TSTP Solution File: LCL236-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL236-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:50:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of clauses : 93 ( 52 unt; 0 nHn; 50 RR)
% Number of literals : 149 ( 66 equ; 59 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; 2 con; 0-2 aty)
% Number of variables : 165 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(or(not(p),not(q)),not(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,$fot(not(q)))]]) ).
cnf(refute_0_6,plain,
implies(or(not(p),not(q)),not(and(p,q))) = implies(or(not(p),not(q)),not(and(p,q))),
introduced(tautology,[refl,[$fot(implies(or(not(p),not(q)),not(and(p,q))))]]) ).
cnf(refute_0_7,plain,
( implies(or(not(p),not(q)),not(and(p,q))) != implies(or(not(p),not(q)),not(and(p,q)))
| or(not(p),not(q)) != implies(p,not(q))
| implies(or(not(p),not(q)),not(and(p,q))) = implies(implies(p,not(q)),not(and(p,q))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(p),not(q)),not(and(p,q))),implies(or(not(p),not(q)),not(and(p,q)))) ),[1,0],$fot(implies(p,not(q)))]]) ).
cnf(refute_0_8,plain,
( or(not(p),not(q)) != implies(p,not(q))
| implies(or(not(p),not(q)),not(and(p,q))) = implies(implies(p,not(q)),not(and(p,q))) ),
inference(resolve,[$cnf( $equal(implies(or(not(p),not(q)),not(and(p,q))),implies(or(not(p),not(q)),not(and(p,q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(or(not(p),not(q)),not(and(p,q))) = implies(implies(p,not(q)),not(and(p,q))),
inference(resolve,[$cnf( $equal(or(not(p),not(q)),implies(p,not(q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(or(not(p),not(q)),not(and(p,q))) != implies(implies(p,not(q)),not(and(p,q)))
| ~ theorem(implies(implies(p,not(q)),not(and(p,q))))
| theorem(implies(or(not(p),not(q)),not(and(p,q)))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(implies(or(not(p),not(q)),not(and(p,q)))) ),[0],$fot(implies(implies(p,not(q)),not(and(p,q))))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(implies(p,not(q)),not(and(p,q))))
| theorem(implies(or(not(p),not(q)),not(and(p,q)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(p),not(q)),not(and(p,q))),implies(implies(p,not(q)),not(and(p,q)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ theorem(implies(implies(p,not(q)),not(and(p,q)))),
inference(resolve,[$cnf( theorem(implies(or(not(p),not(q)),not(and(p,q)))) )],[refute_0_11,prove_this]) ).
cnf(refute_0_13,plain,
implies(implies(X_19,not(X_20)),Y) = or(not(implies(X_19,not(X_20))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_19,not(X_20))))]]) ).
cnf(refute_0_14,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_15,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_16,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_17,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_20,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_20]) ).
cnf(refute_0_22,plain,
and(X_19,X_20) = not(implies(X_19,not(X_20))),
inference(subst,[],[refute_0_21:[bind(P,$fot(X_19)),bind(Q,$fot(X_20))]]) ).
cnf(refute_0_23,plain,
( and(X_19,X_20) != not(implies(X_19,not(X_20)))
| not(implies(X_19,not(X_20))) = and(X_19,X_20) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_19,X_20))),bind(Y0,$fot(not(implies(X_19,not(X_20)))))]]) ).
cnf(refute_0_24,plain,
not(implies(X_19,not(X_20))) = and(X_19,X_20),
inference(resolve,[$cnf( $equal(and(X_19,X_20),not(implies(X_19,not(X_20)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(implies(X_19,not(X_20)),Y) != or(not(implies(X_19,not(X_20))),Y)
| not(implies(X_19,not(X_20))) != and(X_19,X_20)
| implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_19,not(X_20)),Y),or(not(implies(X_19,not(X_20))),Y)) ),[1,0],$fot(and(X_19,X_20))]]) ).
cnf(refute_0_26,plain,
( implies(implies(X_19,not(X_20)),Y) != or(not(implies(X_19,not(X_20))),Y)
| implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_19,not(X_20))),and(X_19,X_20)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(X_19,not(X_20)),Y) = or(and(X_19,X_20),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_19,not(X_20)),Y),or(not(implies(X_19,not(X_20))),Y)) )],[refute_0_13,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(implies(p,not(q)),not(and(p,q))) = or(and(p,q),not(and(p,q))),
inference(subst,[],[refute_0_27:[bind(Y,$fot(not(and(p,q)))),bind(X_19,$fot(p)),bind(X_20,$fot(q))]]) ).
