TSTP Solution File: LCL077-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL077-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:49:15 EDT 2022
% Result : Unsatisfiable 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 61 ( 35 unt; 0 nHn; 25 RR)
% Number of literals : 94 ( 0 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 126 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(prove_cn_39,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X_285,X_285),X_284))
| ~ is_a_theorem(implies(implies(implies(X_285,X_285),X_284),X_284))
| is_a_theorem(X_284) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_285,X_285),X_284))),bind(Y,$fot(X_284))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_7,implies(Y,X_7))),
inference(subst,[],[cn_18:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_7)
| ~ is_a_theorem(implies(X_7,implies(Y,X_7)))
| is_a_theorem(implies(Y,X_7)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_7)),bind(Y,$fot(implies(Y,X_7)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_7)
| is_a_theorem(implies(Y,X_7)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_7,implies(Y,X_7))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_97,X_97))
| is_a_theorem(implies(Y,implies(X_97,X_97))) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(implies(X_97,X_97)))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))
| is_a_theorem(implies(Y,implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61))))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| ~ is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z))))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,implies(Y,Z)))),bind(Y,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) )],[cn_35,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(X_59,X_58),implies(X_59,X_59)))
| is_a_theorem(implies(implies(implies(X_59,X_58),X_59),implies(implies(X_59,X_58),X_59))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(implies(X_59,X_58))),bind(Y,$fot(X_59)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(X_55,implies(X_54,X_55))),
inference(subst,[],[cn_18:[bind(X,$fot(X_55)),bind(Y,$fot(X_54))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(X_55,implies(X_54,X_55)))
| is_a_theorem(implies(implies(X_55,X_54),implies(X_55,X_55))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_55)),bind(Y,$fot(X_54)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(X_55,X_54),implies(X_55,X_55))),
inference(resolve,[$cnf( is_a_theorem(implies(X_55,implies(X_54,X_55))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(X_59,X_58),implies(X_59,X_59))),
inference(subst,[],[refute_0_11:[bind(X_54,$fot(X_58)),bind(X_55,$fot(X_59))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(X_59,X_58),X_59),implies(implies(X_59,X_58),X_59))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_59,X_58),implies(X_59,X_59))) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61))),
inference(subst,[],[refute_0_13:[bind(X_58,$fot(X_60)),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(Y,implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61))) )],[refute_0_14,refute_0_5]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_96,implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_96))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(X_59,X_58))
| ~ is_a_theorem(implies(implies(X_59,X_58),implies(X_59,X_59)))
| is_a_theorem(implies(X_59,X_59)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_59,X_58))),bind(Y,$fot(implies(X_59,X_59)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_59,X_58))
| is_a_theorem(implies(X_59,X_59)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_59,X_58),implies(X_59,X_59))) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(X_96,implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61))))
| is_a_theorem(implies(X_96,X_96)) ),
inference(subst,[],[refute_0_18:[bind(X_58,$fot(implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))),bind(X_59,$fot(X_96))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_96,X_96)),
inference(resolve,[$cnf( is_a_theorem(implies(X_96,implies(implies(implies(X_61,X_60),X_61),implies(implies(X_61,X_60),X_61)))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_97,X_97)),
inference(subst,[],[refute_0_20:[bind(X_96,$fot(X_97))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(Y,implies(X_97,X_97))),
inference(resolve,[$cnf( is_a_theorem(implies(X_97,X_97)) )],[refute_0_21,refute_0_4]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(X_97,X_97),X_283),implies(X_97,X_97))),
inference(subst,[],[refute_0_22:[bind(Y,$fot(implies(implies(X_97,X_97),X_283)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(X_107,X_108),X_107))
| ~ is_a_theorem(implies(implies(implies(X_107,X_108),X_107),implies(implies(X_107,X_108),X_108)))
| is_a_theorem(implies(implies(X_107,X_108),X_108)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_107,X_108),X_107))),bind(Y,$fot(implies(implies(X_107,X_108),X_108)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(Y,Z),implies(Y,Z)))
| is_a_theorem(implies(implies(implies(Y,Z),Y),implies(implies(Y,Z),Z))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(implies(Y,Z)))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(Y,Z),implies(Y,Z))),
inference(subst,[],[refute_0_20:[bind(X_96,$fot(implies(Y,Z)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(Y,Z),Y),implies(implies(Y,Z),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(Y,Z),implies(Y,Z))) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(X_107,X_108),X_107),implies(implies(X_107,X_108),X_108))),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_107)),bind(Z,$fot(X_108))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_107,X_108),X_107))
