TSTP Solution File: LCL180-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL180-3 : 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 12:50:16 EDT 2022
% Result : Unsatisfiable 187.52s 187.75s
% Output : CNFRefutation 187.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 14
% Syntax : Number of clauses : 101 ( 57 unt; 0 nHn; 43 RR)
% Number of literals : 157 ( 22 equ; 57 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 190 ( 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(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
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(prove_this,negated_conjecture,
~ theorem(implies(not(not(p)),p)) ).
cnf(refute_0_0,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,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_108431,not(not(not(X_108431)))))
| theorem(or(not(not(not(X_108431))),X_108431)) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_108431)),bind(X_8,$fot(not(not(not(X_108431)))))]]) ).
cnf(refute_0_6,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_6]) ).
cnf(refute_0_8,plain,
theorem(implies(or(X_64,X_64),X_64)),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_64))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(implies(or(X_64,X_64),X_64))
| ~ theorem(or(X_64,X_64))
| theorem(X_64) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_64)),bind(Y,$fot(or(X_64,X_64)))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(X_64,X_64))
| theorem(X_64) ),
inference(resolve,[$cnf( theorem(implies(or(X_64,X_64),X_64)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ theorem(or(or(X_1155,not(X_1155)),or(X_1155,not(X_1155))))
| theorem(or(X_1155,not(X_1155))) ),
inference(subst,[],[refute_0_10:[bind(X_64,$fot(or(X_1155,not(X_1155))))]]) ).
cnf(refute_0_12,plain,
( ~ axiom(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25))))
| theorem(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))))]]) ).
cnf(refute_0_13,plain,
axiom(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_23)),bind(B,$fot(X_24)),bind(C,$fot(X_25))]]) ).
cnf(refute_0_14,plain,
theorem(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))),
inference(resolve,[$cnf( axiom(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( ~ theorem(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25))))
| ~ theorem(or(X_23,or(X_24,X_25)))
| theorem(or(X_24,or(X_23,X_25))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_24,or(X_23,X_25)))),bind(Y,$fot(or(X_23,or(X_24,X_25))))]]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(X_23,or(X_24,X_25)))
| theorem(or(X_24,or(X_23,X_25))) ),
inference(resolve,[$cnf( theorem(implies(or(X_23,or(X_24,X_25)),or(X_24,or(X_23,X_25)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(X_943,or(X_944,not(X_943))))
| theorem(or(X_944,or(X_943,not(X_943)))) ),
inference(subst,[],[refute_0_16:[bind(X_23,$fot(X_943)),bind(X_24,$fot(X_944)),bind(X_25,$fot(not(X_943)))]]) ).
cnf(refute_0_18,plain,
( ~ theorem(or(or(X_942,not(X_941)),X_941))
| theorem(or(X_941,or(X_942,not(X_941)))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(or(X_942,not(X_941)))),bind(X_8,$fot(X_941))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(or(or(X_940,not(X_938)),X_938),or(or(X_940,not(X_938)),X_938)))
| theorem(or(or(X_940,not(X_938)),X_938)) ),
inference(subst,[],[refute_0_10:[bind(X_64,$fot(or(or(X_940,not(X_938)),X_938)))]]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(or(X_831,not(X_829)),or(X_830,X_829)))
| theorem(or(X_830,or(or(X_831,not(X_829)),X_829))) ),
inference(subst,[],[refute_0_16:[bind(X_23,$fot(or(X_831,not(X_829)))),bind(X_24,$fot(X_830)),bind(X_25,$fot(X_829))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(or(or(X_827,X_826),or(X_828,not(X_826))))
| theorem(or(or(X_828,not(X_826)),or(X_827,X_826))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(or(X_827,X_826))),bind(X_8,$fot(or(X_828,not(X_826))))]]) ).
cnf(refute_0_22,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_23,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_24,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
theorem(implies(X_65,or(X_4,X_65))),
inference(subst,[],[refute_0_24:[bind(X_3,$fot(X_65))]]) ).