cnf(refute_0_29,plain,
( implies(implies(p,not(q)),not(and(p,q))) != or(and(p,q),not(and(p,q)))
| ~ theorem(or(and(p,q),not(and(p,q))))
| theorem(implies(implies(p,not(q)),not(and(p,q)))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(implies(implies(p,not(q)),not(and(p,q)))) ),[0],$fot(or(and(p,q),not(and(p,q))))]]) ).
cnf(refute_0_30,plain,
( ~ theorem(or(and(p,q),not(and(p,q))))
| theorem(implies(implies(p,not(q)),not(and(p,q)))) ),
inference(resolve,[$cnf( $equal(implies(implies(p,not(q)),not(and(p,q))),or(and(p,q),not(and(p,q)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
~ theorem(or(and(p,q),not(and(p,q)))),
inference(resolve,[$cnf( theorem(implies(implies(p,not(q)),not(and(p,q)))) )],[refute_0_30,refute_0_12]) ).
cnf(refute_0_32,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,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_33,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_34,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
theorem(implies(or(not(X),X_12),or(X_12,not(X)))),
inference(subst,[],[refute_0_34:[bind(X_7,$fot(not(X))),bind(X_8,$fot(X_12))]]) ).
cnf(refute_0_36,plain,
implies(X,X_12) = or(not(X),X_12),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_12))]]) ).
cnf(refute_0_37,plain,
( implies(X,X_12) != or(not(X),X_12)
| or(not(X),X_12) = implies(X,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_12))),bind(Y0,$fot(or(not(X),X_12)))]]) ).
cnf(refute_0_38,plain,
or(not(X),X_12) = implies(X,X_12),
inference(resolve,[$cnf( $equal(implies(X,X_12),or(not(X),X_12)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( or(not(X),X_12) != implies(X,X_12)
| ~ theorem(implies(or(not(X),X_12),or(X_12,not(X))))
| theorem(implies(implies(X,X_12),or(X_12,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_12),or(X_12,not(X)))) ),[0,0],$fot(implies(X,X_12))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(or(not(X),X_12),or(X_12,not(X))))
| theorem(implies(implies(X,X_12),or(X_12,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_12),implies(X,X_12)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X,X_12),or(X_12,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_12),or(X_12,not(X)))) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X,X_12))
| ~ theorem(implies(implies(X,X_12),or(X_12,not(X))))
| theorem(or(X_12,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_12,not(X)))),bind(Y,$fot(implies(X,X_12)))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X,X_12))
| theorem(or(X_12,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_12),or(X_12,not(X)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(X_398,X_398))
| theorem(or(X_398,not(X_398))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_398)),bind(X_12,$fot(X_398))]]) ).
cnf(refute_0_45,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_46,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_45]) ).
cnf(refute_0_47,plain,
theorem(implies(or(X_94,X_94),X_94)),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_94))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(implies(or(X_94,X_94),X_94))
| ~ theorem(or(X_94,X_94))
| theorem(X_94) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_94)),bind(Y,$fot(or(X_94,X_94)))]]) ).
cnf(refute_0_49,plain,
( ~ theorem(or(X_94,X_94))
| theorem(X_94) ),
inference(resolve,[$cnf( theorem(implies(or(X_94,X_94),X_94)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(implies(X_397,X_397),implies(X_397,X_397)))
| theorem(implies(X_397,X_397)) ),
inference(subst,[],[refute_0_49:[bind(X_94,$fot(implies(X_397,X_397)))]]) ).
cnf(refute_0_51,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,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_52,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_53,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
theorem(implies(X_393,or(X_392,X_393))),
inference(subst,[],[refute_0_53:[bind(X_3,$fot(X_393)),bind(X_4,$fot(X_392))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(implies(X_120,or(X_121,X_122)))
| ~ theorem(implies(implies(X_120,or(X_121,X_122)),or(X_121,implies(X_120,X_122))))
| theorem(or(X_121,implies(X_120,X_122))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_121,implies(X_120,X_122)))),bind(Y,$fot(implies(X_120,or(X_121,X_122))))]]) ).
cnf(refute_0_56,plain,
( ~ axiom(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35))))
| theorem(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35)))))]]) ).
cnf(refute_0_57,plain,
axiom(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_33)),bind(B,$fot(X_34)),bind(C,$fot(X_35))]]) ).
cnf(refute_0_58,plain,
theorem(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35)))),
inference(resolve,[$cnf( axiom(implies(or(X_33,or(X_34,X_35)),or(X_34,or(X_33,X_35)))) )],[refute_0_57,refute_0_56]) ).
