(X_84,or(X_4,X_84))),
inference(subst,[],[refute_0_75:[bind(X_3,$fot(X_84))]]) ).
cnf(refute_0_77,plain,
( ~ theorem(X_84)
| ~ theorem(implies(X_84,or(X_4,X_84)))
| theorem(or(X_4,X_84)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_84))),bind(Y,$fot(X_84))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(X_84)
| theorem(or(X_4,X_84)) ),
inference(resolve,[$cnf( theorem(implies(X_84,or(X_4,X_84))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ theorem(or(or(X_132,X_131),not(X_131)))
| theorem(or(X_4,or(or(X_132,X_131),not(X_131)))) ),
inference(subst,[],[refute_0_78:[bind(X_84,$fot(or(or(X_132,X_131),not(X_131))))]]) ).
cnf(refute_0_80,plain,
theorem(implies(X_124,or(X_4,X_124))),
inference(subst,[],[refute_0_75:[bind(X_3,$fot(X_124))]]) ).
cnf(refute_0_81,plain,
theorem(implies(or(not(X),X_18),or(X_18,not(X)))),
inference(subst,[],[refute_0_46:[bind(X_5,$fot(not(X))),bind(X_6,$fot(X_18))]]) ).
cnf(refute_0_82,plain,
implies(X,X_18) = or(not(X),X_18),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_18))]]) ).
cnf(refute_0_83,plain,
( implies(X,X_18) != or(not(X),X_18)
| or(not(X),X_18) = implies(X,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_18))),bind(Y0,$fot(or(not(X),X_18)))]]) ).
cnf(refute_0_84,plain,
or(not(X),X_18) = implies(X,X_18),
inference(resolve,[$cnf( $equal(implies(X,X_18),or(not(X),X_18)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( or(not(X),X_18) != implies(X,X_18)
| ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) ),[0,0],$fot(implies(X,X_18))]]) ).
cnf(refute_0_86,plain,
( ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_18),implies(X,X_18)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(implies(X,X_18),or(X_18,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ theorem(implies(X,X_18))
| ~ theorem(implies(implies(X,X_18),or(X_18,not(X))))
| theorem(or(X_18,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X)))),bind(Y,$fot(implies(X,X_18)))]]) ).
cnf(refute_0_89,plain,
( ~ theorem(implies(X,X_18))
| theorem(or(X_18,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_18),or(X_18,not(X)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ theorem(implies(X_124,or(X_4,X_124)))
| theorem(or(or(X_4,X_124),not(X_124))) ),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_124)),bind(X_18,$fot(or(X_4,X_124)))]]) ).
cnf(refute_0_91,plain,
theorem(or(or(X_4,X_124),not(X_124))),
inference(resolve,[$cnf( theorem(implies(X_124,or(X_4,X_124))) )],[refute_0_80,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(or(or(X_132,X_131),not(X_131))),
inference(subst,[],[refute_0_91:[bind(X_124,$fot(X_131)),bind(X_4,$fot(X_132))]]) ).
cnf(refute_0_93,plain,
theorem(or(X_4,or(or(X_132,X_131),not(X_131)))),
inference(resolve,[$cnf( theorem(or(or(X_132,X_131),not(X_131))) )],[refute_0_92,refute_0_79]) ).
cnf(refute_0_94,plain,
theorem(or(X_908,or(or(X_132,X_131),not(X_131)))),
inference(subst,[],[refute_0_93:[bind(X_4,$fot(X_908))]]) ).
cnf(refute_0_95,plain,
( ~ theorem(or(X_908,or(or(X_132,X_131),not(X_131))))
| theorem(or(or(X_132,X_131),or(X_908,not(X_131)))) ),
inference(subst,[],[refute_0_67:[bind(X_37,$fot(X_908)),bind(X_38,$fot(or(X_132,X_131))),bind(X_39,$fot(not(X_131)))]]) ).
cnf(refute_0_96,plain,
theorem(or(or(X_132,X_131),or(X_908,not(X_131)))),
inference(resolve,[$cnf( theorem(or(X_908,or(or(X_132,X_131),not(X_131)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
theorem(or(or(X_966,X_965),or(X_967,not(X_965)))),
inference(subst,[],[refute_0_96:[bind(X_131,$fot(X_965)),bind(X_132,$fot(X_966)),bind(X_908,$fot(X_967))]]) ).
cnf(refute_0_98,plain,
theorem(or(or(X_967,not(X_965)),or(X_966,X_965))),
inference(resolve,[$cnf( theorem(or(or(X_966,X_965),or(X_967,not(X_965)))) )],[refute_0_97,refute_0_72]) ).
cnf(refute_0_99,plain,
theorem(or(or(X_1302,not(X_1300)),or(X_1301,X_1300))),
inference(subst,[],[refute_0_98:[bind(X_965,$fot(X_1300)),bind(X_966,$fot(X_1301)),bind(X_967,$fot(X_1302))]]) ).
cnf(refute_0_100,plain,
theorem(or(X_1301,or(or(X_1302,not(X_1300)),X_1300))),
inference(resolve,[$cnf( theorem(or(or(X_1302,not(X_1300)),or(X_1301,X_1300))) )],[refute_0_99,refute_0_71]) ).
cnf(refute_0_101,plain,
theorem(or(or(or(X_1305,not(X_1303)),X_1303),or(or(X_1305,not(X_1303)),X_1303))),
inference(subst,[],[refute_0_100:[bind(X_1300,$fot(X_1303)),bind(X_1301,$fot(or(or(X_1305,not(X_1303)),X_1303))),bind(X_1302,$fot(X_1305))]]) ).