cnf(refute_0_26,plain,
( ~ theorem(X_65)
| ~ theorem(implies(X_65,or(X_4,X_65)))
| theorem(or(X_4,X_65)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_65))),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(X_65)
| theorem(or(X_4,X_65)) ),
inference(resolve,[$cnf( theorem(implies(X_65,or(X_4,X_65))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(or(X_281,X_280),not(X_280)))
| theorem(or(X_4,or(or(X_281,X_280),not(X_280)))) ),
inference(subst,[],[refute_0_27:[bind(X_65,$fot(or(or(X_281,X_280),not(X_280))))]]) ).
cnf(refute_0_29,plain,
theorem(implies(X_268,or(X_4,X_268))),
inference(subst,[],[refute_0_24:[bind(X_3,$fot(X_268))]]) ).
cnf(refute_0_30,plain,
theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))),
inference(subst,[],[refute_0_2:[bind(X_7,$fot(not(X_11)))]]) ).
cnf(refute_0_31,plain,
implies(X_11,X_8) = or(not(X_11),X_8),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_32,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_33,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_34,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(X_11,X_8) != or(not(X_11),X_8)
| or(not(X_11),X_8) = implies(X_11,X_8) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(implies(X_11,X_8))),bind(Y0,$fot(or(not(X_11),X_8)))]]) ).
cnf(refute_0_36,plain,
or(not(X_11),X_8) = implies(X_11,X_8),
inference(resolve,[$cnf( $equal(implies(X_11,X_8),or(not(X_11),X_8)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
( or(not(X_11),X_8) != implies(X_11,X_8)
| ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) ),[0,0],$fot(implies(X_11,X_8))]]) ).
cnf(refute_0_38,plain,
( ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_8),implies(X_11,X_8)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(X_11,X_8))
| ~ theorem(implies(implies(X_11,X_8),or(X_8,not(X_11))))
| theorem(or(X_8,not(X_11))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,not(X_11)))),bind(Y,$fot(implies(X_11,X_8)))]]) ).
cnf(refute_0_41,plain,
( ~ theorem(implies(X_11,X_8))
| theorem(or(X_8,not(X_11))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X_268,or(X_4,X_268)))
| theorem(or(or(X_4,X_268),not(X_268))) ),
inference(subst,[],[refute_0_41:[bind(X_11,$fot(X_268)),bind(X_8,$fot(or(X_4,X_268)))]]) ).
cnf(refute_0_43,plain,
theorem(or(or(X_4,X_268),not(X_268))),
inference(resolve,[$cnf( theorem(implies(X_268,or(X_4,X_268))) )],[refute_0_29,refute_0_42]) ).
cnf(refute_0_44,plain,
theorem(or(or(X_281,X_280),not(X_280))),
inference(subst,[],[refute_0_43:[bind(X_268,$fot(X_280)),bind(X_4,$fot(X_281))]]) ).
cnf(refute_0_45,plain,
theorem(or(X_4,or(or(X_281,X_280),not(X_280)))),
inference(resolve,[$cnf( theorem(or(or(X_281,X_280),not(X_280))) )],[refute_0_44,refute_0_28]) ).
cnf(refute_0_46,plain,
theorem(or(X_806,or(or(X_281,X_280),not(X_280)))),
inference(subst,[],[refute_0_45:[bind(X_4,$fot(X_806))]]) ).
cnf(refute_0_47,plain,
( ~ theorem(or(X_806,or(or(X_281,X_280),not(X_280))))
| theorem(or(or(X_281,X_280),or(X_806,not(X_280)))) ),
inference(subst,[],[refute_0_16:[bind(X_23,$fot(X_806)),bind(X_24,$fot(or(X_281,X_280))),bind(X_25,$fot(not(X_280)))]]) ).
cnf(refute_0_48,plain,
theorem(or(or(X_281,X_280),or(X_806,not(X_280)))),
inference(resolve,[$cnf( theorem(or(X_806,or(or(X_281,X_280),not(X_280)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
theorem(or(or(X_827,X_826),or(X_828,not(X_826)))),
inference(subst,[],[refute_0_48:[bind(X_280,$fot(X_826)),bind(X_281,$fot(X_827)),bind(X_806,$fot(X_828))]]) ).