cnf(refute_0_59,plain,
theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,or(not(X),X_58)))),
inference(subst,[],[refute_0_58:[bind(X_33,$fot(not(X))),bind(X_34,$fot(X_57)),bind(X_35,$fot(X_58))]]) ).
cnf(refute_0_60,plain,
implies(X,X_58) = or(not(X),X_58),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_58))]]) ).
cnf(refute_0_61,plain,
( implies(X,X_58) != or(not(X),X_58)
| or(not(X),X_58) = implies(X,X_58) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_58))),bind(Y0,$fot(or(not(X),X_58)))]]) ).
cnf(refute_0_62,plain,
or(not(X),X_58) = implies(X,X_58),
inference(resolve,[$cnf( $equal(implies(X,X_58),or(not(X),X_58)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( or(not(X),X_58) != implies(X,X_58)
| ~ theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,or(not(X),X_58))))
| theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,or(not(X),X_58)))) ),[0,1,1],$fot(implies(X,X_58))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,or(not(X),X_58))))
| theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_58),implies(X,X_58)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,or(not(X),X_58)))) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
or(not(X),or(X_57,X_58)) = implies(X,or(X_57,X_58)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_57,X_58)))]]) ).
cnf(refute_0_67,plain,
implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) = implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))))]]) ).
cnf(refute_0_68,plain,
( implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) != implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))
| or(not(X),or(X_57,X_58)) != implies(X,or(X_57,X_58))
| implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) = implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))),implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),[1,0],$fot(implies(X,or(X_57,X_58)))]]) ).
cnf(refute_0_69,plain,
( or(not(X),or(X_57,X_58)) != implies(X,or(X_57,X_58))
| implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) = implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))),implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) = implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_57,X_58)),implies(X,or(X_57,X_58))) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))) != implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58)))
| ~ theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))))
| theorem(implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),[0],$fot(implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58))))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))))
| theorem(implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58))),implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
theorem(implies(implies(X,or(X_57,X_58)),or(X_57,implies(X,X_58)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_57,X_58)),or(X_57,implies(X,X_58)))) )],[refute_0_65,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(implies(X_120,or(X_121,X_122)),or(X_121,implies(X_120,X_122)))),
inference(subst,[],[refute_0_73:[bind(X,$fot(X_120)),bind(X_57,$fot(X_121)),bind(X_58,$fot(X_122))]]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(X_120,or(X_121,X_122)))
| theorem(or(X_121,implies(X_120,X_122))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_120,or(X_121,X_122)),or(X_121,implies(X_120,X_122)))) )],[refute_0_74,refute_0_55]) ).
cnf(refute_0_76,plain,
( ~ theorem(implies(X_393,or(X_392,X_393)))
| theorem(or(X_392,implies(X_393,X_393))) ),
inference(subst,[],[refute_0_75:[bind(X_120,$fot(X_393)),bind(X_121,$fot(X_392)),bind(X_122,$fot(X_393))]]) ).
cnf(refute_0_77,plain,
theorem(or(X_392,implies(X_393,X_393))),
inference(resolve,[$cnf( theorem(implies(X_393,or(X_392,X_393))) )],[refute_0_54,refute_0_76]) ).
cnf(refute_0_78,plain,
theorem(or(implies(X_397,X_397),implies(X_397,X_397))),
inference(subst,[],[refute_0_77:[bind(X_392,$fot(implies(X_397,X_397))),bind(X_393,$fot(X_397))]]) ).
cnf(refute_0_79,plain,
theorem(implies(X_397,X_397)),
inference(resolve,[$cnf( theorem(or(implies(X_397,X_397),implies(X_397,X_397))) )],[refute_0_78,refute_0_50]) ).
cnf(refute_0_80,plain,
theorem(implies(X_398,X_398)),
inference(subst,[],[refute_0_79:[bind(X_397,$fot(X_398))]]) ).
cnf(refute_0_81,plain,
theorem(or(X_398,not(X_398))),
inference(resolve,[$cnf( theorem(implies(X_398,X_398)) )],[refute_0_80,refute_0_44]) ).
cnf(refute_0_82,plain,
theorem(or(and(p,q),not(and(p,q)))),
inference(subst,[],[refute_0_81:[bind(X_398,$fot(and(p,q)))]]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( theorem(or(and(p,q),not(and(p,q)))) )],[refute_0_82,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : LCL236-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 21:39:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.53
%------------------------------------------------------------------------------