TSTP Solution File: LCL297-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL297-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:51:25 EDT 2022
% Result : Unsatisfiable 1.08s 1.25s
% Output : CNFRefutation 1.08s
% 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(p,not(q))),and(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( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
not(implies(p,not(q))) = and(p,q),
inference(subst,[],[refute_0_14:[bind(P,$fot(p)),bind(Q,$fot(q))]]) ).
cnf(refute_0_16,plain,
equivalent(not(implies(p,not(q))),and(p,q)) = equivalent(not(implies(p,not(q))),and(p,q)),
introduced(tautology,[refl,[$fot(equivalent(not(implies(p,not(q))),and(p,q)))]]) ).
cnf(refute_0_17,plain,
( equivalent(not(implies(p,not(q))),and(p,q)) != equivalent(not(implies(p,not(q))),and(p,q))
| not(implies(p,not(q))) != and(p,q)
| equivalent(not(implies(p,not(q))),and(p,q)) = equivalent(and(p,q),and(p,q)) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(not(implies(p,not(q))),and(p,q)),equivalent(not(implies(p,not(q))),and(p,q))) ),[1,0],$fot(and(p,q))]]) ).
cnf(refute_0_18,plain,
( not(implies(p,not(q))) != and(p,q)
| equivalent(not(implies(p,not(q))),and(p,q)) = equivalent(and(p,q),and(p,q)) ),
inference(resolve,[$cnf( $equal(equivalent(not(implies(p,not(q))),and(p,q)),equivalent(not(implies(p,not(q))),and(p,q))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
equivalent(not(implies(p,not(q))),and(p,q)) = equivalent(and(p,q),and(p,q)),
inference(resolve,[$cnf( $equal(not(implies(p,not(q))),and(p,q)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( equivalent(not(implies(p,not(q))),and(p,q)) != equivalent(and(p,q),and(p,q))
| ~ theorem(equivalent(and(p,q),and(p,q)))
| theorem(equivalent(not(implies(p,not(q))),and(p,q))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(equivalent(not(implies(p,not(q))),and(p,q))) ),[0],$fot(equivalent(and(p,q),and(p,q)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(equivalent(and(p,q),and(p,q)))
| theorem(equivalent(not(implies(p,not(q))),and(p,q))) ),
inference(resolve,[$cnf( $equal(equivalent(not(implies(p,not(q))),and(p,q)),equivalent(and(p,q),and(p,q))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
~ theorem(equivalent(and(p,q),and(p,q))),
inference(resolve,[$cnf( theorem(equivalent(not(implies(p,not(q))),and(p,q))) )],[refute_0_21,prove_this]) ).
cnf(refute_0_23,plain,
( ~ theorem(X_116)
| ~ theorem(implies(X_116,and(X_116,X_116)))
| theorem(and(X_116,X_116)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_116,X_116))),bind(Y,$fot(X_116))]]) ).
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_13,not(X_14)),Y) = or(not(implies(X_13,not(X_14))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_13,not(X_14))))]]) ).
cnf(refute_0_34,plain,
and(X_13,X_14) = not(implies(X_13,not(X_14))),
inference(subst,[],[refute_0_12:[bind(P,$fot(X_13)),bind(Q,$fot(X_14))]]) ).
cnf(refute_0_35,plain,
( and(X_13,X_14) != not(implies(X_13,not(X_14)))
| not(implies(X_13,not(X_14))) = and(X_13,X_14) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_13,X_14))),bind(Y0,$fot(not(implies(X_13,not(X_14)))))]]) ).
cnf(refute_0_36,plain,
not(implies(X_13,not(X_14))) = and(X_13,X_14),
inference(resolve,[$cnf( $equal(and(X_13,X_14),not(implies(X_13,not(X_14)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( implies(implies(X_13,not(X_14)),Y) != or(not(implies(X_13,not(X_14))),Y)
| not(implies(X_13,not(X_14))) != and(X_13,X_14)
| implies(implies(X_13,not(X_14)),Y) = or(and(X_13,X_14),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,not(X_14)),Y),or(not(implies(X_13,not(X_14))),Y)) ),[1,0],$fot(and(X_13,X_14))]]) ).