cnf(refute_0_102,plain,
theorem(or(or(X_1305,not(X_1303)),X_1303)),
inference(resolve,[$cnf( theorem(or(or(or(X_1305,not(X_1303)),X_1303),or(or(X_1305,not(X_1303)),X_1303))) )],[refute_0_101,refute_0_70]) ).
cnf(refute_0_103,plain,
theorem(or(or(X_1307,not(X_1306)),X_1306)),
inference(subst,[],[refute_0_102:[bind(X_1303,$fot(X_1306)),bind(X_1305,$fot(X_1307))]]) ).
cnf(refute_0_104,plain,
theorem(or(X_1306,or(X_1307,not(X_1306)))),
inference(resolve,[$cnf( theorem(or(or(X_1307,not(X_1306)),X_1306)) )],[refute_0_103,refute_0_69]) ).
cnf(refute_0_105,plain,
theorem(or(X_1308,or(X_1309,not(X_1308)))),
inference(subst,[],[refute_0_104:[bind(X_1306,$fot(X_1308)),bind(X_1307,$fot(X_1309))]]) ).
cnf(refute_0_106,plain,
theorem(or(X_1309,or(X_1308,not(X_1308)))),
inference(resolve,[$cnf( theorem(or(X_1308,or(X_1309,not(X_1308)))) )],[refute_0_105,refute_0_68]) ).
cnf(refute_0_107,plain,
theorem(or(or(X_1310,not(X_1310)),or(X_1310,not(X_1310)))),
inference(subst,[],[refute_0_106:[bind(X_1308,$fot(X_1310)),bind(X_1309,$fot(or(X_1310,not(X_1310))))]]) ).
cnf(refute_0_108,plain,
theorem(or(X_1310,not(X_1310))),
inference(resolve,[$cnf( theorem(or(or(X_1310,not(X_1310)),or(X_1310,not(X_1310)))) )],[refute_0_107,refute_0_62]) ).
cnf(refute_0_109,plain,
theorem(or(X_1312,not(X_1312))),
inference(subst,[],[refute_0_108:[bind(X_1310,$fot(X_1312))]]) ).
cnf(refute_0_110,plain,
theorem(or(not(X_1312),X_1312)),
inference(resolve,[$cnf( theorem(or(X_1312,not(X_1312))) )],[refute_0_109,refute_0_58]) ).
cnf(refute_0_111,plain,
or(not(X_1312),X_1312) = implies(X_1312,X_1312),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_1312)),bind(Y,$fot(X_1312))]]) ).
cnf(refute_0_112,plain,
( or(not(X_1312),X_1312) != implies(X_1312,X_1312)
| ~ theorem(or(not(X_1312),X_1312))
| theorem(implies(X_1312,X_1312)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_1312),X_1312)) ),[0],$fot(implies(X_1312,X_1312))]]) ).
cnf(refute_0_113,plain,
( ~ theorem(or(not(X_1312),X_1312))
| theorem(implies(X_1312,X_1312)) ),
inference(resolve,[$cnf( $equal(or(not(X_1312),X_1312),implies(X_1312,X_1312)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
theorem(implies(X_1312,X_1312)),
inference(resolve,[$cnf( theorem(or(not(X_1312),X_1312)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
theorem(implies(X_1313,X_1313)),
inference(subst,[],[refute_0_114:[bind(X_1312,$fot(X_1313))]]) ).
cnf(refute_0_116,plain,
theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313))),
inference(resolve,[$cnf( theorem(implies(X_1313,X_1313)) )],[refute_0_115,refute_0_57]) ).
cnf(refute_0_117,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_2:[bind(X0,$fot(equivalent(P,Q))),bind(Y0,$fot(and(implies(P,Q),implies(Q,P))))]]) ).
cnf(refute_0_118,plain,
and(implies(P,Q),implies(Q,P)) = equivalent(P,Q),
inference(resolve,[$cnf( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_117]) ).
cnf(refute_0_119,plain,
and(implies(X_1313,X_1313),implies(X_1313,X_1313)) = equivalent(X_1313,X_1313),
inference(subst,[],[refute_0_118:[bind(P,$fot(X_1313)),bind(Q,$fot(X_1313))]]) ).
cnf(refute_0_120,plain,
( and(implies(X_1313,X_1313),implies(X_1313,X_1313)) != equivalent(X_1313,X_1313)
| ~ theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313)))
| theorem(equivalent(X_1313,X_1313)) ),
introduced(tautology,[equality,[$cnf( theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313))) ),[0],$fot(equivalent(X_1313,X_1313))]]) ).
cnf(refute_0_121,plain,
( ~ theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313)))
| theorem(equivalent(X_1313,X_1313)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1313,X_1313),implies(X_1313,X_1313)),equivalent(X_1313,X_1313)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
theorem(equivalent(X_1313,X_1313)),
inference(resolve,[$cnf( theorem(and(implies(X_1313,X_1313),implies(X_1313,X_1313))) )],[refute_0_116,refute_0_121]) ).
cnf(refute_0_123,plain,
theorem(equivalent(and(not(p),q),and(not(p),q))),
inference(subst,[],[refute_0_122:[bind(X_1313,$fot(and(not(p),q)))]]) ).
cnf(refute_0_124,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(and(not(p),q),and(not(p),q))) )],[refute_0_123,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 17:47:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.23/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/1.40
% 1.23/1.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.23/1.41
%------------------------------------------------------------------------------