TSTP Solution File: LCL311-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL311-3 : 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 12:51:29 EDT 2022
% Result : Unsatisfiable 82.45s 82.61s
% Output : CNFRefutation 82.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 28
% Syntax : Number of clauses : 129 ( 70 unt; 0 nHn; 60 RR)
% Number of literals : 208 ( 79 equ; 80 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 240 ( 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(equivalent_defn,axiom,
equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ).
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(implies(p,not(p)),not(p))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_28331,or(X_28331,X_28331)))
| ~ theorem(implies(implies(X_28331,or(X_28331,X_28331)),equivalent(or(X_28331,X_28331),X_28331)))
| theorem(equivalent(or(X_28331,X_28331),X_28331)) ),
inference(subst,[],[rule_2:[bind(X,$fot(equivalent(or(X_28331,X_28331),X_28331))),bind(Y,$fot(implies(X_28331,or(X_28331,X_28331))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(X_31,not(X_30)),implies(X_30,X_31)))
| theorem(implies(or(X_31,not(X_30)),implies(X_30,X_31))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_31,not(X_30)),implies(X_30,X_31))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(X_18,not(X)),or(not(X),X_18))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_18)),bind(B,$fot(not(X)))]]) ).
cnf(refute_0_3,plain,
implies(X,X_18) = or(not(X),X_18),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_18))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X,X_18) != or(not(X),X_18)
| or(not(X),X_18) = implies(X,X_18) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_18))),bind(Y0,$fot(or(not(X),X_18)))]]) ).
cnf(refute_0_8,plain,
or(not(X),X_18) = implies(X,X_18),
inference(resolve,[$cnf( $equal(implies(X,X_18),or(not(X),X_18)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X),X_18) != implies(X,X_18)
| ~ axiom(implies(or(X_18,not(X)),or(not(X),X_18)))
| axiom(implies(or(X_18,not(X)),implies(X,X_18))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_18,not(X)),or(not(X),X_18))) ),[0,1],$fot(implies(X,X_18))]]) ).
cnf(refute_0_10,plain,
( ~ axiom(implies(or(X_18,not(X)),or(not(X),X_18)))
| axiom(implies(or(X_18,not(X)),implies(X,X_18))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_18),implies(X,X_18)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
axiom(implies(or(X_18,not(X)),implies(X,X_18))),
inference(resolve,[$cnf( axiom(implies(or(X_18,not(X)),or(not(X),X_18))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
axiom(implies(or(X_31,not(X_30)),implies(X_30,X_31))),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_30)),bind(X_18,$fot(X_31))]]) ).
cnf(refute_0_13,plain,
theorem(implies(or(X_31,not(X_30)),implies(X_30,X_31))),
inference(resolve,[$cnf( axiom(implies(or(X_31,not(X_30)),implies(X_30,X_31))) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
( ~ theorem(implies(or(X_31,not(X_30)),implies(X_30,X_31)))
| ~ theorem(or(X_31,not(X_30)))
| theorem(implies(X_30,X_31)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(or(X_31,not(X_30))))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(X_31,not(X_30)))
| theorem(implies(X_30,X_31)) ),
inference(resolve,[$cnf( theorem(implies(or(X_31,not(X_30)),implies(X_30,X_31))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(not(X),not(X_257)))
| theorem(implies(X_257,not(X))) ),
inference(subst,[],[refute_0_15:[bind(X_30,$fot(X_257)),bind(X_31,$fot(not(X)))]]) ).
cnf(refute_0_17,plain,
implies(X,not(X_257)) = or(not(X),not(X_257)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_257)))]]) ).
cnf(refute_0_18,plain,
( implies(X,not(X_257)) != or(not(X),not(X_257))
| or(not(X),not(X_257)) = implies(X,not(X_257)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,not(X_257)))),bind(Y0,$fot(or(not(X),not(X_257))))]]) ).