cnf(refute_0_50,plain,
theorem(or(or(X_828,not(X_826)),or(X_827,X_826))),
inference(resolve,[$cnf( theorem(or(or(X_827,X_826),or(X_828,not(X_826)))) )],[refute_0_49,refute_0_21]) ).
cnf(refute_0_51,plain,
theorem(or(or(X_831,not(X_829)),or(X_830,X_829))),
inference(subst,[],[refute_0_50:[bind(X_826,$fot(X_829)),bind(X_827,$fot(X_830)),bind(X_828,$fot(X_831))]]) ).
cnf(refute_0_52,plain,
theorem(or(X_830,or(or(X_831,not(X_829)),X_829))),
inference(resolve,[$cnf( theorem(or(or(X_831,not(X_829)),or(X_830,X_829))) )],[refute_0_51,refute_0_20]) ).
cnf(refute_0_53,plain,
theorem(or(or(or(X_940,not(X_938)),X_938),or(or(X_940,not(X_938)),X_938))),
inference(subst,[],[refute_0_52:[bind(X_829,$fot(X_938)),bind(X_830,$fot(or(or(X_940,not(X_938)),X_938))),bind(X_831,$fot(X_940))]]) ).
cnf(refute_0_54,plain,
theorem(or(or(X_940,not(X_938)),X_938)),
inference(resolve,[$cnf( theorem(or(or(or(X_940,not(X_938)),X_938),or(or(X_940,not(X_938)),X_938))) )],[refute_0_53,refute_0_19]) ).
cnf(refute_0_55,plain,
theorem(or(or(X_942,not(X_941)),X_941)),
inference(subst,[],[refute_0_54:[bind(X_938,$fot(X_941)),bind(X_940,$fot(X_942))]]) ).
cnf(refute_0_56,plain,
theorem(or(X_941,or(X_942,not(X_941)))),
inference(resolve,[$cnf( theorem(or(or(X_942,not(X_941)),X_941)) )],[refute_0_55,refute_0_18]) ).
cnf(refute_0_57,plain,
theorem(or(X_943,or(X_944,not(X_943)))),
inference(subst,[],[refute_0_56:[bind(X_941,$fot(X_943)),bind(X_942,$fot(X_944))]]) ).
cnf(refute_0_58,plain,
theorem(or(X_944,or(X_943,not(X_943)))),
inference(resolve,[$cnf( theorem(or(X_943,or(X_944,not(X_943)))) )],[refute_0_57,refute_0_17]) ).
cnf(refute_0_59,plain,
theorem(or(or(X_1155,not(X_1155)),or(X_1155,not(X_1155)))),
inference(subst,[],[refute_0_58:[bind(X_943,$fot(X_1155)),bind(X_944,$fot(or(X_1155,not(X_1155))))]]) ).
cnf(refute_0_60,plain,
theorem(or(X_1155,not(X_1155))),
inference(resolve,[$cnf( theorem(or(or(X_1155,not(X_1155)),or(X_1155,not(X_1155)))) )],[refute_0_59,refute_0_11]) ).
cnf(refute_0_61,plain,
theorem(or(X_108430,not(X_108430))),
inference(subst,[],[refute_0_60:[bind(X_1155,$fot(X_108430))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(implies(or(X_5271,X_5270),or(X_5271,not(not(X_5270)))))
| ~ theorem(or(X_5271,X_5270))
| theorem(or(X_5271,not(not(X_5270)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_5271,not(not(X_5270))))),bind(Y,$fot(or(X_5271,X_5270)))]]) ).
cnf(refute_0_63,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_60:[bind(X_1155,$fot(not(X)))]]) ).
cnf(refute_0_64,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_65,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_66,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
theorem(implies(X_5267,not(not(X_5267)))),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_5267))]]) ).
cnf(refute_0_71,plain,
( ~ axiom(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27))))
| theorem(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))))]]) ).
cnf(refute_0_72,plain,
axiom(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_26)),bind(B,$fot(X_27)),bind(C,$fot(X_28))]]) ).
cnf(refute_0_73,plain,
theorem(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))),
inference(resolve,[$cnf( axiom(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))) )],[refute_0_72,refute_0_71]) ).