cnf(refute_0_38,plain,
( implies(implies(X_13,not(X_14)),Y) != or(not(implies(X_13,not(X_14))),Y)
| implies(implies(X_13,not(X_14)),Y) = or(and(X_13,X_14),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_13,not(X_14))),and(X_13,X_14)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(implies(X_13,not(X_14)),Y) = or(and(X_13,X_14),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_13,not(X_14)),Y),or(not(implies(X_13,not(X_14))),Y)) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(X_7,not(X_7)),not(X_7)) = or(and(X_7,X_7),not(X_7)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(not(X_7))),bind(X_13,$fot(X_7)),bind(X_14,$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_19,X_20),or(X_20,X_19)))
| theorem(implies(or(X_19,X_20),or(X_20,X_19))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_19,X_20),or(X_20,X_19))))]]) ).
cnf(refute_0_45,plain,
axiom(implies(or(X_19,X_20),or(X_20,X_19))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_19)),bind(B,$fot(X_20))]]) ).
cnf(refute_0_46,plain,
theorem(implies(or(X_19,X_20),or(X_20,X_19))),
inference(resolve,[$cnf( axiom(implies(or(X_19,X_20),or(X_20,X_19))) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(or(X_19,X_20),or(X_20,X_19)))
| ~ theorem(or(X_19,X_20))
| theorem(or(X_20,X_19)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_20,X_19))),bind(Y,$fot(or(X_19,X_20)))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(or(X_19,X_20))
| theorem(or(X_20,X_19)) ),
inference(resolve,[$cnf( theorem(implies(or(X_19,X_20),or(X_20,X_19))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(and(X_7,X_7),not(X_7)))
| theorem(or(not(X_7),and(X_7,X_7))) ),
inference(subst,[],[refute_0_48:[bind(X_19,$fot(and(X_7,X_7))),bind(X_20,$fot(not(X_7)))]]) ).
cnf(refute_0_50,plain,
theorem(or(not(X_7),and(X_7,X_7))),
inference(resolve,[$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_116,and(X_116,X_116))),
inference(subst,[],[refute_0_54:[bind(X_7,$fot(X_116))]]) ).
cnf(refute_0_56,plain,
( ~ theorem(X_116)
| theorem(and(X_116,X_116)) ),
inference(resolve,[$cnf( theorem(implies(X_116,and(X_116,X_116))) )],[refute_0_55,refute_0_23]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(X_1163,X_1163))
| theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163))) ),
inference(subst,[],[refute_0_56:[bind(X_116,$fot(implies(X_1163,X_1163)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_1162,not(X_1162)))
| theorem(or(not(X_1162),X_1162)) ),
inference(subst,[],[refute_0_48:[bind(X_19,$fot(X_1162)),bind(X_20,$fot(not(X_1162)))]]) ).
cnf(refute_0_59,plain,
theorem(implies(or(X_92,X_92),X_92)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_92))]]) ).
cnf(refute_0_60,plain,
( ~ theorem(implies(or(X_92,X_92),X_92))
| ~ theorem(or(X_92,X_92))
| theorem(X_92) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_92)),bind(Y,$fot(or(X_92,X_92)))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(or(X_92,X_92))
| theorem(X_92) ),
inference(resolve,[$cnf( theorem(implies(or(X_92,X_92),X_92)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ theorem(or(or(X_1160,not(X_1160)),or(X_1160,not(X_1160))))
| theorem(or(X_1160,not(X_1160))) ),
inference(subst,[],[refute_0_61:[bind(X_92,$fot(or(X_1160,not(X_1160))))]]) ).
cnf(refute_0_63,plain,
( ~ axiom(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48))))
| theorem(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))))]]) ).
cnf(refute_0_64,plain,
axiom(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_46)),bind(B,$fot(X_47)),bind(C,$fot(X_48))]]) ).