cnf(refute_0_19,plain,
or(not(X),not(X_257)) = implies(X,not(X_257)),
inference(resolve,[$cnf( $equal(implies(X,not(X_257)),or(not(X),not(X_257))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( or(not(X),not(X_257)) != implies(X,not(X_257))
| ~ theorem(implies(X,not(X_257)))
| theorem(or(not(X),not(X_257))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),not(X_257))) ),[0],$fot(implies(X,not(X_257)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(X,not(X_257)))
| theorem(or(not(X),not(X_257))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_257)),implies(X,not(X_257))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(X,not(X_257)))
| theorem(implies(X_257,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),not(X_257))) )],[refute_0_21,refute_0_16]) ).
cnf(refute_0_23,plain,
( ~ theorem(implies(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)),not(X_257)))
| theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))]]) ).
cnf(refute_0_24,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_25,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ theorem(X_1555)
| ~ theorem(implies(X_1555,implies(implies(X_1555,X_1556),X_1556)))
| theorem(implies(implies(X_1555,X_1556),X_1556)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X_1555,X_1556),X_1556))),bind(Y,$fot(X_1555))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45))))
| theorem(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45)))))]]) ).
cnf(refute_0_28,plain,
axiom(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_43)),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_29,plain,
theorem(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45)))),
inference(resolve,[$cnf( axiom(implies(or(X_43,or(X_44,X_45)),or(X_44,or(X_43,X_45)))) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))),
inference(subst,[],[refute_0_29:[bind(X_43,$fot(not(X))),bind(X_44,$fot(X_77)),bind(X_45,$fot(X_78))]]) ).
cnf(refute_0_31,plain,
implies(X,X_78) = or(not(X),X_78),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_78))]]) ).
cnf(refute_0_32,plain,
( implies(X,X_78) != or(not(X),X_78)
| or(not(X),X_78) = implies(X,X_78) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_78))),bind(Y0,$fot(or(not(X),X_78)))]]) ).
cnf(refute_0_33,plain,
or(not(X),X_78) = implies(X,X_78),
inference(resolve,[$cnf( $equal(implies(X,X_78),or(not(X),X_78)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( or(not(X),X_78) != implies(X,X_78)
| ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78))))
| theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))) ),[0,1,1],$fot(implies(X,X_78))]]) ).
cnf(refute_0_35,plain,
( ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78))))
| theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_78),implies(X,X_78)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_38,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_37]) ).
cnf(refute_0_39,plain,
or(not(X),or(X_77,X_78)) = implies(X,or(X_77,X_78)),
inference(subst,[],[refute_0_38:[bind(Y,$fot(or(X_77,X_78)))]]) ).
cnf(refute_0_40,plain,
implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))]]) ).
cnf(refute_0_41,plain,
( implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) != implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))
| or(not(X),or(X_77,X_78)) != implies(X,or(X_77,X_78))
| implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),[1,0],$fot(implies(X,or(X_77,X_78)))]]) ).
cnf(refute_0_42,plain,
( or(not(X),or(X_77,X_78)) != implies(X,or(X_77,X_78))
| implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_77,X_78)),implies(X,or(X_77,X_78))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) != implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))
| ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),[0],$fot(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))))]]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_36,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ theorem(implies(X,or(X_77,X_78)))
| ~ theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(or(X_77,implies(X,X_78))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_77,implies(X,X_78)))),bind(Y,$fot(implies(X,or(X_77,X_78))))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(implies(X,or(X_77,X_78)))
| theorem(or(X_77,implies(X,X_78))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ theorem(implies(or(X_77,X_78),or(X_77,X_78)))
| theorem(or(X_77,implies(or(X_77,X_78),X_78))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(or(X_77,X_78)))]]) ).
cnf(refute_0_50,plain,
theorem(implies(or(X_88,X_88),X_88)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_88))]]) ).
cnf(refute_0_51,plain,
( ~ theorem(implies(or(X_88,X_88),X_88))
| ~ theorem(or(X_88,X_88))
| theorem(X_88) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_88)),bind(Y,$fot(or(X_88,X_88)))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(or(X_88,X_88))
| theorem(X_88) ),
inference(resolve,[$cnf( theorem(implies(or(X_88,X_88),X_88)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ theorem(or(implies(X_1478,X_1478),implies(X_1478,X_1478)))
| theorem(implies(X_1478,X_1478)) ),
inference(subst,[],[refute_0_52:[bind(X_88,$fot(implies(X_1478,X_1478)))]]) ).