cnf(refute_0_74,plain,
( ~ theorem(implies(X_26,X_27))
| ~ theorem(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27))))
| theorem(implies(or(X_28,X_26),or(X_28,X_27))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_28,X_26),or(X_28,X_27)))),bind(Y,$fot(implies(X_26,X_27)))]]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(X_26,X_27))
| theorem(implies(or(X_28,X_26),or(X_28,X_27))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_26,X_27),implies(or(X_28,X_26),or(X_28,X_27)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ theorem(implies(X_5267,not(not(X_5267))))
| theorem(implies(or(X_5269,X_5267),or(X_5269,not(not(X_5267))))) ),
inference(subst,[],[refute_0_75:[bind(X_26,$fot(X_5267)),bind(X_27,$fot(not(not(X_5267)))),bind(X_28,$fot(X_5269))]]) ).
cnf(refute_0_77,plain,
theorem(implies(or(X_5269,X_5267),or(X_5269,not(not(X_5267))))),
inference(resolve,[$cnf( theorem(implies(X_5267,not(not(X_5267)))) )],[refute_0_70,refute_0_76]) ).
cnf(refute_0_78,plain,
theorem(implies(or(X_5271,X_5270),or(X_5271,not(not(X_5270))))),
inference(subst,[],[refute_0_77:[bind(X_5267,$fot(X_5270)),bind(X_5269,$fot(X_5271))]]) ).
cnf(refute_0_79,plain,
( ~ theorem(or(X_5271,X_5270))
| theorem(or(X_5271,not(not(X_5270)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_5271,X_5270),or(X_5271,not(not(X_5270))))) )],[refute_0_78,refute_0_62]) ).
cnf(refute_0_80,plain,
( ~ theorem(or(X_108430,not(X_108430)))
| theorem(or(X_108430,not(not(not(X_108430))))) ),
inference(subst,[],[refute_0_79:[bind(X_5270,$fot(not(X_108430))),bind(X_5271,$fot(X_108430))]]) ).
cnf(refute_0_81,plain,
theorem(or(X_108430,not(not(not(X_108430))))),
inference(resolve,[$cnf( theorem(or(X_108430,not(X_108430))) )],[refute_0_61,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(or(X_108431,not(not(not(X_108431))))),
inference(subst,[],[refute_0_81:[bind(X_108430,$fot(X_108431))]]) ).
cnf(refute_0_83,plain,
theorem(or(not(not(not(X_108431))),X_108431)),
inference(resolve,[$cnf( theorem(or(X_108431,not(not(not(X_108431))))) )],[refute_0_82,refute_0_5]) ).
cnf(refute_0_84,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_85,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_84]) ).
cnf(refute_0_86,plain,
or(not(not(not(X_108431))),X_108431) = implies(not(not(X_108431)),X_108431),
inference(subst,[],[refute_0_85:[bind(X,$fot(not(not(X_108431)))),bind(Y,$fot(X_108431))]]) ).
cnf(refute_0_87,plain,
( or(not(not(not(X_108431))),X_108431) != implies(not(not(X_108431)),X_108431)
| ~ theorem(or(not(not(not(X_108431))),X_108431))
| theorem(implies(not(not(X_108431)),X_108431)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(not(X_108431))),X_108431)) ),[0],$fot(implies(not(not(X_108431)),X_108431))]]) ).
cnf(refute_0_88,plain,
( ~ theorem(or(not(not(not(X_108431))),X_108431))
| theorem(implies(not(not(X_108431)),X_108431)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X_108431))),X_108431),implies(not(not(X_108431)),X_108431)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
theorem(implies(not(not(X_108431)),X_108431)),
inference(resolve,[$cnf( theorem(or(not(not(not(X_108431))),X_108431)) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
theorem(implies(not(not(p)),p)),
inference(subst,[],[refute_0_89:[bind(X_108431,$fot(p))]]) ).
cnf(refute_0_91,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(not(p)),p)) )],[refute_0_90,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL180-3 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 00:21:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 187.52/187.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.52/187.75
% 187.52/187.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 187.52/187.75
%------------------------------------------------------------------------------