cnf(refute_0_65,plain,
theorem(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))),
inference(resolve,[$cnf( axiom(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))) )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
( ~ theorem(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48))))
| ~ theorem(or(X_46,or(X_47,X_48)))
| theorem(or(X_47,or(X_46,X_48))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_47,or(X_46,X_48)))),bind(Y,$fot(or(X_46,or(X_47,X_48))))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(or(X_46,or(X_47,X_48)))
| theorem(or(X_47,or(X_46,X_48))) ),
inference(resolve,[$cnf( theorem(implies(or(X_46,or(X_47,X_48)),or(X_47,or(X_46,X_48)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ theorem(or(X_1158,or(X_1159,not(X_1158))))
| theorem(or(X_1159,or(X_1158,not(X_1158)))) ),
inference(subst,[],[refute_0_67:[bind(X_46,$fot(X_1158)),bind(X_47,$fot(X_1159)),bind(X_48,$fot(not(X_1158)))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(or(or(X_1157,not(X_1156)),X_1156))
| theorem(or(X_1156,or(X_1157,not(X_1156)))) ),
inference(subst,[],[refute_0_48:[bind(X_19,$fot(or(X_1157,not(X_1156)))),bind(X_20,$fot(X_1156))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(or(or(or(X_1155,not(X_1153)),X_1153),or(or(X_1155,not(X_1153)),X_1153)))
| theorem(or(or(X_1155,not(X_1153)),X_1153)) ),
inference(subst,[],[refute_0_61:[bind(X_92,$fot(or(or(X_1155,not(X_1153)),X_1153)))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(or(or(X_978,not(X_976)),or(X_977,X_976)))
| theorem(or(X_977,or(or(X_978,not(X_976)),X_976))) ),
inference(subst,[],[refute_0_67:[bind(X_46,$fot(or(X_978,not(X_976)))),bind(X_47,$fot(X_977)),bind(X_48,$fot(X_976))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(or(or(X_754,X_753),or(X_755,not(X_753))))
| theorem(or(or(X_755,not(X_753)),or(X_754,X_753))) ),
inference(subst,[],[refute_0_48:[bind(X_19,$fot(or(X_754,X_753))),bind(X_20,$fot(or(X_755,not(X_753))))]]) ).
cnf(refute_0_73,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$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,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
theorem(implies(X_93,or(X_4,X_93))),
inference(subst,[],[refute_0_75:[bind(X_3,$fot(X_93))]]) ).
cnf(refute_0_77,plain,
( ~ theorem(X_93)
| ~ theorem(implies(X_93,or(X_4,X_93)))
| theorem(or(X_4,X_93)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_93))),bind(Y,$fot(X_93))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(X_93)
| theorem(or(X_4,X_93)) ),
inference(resolve,[$cnf( theorem(implies(X_93,or(X_4,X_93))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ theorem(or(or(X_335,X_334),not(X_334)))
| theorem(or(X_4,or(or(X_335,X_334),not(X_334)))) ),
inference(subst,[],[refute_0_78:[bind(X_93,$fot(or(or(X_335,X_334),not(X_334))))]]) ).
cnf(refute_0_80,plain,
theorem(implies(X_329,or(X_4,X_329))),
inference(subst,[],[refute_0_75:[bind(X_3,$fot(X_329))]]) ).
cnf(refute_0_81,plain,
theorem(implies(or(not(X),X_22),or(X_22,not(X)))),
inference(subst,[],[refute_0_46:[bind(X_19,$fot(not(X))),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_82,plain,
implies(X,X_22) = or(not(X),X_22),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_22))]]) ).
cnf(refute_0_83,plain,
( implies(X,X_22) != or(not(X),X_22)
| or(not(X),X_22) = implies(X,X_22) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_22))),bind(Y0,$fot(or(not(X),X_22)))]]) ).
cnf(refute_0_84,plain,
or(not(X),X_22) = implies(X,X_22),
inference(resolve,[$cnf( $equal(implies(X,X_22),or(not(X),X_22)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( or(not(X),X_22) != implies(X,X_22)
| ~ theorem(implies(or(not(X),X_22),or(X_22,not(X))))
| theorem(implies(implies(X,X_22),or(X_22,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_22),or(X_22,not(X)))) ),[0,0],$fot(implies(X,X_22))]]) ).
cnf(refute_0_86,plain,
( ~ theorem(implies(or(not(X),X_22),or(X_22,not(X))))
| theorem(implies(implies(X,X_22),or(X_22,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_22),implies(X,X_22)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(implies(X,X_22),or(X_22,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_22),or(X_22,not(X)))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ theorem(implies(X,X_22))
| ~ theorem(implies(implies(X,X_22),or(X_22,not(X))))
| theorem(or(X_22,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_22,not(X)))),bind(Y,$fot(implies(X,X_22)))]]) ).