cnf(refute_0_54,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_55,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_56,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
theorem(implies(X_1476,or(X_1475,X_1476))),
inference(subst,[],[refute_0_56:[bind(X_3,$fot(X_1476)),bind(X_4,$fot(X_1475))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(X_1476,or(X_1475,X_1476)))
| theorem(or(X_1475,implies(X_1476,X_1476))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_1476)),bind(X_77,$fot(X_1475)),bind(X_78,$fot(X_1476))]]) ).
cnf(refute_0_59,plain,
theorem(or(X_1475,implies(X_1476,X_1476))),
inference(resolve,[$cnf( theorem(implies(X_1476,or(X_1475,X_1476))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
theorem(or(implies(X_1478,X_1478),implies(X_1478,X_1478))),
inference(subst,[],[refute_0_59:[bind(X_1475,$fot(implies(X_1478,X_1478))),bind(X_1476,$fot(X_1478))]]) ).
cnf(refute_0_61,plain,
theorem(implies(X_1478,X_1478)),
inference(resolve,[$cnf( theorem(or(implies(X_1478,X_1478),implies(X_1478,X_1478))) )],[refute_0_60,refute_0_53]) ).
cnf(refute_0_62,plain,
theorem(implies(or(X_77,X_78),or(X_77,X_78))),
inference(subst,[],[refute_0_61:[bind(X_1478,$fot(or(X_77,X_78)))]]) ).
cnf(refute_0_63,plain,
theorem(or(X_77,implies(or(X_77,X_78),X_78))),
inference(resolve,[$cnf( theorem(implies(or(X_77,X_78),or(X_77,X_78))) )],[refute_0_62,refute_0_49]) ).
cnf(refute_0_64,plain,
theorem(or(not(X),implies(or(not(X),X_1554),X_1554))),
inference(subst,[],[refute_0_63:[bind(X_77,$fot(not(X))),bind(X_78,$fot(X_1554))]]) ).
cnf(refute_0_65,plain,
implies(X,X_1554) = or(not(X),X_1554),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_1554))]]) ).
cnf(refute_0_66,plain,
( implies(X,X_1554) != or(not(X),X_1554)
| or(not(X),X_1554) = implies(X,X_1554) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_1554))),bind(Y0,$fot(or(not(X),X_1554)))]]) ).
cnf(refute_0_67,plain,
or(not(X),X_1554) = implies(X,X_1554),
inference(resolve,[$cnf( $equal(implies(X,X_1554),or(not(X),X_1554)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( or(not(X),X_1554) != implies(X,X_1554)
| ~ theorem(or(not(X),implies(or(not(X),X_1554),X_1554)))
| theorem(or(not(X),implies(implies(X,X_1554),X_1554))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(or(not(X),X_1554),X_1554))) ),[0,1,0],$fot(implies(X,X_1554))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(or(not(X),implies(or(not(X),X_1554),X_1554)))
| theorem(or(not(X),implies(implies(X,X_1554),X_1554))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_1554),implies(X,X_1554)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
theorem(or(not(X),implies(implies(X,X_1554),X_1554))),
inference(resolve,[$cnf( theorem(or(not(X),implies(or(not(X),X_1554),X_1554))) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
or(not(X),implies(implies(X,X_1554),X_1554)) = implies(X,implies(implies(X,X_1554),X_1554)),
inference(subst,[],[refute_0_38:[bind(Y,$fot(implies(implies(X,X_1554),X_1554)))]]) ).