| is_a_theorem(implies(implies(X_107,X_108),X_108)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_107,X_108),X_107),implies(implies(X_107,X_108),X_108))) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(X_97,X_97),X_283),implies(X_97,X_97)))
| is_a_theorem(implies(implies(implies(X_97,X_97),X_283),X_283)) ),
inference(subst,[],[refute_0_29:[bind(X_107,$fot(implies(X_97,X_97))),bind(X_108,$fot(X_283))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_97,X_97),X_283),X_283)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_97,X_97),X_283),implies(X_97,X_97))) )],[refute_0_23,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(X_285,X_285),X_284),X_284)),
inference(subst,[],[refute_0_31:[bind(X_283,$fot(X_284)),bind(X_97,$fot(X_285))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_285,X_285),X_284))
| is_a_theorem(X_284) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_285,X_285),X_284),X_284)) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(not(not(X_682)),not(not(X_682))),implies(not(not(X_682)),X_682)))
| is_a_theorem(implies(not(not(X_682)),X_682)) ),
inference(subst,[],[refute_0_33:[bind(X_284,$fot(implies(not(not(X_682)),X_682))),bind(X_285,$fot(not(not(X_682))))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(not(not(X_656)),implies(X_657,X_656)))
| is_a_theorem(implies(implies(not(not(X_656)),X_657),implies(not(not(X_656)),X_656))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(not(not(X_656)))),bind(Y,$fot(X_657)),bind(Z,$fot(X_656))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(X_70,implies(not(X_68),not(X_69))))
| ~ is_a_theorem(implies(implies(X_70,implies(not(X_68),not(X_69))),implies(X_70,implies(X_69,X_68))))
| is_a_theorem(implies(X_70,implies(X_69,X_68))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_70,implies(not(X_68),not(X_69))))),bind(Y,$fot(implies(X_70,implies(X_69,X_68))))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_9)),bind(X_7,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(X_53,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(subst,[],[refute_0_38:[bind(X_9,$fot(X_53))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(X_53,implies(implies(not(X),not(Y)),implies(Y,X))))
| is_a_theorem(implies(implies(X_53,implies(not(X),not(Y))),implies(X_53,implies(Y,X)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_53)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(X_53,implies(not(X),not(Y))),implies(X_53,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_53,implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_70,implies(not(X_68),not(X_69))),implies(X_70,implies(X_69,X_68)))),
inference(subst,[],[refute_0_41:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(X_53,$fot(X_70))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(X_70,implies(not(X_68),not(X_69))))
| is_a_theorem(implies(X_70,implies(X_69,X_68))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_70,implies(not(X_68),not(X_69))),implies(X_70,implies(X_69,X_68)))) )],[refute_0_42,refute_0_36]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(not(not(X_68)),implies(not(X_68),not(X_69))))
| is_a_theorem(implies(not(not(X_68)),implies(X_69,X_68))) ),
inference(subst,[],[refute_0_43:[bind(X_70,$fot(not(not(X_68))))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(not(X_646),implies(not(X_645),not(X_646)))),
inference(subst,[],[cn_18:[bind(X,$fot(not(X_646))),bind(Y,$fot(not(X_645)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(not(X_646),implies(not(X_645),not(X_646))))
| is_a_theorem(implies(not(X_646),implies(X_646,X_645))) ),
inference(subst,[],[refute_0_43:[bind(X_68,$fot(X_645)),bind(X_69,$fot(X_646)),bind(X_70,$fot(not(X_646)))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(not(X_646),implies(X_646,X_645))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_646),implies(not(X_645),not(X_646)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(not(not(X_68)),implies(not(X_68),not(X_69)))),
inference(subst,[],[refute_0_47:[bind(X_645,$fot(not(X_69))),bind(X_646,$fot(not(X_68)))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(not(not(X_68)),implies(X_69,X_68))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_68)),implies(not(X_68),not(X_69)))) )],[refute_0_48,refute_0_44]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(not(not(X_656)),implies(X_657,X_656))),
inference(subst,[],[refute_0_49:[bind(X_68,$fot(X_656)),bind(X_69,$fot(X_657))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(not(not(X_656)),X_657),implies(not(not(X_656)),X_656))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_656)),implies(X_657,X_656))) )],[refute_0_50,refute_0_35]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(not(not(X_682)),not(not(X_682))),implies(not(not(X_682)),X_682))),
inference(subst,[],[refute_0_51:[bind(X_656,$fot(X_682)),bind(X_657,$fot(not(not(X_682))))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(not(not(X_682)),X_682)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_682)),not(not(X_682))),implies(not(not(X_682)),X_682))) )],[refute_0_52,refute_0_34]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(not(not(a)),a)),
inference(subst,[],[refute_0_53:[bind(X_682,$fot(a))]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(not(not(a)),a)) )],[refute_0_54,prove_cn_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL077-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jul 3 12:39:09 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51
% 0.18/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.52
%------------------------------------------------------------------------------