cnf(refute_0_89,plain,
( ~ theorem(implies(X,X_22))
| theorem(or(X_22,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_22),or(X_22,not(X)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ theorem(implies(X_329,or(X_4,X_329)))
| theorem(or(or(X_4,X_329),not(X_329))) ),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_329)),bind(X_22,$fot(or(X_4,X_329)))]]) ).
cnf(refute_0_91,plain,
theorem(or(or(X_4,X_329),not(X_329))),
inference(resolve,[$cnf( theorem(implies(X_329,or(X_4,X_329))) )],[refute_0_80,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(or(or(X_335,X_334),not(X_334))),
inference(subst,[],[refute_0_91:[bind(X_329,$fot(X_334)),bind(X_4,$fot(X_335))]]) ).
cnf(refute_0_93,plain,
theorem(or(X_4,or(or(X_335,X_334),not(X_334)))),
inference(resolve,[$cnf( theorem(or(or(X_335,X_334),not(X_334))) )],[refute_0_92,refute_0_79]) ).
cnf(refute_0_94,plain,
theorem(or(X_739,or(or(X_335,X_334),not(X_334)))),
inference(subst,[],[refute_0_93:[bind(X_4,$fot(X_739))]]) ).
cnf(refute_0_95,plain,
( ~ theorem(or(X_739,or(or(X_335,X_334),not(X_334))))
| theorem(or(or(X_335,X_334),or(X_739,not(X_334)))) ),
inference(subst,[],[refute_0_67:[bind(X_46,$fot(X_739)),bind(X_47,$fot(or(X_335,X_334))),bind(X_48,$fot(not(X_334)))]]) ).
cnf(refute_0_96,plain,
theorem(or(or(X_335,X_334),or(X_739,not(X_334)))),
inference(resolve,[$cnf( theorem(or(X_739,or(or(X_335,X_334),not(X_334)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
theorem(or(or(X_754,X_753),or(X_755,not(X_753)))),
inference(subst,[],[refute_0_96:[bind(X_334,$fot(X_753)),bind(X_335,$fot(X_754)),bind(X_739,$fot(X_755))]]) ).
cnf(refute_0_98,plain,
theorem(or(or(X_755,not(X_753)),or(X_754,X_753))),
inference(resolve,[$cnf( theorem(or(or(X_754,X_753),or(X_755,not(X_753)))) )],[refute_0_97,refute_0_72]) ).
cnf(refute_0_99,plain,
theorem(or(or(X_978,not(X_976)),or(X_977,X_976))),
inference(subst,[],[refute_0_98:[bind(X_753,$fot(X_976)),bind(X_754,$fot(X_977)),bind(X_755,$fot(X_978))]]) ).
cnf(refute_0_100,plain,
theorem(or(X_977,or(or(X_978,not(X_976)),X_976))),
inference(resolve,[$cnf( theorem(or(or(X_978,not(X_976)),or(X_977,X_976))) )],[refute_0_99,refute_0_71]) ).
cnf(refute_0_101,plain,
theorem(or(or(or(X_1155,not(X_1153)),X_1153),or(or(X_1155,not(X_1153)),X_1153))),
inference(subst,[],[refute_0_100:[bind(X_976,$fot(X_1153)),bind(X_977,$fot(or(or(X_1155,not(X_1153)),X_1153))),bind(X_978,$fot(X_1155))]]) ).
cnf(refute_0_102,plain,
theorem(or(or(X_1155,not(X_1153)),X_1153)),
inference(resolve,[$cnf( theorem(or(or(or(X_1155,not(X_1153)),X_1153),or(or(X_1155,not(X_1153)),X_1153))) )],[refute_0_101,refute_0_70]) ).
cnf(refute_0_103,plain,
theorem(or(or(X_1157,not(X_1156)),X_1156)),
inference(subst,[],[refute_0_102:[bind(X_1153,$fot(X_1156)),bind(X_1155,$fot(X_1157))]]) ).
cnf(refute_0_104,plain,
theorem(or(X_1156,or(X_1157,not(X_1156)))),
inference(resolve,[$cnf( theorem(or(or(X_1157,not(X_1156)),X_1156)) )],[refute_0_103,refute_0_69]) ).