cnf(refute_0_72,plain,
( or(not(X),implies(implies(X,X_1554),X_1554)) != implies(X,implies(implies(X,X_1554),X_1554))
| ~ theorem(or(not(X),implies(implies(X,X_1554),X_1554)))
| theorem(implies(X,implies(implies(X,X_1554),X_1554))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(implies(X,X_1554),X_1554))) ),[0],$fot(implies(X,implies(implies(X,X_1554),X_1554)))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(or(not(X),implies(implies(X,X_1554),X_1554)))
| theorem(implies(X,implies(implies(X,X_1554),X_1554))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(implies(X,X_1554),X_1554)),implies(X,implies(implies(X,X_1554),X_1554))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(X,implies(implies(X,X_1554),X_1554))),
inference(resolve,[$cnf( theorem(or(not(X),implies(implies(X,X_1554),X_1554))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
theorem(implies(X_1555,implies(implies(X_1555,X_1556),X_1556))),
inference(subst,[],[refute_0_74:[bind(X,$fot(X_1555)),bind(X_1554,$fot(X_1556))]]) ).
cnf(refute_0_76,plain,
( ~ theorem(X_1555)
| theorem(implies(implies(X_1555,X_1556),X_1556)) ),
inference(resolve,[$cnf( theorem(implies(X_1555,implies(implies(X_1555,X_1556),X_1556))) )],[refute_0_75,refute_0_26]) ).
cnf(refute_0_77,plain,
( ~ theorem(implies(or(A,A),A))
| theorem(implies(implies(implies(or(A,A),A),X_28288),X_28288)) ),
inference(subst,[],[refute_0_76:[bind(X_1555,$fot(implies(or(A,A),A))),bind(X_1556,$fot(X_28288))]]) ).
cnf(refute_0_78,plain,
theorem(implies(implies(implies(or(A,A),A),X_28288),X_28288)),
inference(resolve,[$cnf( theorem(implies(or(A,A),A)) )],[refute_0_25,refute_0_77]) ).
cnf(refute_0_79,plain,
theorem(implies(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)),not(X_257))),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_28299)),bind(X_28288,$fot(not(X_257)))]]) ).
cnf(refute_0_80,plain,
theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))),
inference(resolve,[$cnf( theorem(implies(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)),not(X_257))) )],[refute_0_79,refute_0_23]) ).
cnf(refute_0_81,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_38:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_82,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_83,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_84,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_87,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_87]) ).
cnf(refute_0_89,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_90,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))) = and(implies(or(X_28299,X_28299),X_28299),X_257),
inference(subst,[],[refute_0_90:[bind(P,$fot(implies(or(X_28299,X_28299),X_28299))),bind(Q,$fot(X_257))]]) ).
cnf(refute_0_92,plain,
implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) = implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))),
introduced(tautology,[refl,[$fot(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))))]]) ).
cnf(refute_0_93,plain,
( implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) != implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))
| not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))) != and(implies(or(X_28299,X_28299),X_28299),X_257)
| implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) = implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))),implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))) ),[1,1],$fot(and(implies(or(X_28299,X_28299),X_28299),X_257))]]) ).
cnf(refute_0_94,plain,
( not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))) != and(implies(or(X_28299,X_28299),X_28299),X_257)
| implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) = implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257)) ),
inference(resolve,[$cnf( $equal(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))),implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) = implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257)),
inference(resolve,[$cnf( $equal(not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))),and(implies(or(X_28299,X_28299),X_28299),X_257)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))) != implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257))
| ~ theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))))
| theorem(implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))) ),[0],$fot(implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257)))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))))
| theorem(implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257))) ),
inference(resolve,[$cnf( $equal(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257)))),implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
theorem(implies(X_257,and(implies(or(X_28299,X_28299),X_28299),X_257))),
inference(resolve,[$cnf( theorem(implies(X_257,not(implies(implies(or(X_28299,X_28299),X_28299),not(X_257))))) )],[refute_0_80,refute_0_97]) ).
cnf(refute_0_99,plain,
theorem(implies(implies(X_28330,or(X_28330,X_28330)),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))))),
inference(subst,[],[refute_0_98:[bind(X_257,$fot(implies(X_28330,or(X_28330,X_28330)))),bind(X_28299,$fot(X_28330))]]) ).
cnf(refute_0_100,plain,
equivalent(or(X_28330,X_28330),X_28330) = and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))),
inference(subst,[],[equivalent_defn:[bind(P,$fot(or(X_28330,X_28330))),bind(Q,$fot(X_28330))]]) ).