cnf(refute_0_105,plain,
theorem(or(X_1158,or(X_1159,not(X_1158)))),
inference(subst,[],[refute_0_104:[bind(X_1156,$fot(X_1158)),bind(X_1157,$fot(X_1159))]]) ).
cnf(refute_0_106,plain,
theorem(or(X_1159,or(X_1158,not(X_1158)))),
inference(resolve,[$cnf( theorem(or(X_1158,or(X_1159,not(X_1158)))) )],[refute_0_105,refute_0_68]) ).
cnf(refute_0_107,plain,
theorem(or(or(X_1160,not(X_1160)),or(X_1160,not(X_1160)))),
inference(subst,[],[refute_0_106:[bind(X_1158,$fot(X_1160)),bind(X_1159,$fot(or(X_1160,not(X_1160))))]]) ).
cnf(refute_0_108,plain,
theorem(or(X_1160,not(X_1160))),
inference(resolve,[$cnf( theorem(or(or(X_1160,not(X_1160)),or(X_1160,not(X_1160)))) )],[refute_0_107,refute_0_62]) ).
cnf(refute_0_109,plain,
theorem(or(X_1162,not(X_1162))),
inference(subst,[],[refute_0_108:[bind(X_1160,$fot(X_1162))]]) ).
cnf(refute_0_110,plain,
theorem(or(not(X_1162),X_1162)),
inference(resolve,[$cnf( theorem(or(X_1162,not(X_1162))) )],[refute_0_109,refute_0_58]) ).
cnf(refute_0_111,plain,
or(not(X_1162),X_1162) = implies(X_1162,X_1162),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_1162)),bind(Y,$fot(X_1162))]]) ).
cnf(refute_0_112,plain,
( or(not(X_1162),X_1162) != implies(X_1162,X_1162)
| ~ theorem(or(not(X_1162),X_1162))
| theorem(implies(X_1162,X_1162)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_1162),X_1162)) ),[0],$fot(implies(X_1162,X_1162))]]) ).
cnf(refute_0_113,plain,
( ~ theorem(or(not(X_1162),X_1162))
| theorem(implies(X_1162,X_1162)) ),
inference(resolve,[$cnf( $equal(or(not(X_1162),X_1162),implies(X_1162,X_1162)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
theorem(implies(X_1162,X_1162)),
inference(resolve,[$cnf( theorem(or(not(X_1162),X_1162)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
theorem(implies(X_1163,X_1163)),
inference(subst,[],[refute_0_114:[bind(X_1162,$fot(X_1163))]]) ).
cnf(refute_0_116,plain,
theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163))),
inference(resolve,[$cnf( theorem(implies(X_1163,X_1163)) )],[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( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_117]) ).
cnf(refute_0_119,plain,
and(implies(X_1163,X_1163),implies(X_1163,X_1163)) = equivalent(X_1163,X_1163),
inference(subst,[],[refute_0_118:[bind(P,$fot(X_1163)),bind(Q,$fot(X_1163))]]) ).
cnf(refute_0_120,plain,
( and(implies(X_1163,X_1163),implies(X_1163,X_1163)) != equivalent(X_1163,X_1163)
| ~ theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163)))
| theorem(equivalent(X_1163,X_1163)) ),
introduced(tautology,[equality,[$cnf( theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163))) ),[0],$fot(equivalent(X_1163,X_1163))]]) ).
cnf(refute_0_121,plain,
( ~ theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163)))
| theorem(equivalent(X_1163,X_1163)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1163,X_1163),implies(X_1163,X_1163)),equivalent(X_1163,X_1163)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
theorem(equivalent(X_1163,X_1163)),
inference(resolve,[$cnf( theorem(and(implies(X_1163,X_1163),implies(X_1163,X_1163))) )],[refute_0_116,refute_0_121]) ).
cnf(refute_0_123,plain,
theorem(equivalent(and(p,q),and(p,q))),
inference(subst,[],[refute_0_122:[bind(X_1163,$fot(and(p,q)))]]) ).
cnf(refute_0_124,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(and(p,q),and(p,q))) )],[refute_0_123,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL297-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.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 : Sun Jul 3 16:05:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.08/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/1.25
% 1.08/1.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.08/1.26
%------------------------------------------------------------------------------