cnf(refute_0_101,plain,
( equivalent(or(X_28330,X_28330),X_28330) != and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330)))
| and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))) = equivalent(or(X_28330,X_28330),X_28330) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(equivalent(or(X_28330,X_28330),X_28330))),bind(Y0,$fot(and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330)))))]]) ).
cnf(refute_0_102,plain,
and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))) = equivalent(or(X_28330,X_28330),X_28330),
inference(resolve,[$cnf( $equal(equivalent(or(X_28330,X_28330),X_28330),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))) != equivalent(or(X_28330,X_28330),X_28330)
| ~ theorem(implies(implies(X_28330,or(X_28330,X_28330)),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330)))))
| theorem(implies(implies(X_28330,or(X_28330,X_28330)),equivalent(or(X_28330,X_28330),X_28330))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_28330,or(X_28330,X_28330)),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))))) ),[0,1],$fot(equivalent(or(X_28330,X_28330),X_28330))]]) ).
cnf(refute_0_104,plain,
( ~ theorem(implies(implies(X_28330,or(X_28330,X_28330)),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330)))))
| theorem(implies(implies(X_28330,or(X_28330,X_28330)),equivalent(or(X_28330,X_28330),X_28330))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))),equivalent(or(X_28330,X_28330),X_28330)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
theorem(implies(implies(X_28330,or(X_28330,X_28330)),equivalent(or(X_28330,X_28330),X_28330))),
inference(resolve,[$cnf( theorem(implies(implies(X_28330,or(X_28330,X_28330)),and(implies(or(X_28330,X_28330),X_28330),implies(X_28330,or(X_28330,X_28330))))) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
theorem(implies(implies(X_28331,or(X_28331,X_28331)),equivalent(or(X_28331,X_28331),X_28331))),
inference(subst,[],[refute_0_105:[bind(X_28330,$fot(X_28331))]]) ).
cnf(refute_0_107,plain,
( ~ theorem(implies(X_28331,or(X_28331,X_28331)))
| theorem(equivalent(or(X_28331,X_28331),X_28331)) ),
inference(resolve,[$cnf( theorem(implies(implies(X_28331,or(X_28331,X_28331)),equivalent(or(X_28331,X_28331),X_28331))) )],[refute_0_106,refute_0_0]) ).
cnf(refute_0_108,plain,
theorem(implies(X_28331,or(X_28331,X_28331))),
inference(subst,[],[refute_0_56:[bind(X_3,$fot(X_28331)),bind(X_4,$fot(X_28331))]]) ).
cnf(refute_0_109,plain,
theorem(equivalent(or(X_28331,X_28331),X_28331)),
inference(resolve,[$cnf( theorem(implies(X_28331,or(X_28331,X_28331))) )],[refute_0_108,refute_0_107]) ).
cnf(refute_0_110,plain,
theorem(equivalent(or(not(X),not(X)),not(X))),
inference(subst,[],[refute_0_109:[bind(X_28331,$fot(not(X)))]]) ).
cnf(refute_0_111,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_112,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_113,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ theorem(equivalent(or(not(X),not(X)),not(X)))
| theorem(equivalent(implies(X,not(X)),not(X))) ),
introduced(tautology,[equality,[$cnf( theorem(equivalent(or(not(X),not(X)),not(X))) ),[0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_115,plain,
( ~ theorem(equivalent(or(not(X),not(X)),not(X)))
| theorem(equivalent(implies(X,not(X)),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
theorem(equivalent(implies(X,not(X)),not(X))),
inference(resolve,[$cnf( theorem(equivalent(or(not(X),not(X)),not(X))) )],[refute_0_110,refute_0_115]) ).
cnf(refute_0_117,plain,
theorem(equivalent(implies(p,not(p)),not(p))),
inference(subst,[],[refute_0_116:[bind(X,$fot(p))]]) ).
cnf(refute_0_118,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(implies(p,not(p)),not(p))) )],[refute_0_117,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL311-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 05:39:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 82.45/82.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.45/82.61
% 82.45/82.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 82.45/82.63
%------------------------------------------------------------------------------