TSTP Solution File: LCL076-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL076-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:49:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of clauses : 57 ( 31 unt; 0 nHn; 25 RR)
% Number of literals : 91 ( 0 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 111 ( 9 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(transitivity,axiom,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X1,X3)) ) ).
cnf(prove_cn_40,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(not(not(Y))),not(Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(implies(X_23,implies(Y,X_23))),
inference(subst,[],[cn_18:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_23,implies(Y,X_23)))
| ~ is_a_theorem(implies(implies(Y,X_23),X_25))
| is_a_theorem(implies(X_23,X_25)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(X_23)),bind(X2,$fot(implies(Y,X_23))),bind(X3,$fot(X_25))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(Y,X_23),X_25))
| is_a_theorem(implies(X_23,X_25)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_23,implies(Y,X_23))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(X_368,X_368))),not(not(X_369))),X_369))
| is_a_theorem(implies(not(not(X_369)),X_369)) ),
inference(subst,[],[refute_0_5:[bind(Y,$fot(not(not(implies(X_368,X_368))))),bind(X_23,$fot(not(not(X_369)))),bind(X_25,$fot(X_369))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(X_129)
| ~ is_a_theorem(implies(X_129,implies(implies(not(X_130),not(X_129)),X_130)))
| is_a_theorem(implies(implies(not(X_130),not(X_129)),X_130)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_129)),bind(Y,$fot(implies(implies(not(X_130),not(X_129)),X_130)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_128),not(X_127)),X_127),implies(implies(not(X_128),not(X_127)),X_128)))
| is_a_theorem(implies(X_127,implies(implies(not(X_128),not(X_127)),X_128))) ),
inference(subst,[],[refute_0_5:[bind(Y,$fot(implies(not(X_128),not(X_127)))),bind(X_23,$fot(X_127)),bind(X_25,$fot(implies(implies(not(X_128),not(X_127)),X_128)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(not(X_90),not(X_89)),implies(X_89,X_90))),
inference(subst,[],[cn_49:[bind(X,$fot(X_90)),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| ~ is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z))))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,implies(Y,Z)))),bind(Y,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) )],[cn_35,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(not(X_90),not(X_89)),implies(X_89,X_90)))
| is_a_theorem(implies(implies(implies(not(X_90),not(X_89)),X_89),implies(implies(not(X_90),not(X_89)),X_90))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(implies(not(X_90),not(X_89)))),bind(Y,$fot(X_89)),bind(Z,$fot(X_90))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(not(X_90),not(X_89)),X_89),implies(implies(not(X_90),not(X_89)),X_90))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_90),not(X_89)),implies(X_89,X_90))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(not(X_128),not(X_127)),X_127),implies(implies(not(X_128),not(X_127)),X_128))),
inference(subst,[],[refute_0_13:[bind(X_89,$fot(X_127)),bind(X_90,$fot(X_128))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(X_127,implies(implies(not(X_128),not(X_127)),X_128))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_128),not(X_127)),X_127),implies(implies(not(X_128),not(X_127)),X_128))) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_129,implies(implies(not(X_130),not(X_129)),X_130))),
inference(subst,[],[refute_0_15:[bind(X_127,$fot(X_129)),bind(X_128,$fot(X_130))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_129)
| is_a_theorem(implies(implies(not(X_130),not(X_129)),X_130)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_129,implies(implies(not(X_130),not(X_129)),X_130))) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_254,X_254))
| is_a_theorem(implies(implies(not(X_130),not(implies(X_254,X_254))),X_130)) ),
inference(subst,[],[refute_0_17:[bind(X_129,$fot(implies(X_254,X_254)))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(X_97,X_98),X_97),implies(implies(X_97,X_98),X_98)))
| is_a_theorem(implies(implies(implies(implies(X_97,X_98),X_97),implies(X_97,X_98)),implies(implies(implies(X_97,X_98),X_97),X_98))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(implies(implies(X_97,X_98),X_97))),bind(Y,$fot(implies(X_97,X_98))),bind(Z,$fot(X_98))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(X_95,X_96),implies(X_95,X_96)))
| is_a_theorem(implies(implies(implies(X_95,X_96),X_95),implies(implies(X_95,X_96),X_96))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(implies(X_95,X_96))),bind(Y,$fot(X_95)),bind(Z,$fot(X_96))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(X_93,implies(X_94,X_94)))
| is_a_theorem(implies(implies(X_93,X_94),implies(X_93,X_94))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_93)),bind(Y,$fot(X_94)),bind(Z,$fot(X_94))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(X_92,X_91),implies(X_92,X_92)))
| is_a_theorem(implies(X_91,implies(X_92,X_92))) ),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_92)),bind(X_23,$fot(X_91)),bind(X_25,$fot(implies(X_92,X_92)))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_90,implies(X_89,X_90))),
inference(subst,[],[cn_18:[bind(X,$fot(X_90)),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(X_90,implies(X_89,X_90)))
| is_a_theorem(implies(implies(X_90,X_89),implies(X_90,X_90))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_90)),bind(Y,$fot(X_89)),bind(Z,$fot(X_90))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_90,X_89),implies(X_90,X_90))),
inference(resolve,[$cnf( is_a_theorem(implies(X_90,implies(X_89,X_90))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_92,X_91),implies(X_92,X_92))),
inference(subst,[],[refute_0_25:[bind(X_89,$fot(X_91)),bind(X_90,$fot(X_92))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(X_91,implies(X_92,X_92))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_92,X_91),implies(X_92,X_92))) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(X_93,implies(X_94,X_94))),
inference(subst,[],[refute_0_27:[bind(X_91,$fot(X_93)),bind(X_92,$fot(X_94))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(implies(X_93,X_94),implies(X_93,X_94))),
inference(resolve,[$cnf( is_a_theorem(implies(X_93,implies(X_94,X_94))) )],[refute_0_28,refute_0_21]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(X_95,X_96),implies(X_95,X_96))),
inference(subst,[],[refute_0_29:[bind(X_93,$fot(X_95)),bind(X_94,$fot(X_96))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_95,X_96),X_95),implies(implies(X_95,X_96),X_96))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_95,X_96),implies(X_95,X_96))) )],[refute_0_30,refute_0_20]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(X_97,X_98),X_97),implies(implies(X_97,X_98),X_98))),
inference(subst,[],[refute_0_31:[bind(X_95,$fot(X_97)),bind(X_96,$fot(X_98))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(implies(X_97,X_98),X_97),implies(X_97,X_98)),implies(implies(implies(X_97,X_98),X_97),X_98))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_97,X_98),X_97),implies(implies(X_97,X_98),X_98))) )],[refute_0_32,refute_0_19]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(X_93)
| ~ is_a_theorem(implies(X_93,implies(X_94,X_94)))
| is_a_theorem(implies(X_94,X_94)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_93)),bind(Y,$fot(implies(X_94,X_94)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(X_93)
| is_a_theorem(implies(X_94,X_94)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_93,implies(X_94,X_94))) )],[refute_0_28,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_97,X_98),X_97),implies(X_97,X_98)),implies(implies(implies(X_97,X_98),X_97),X_98)))
| is_a_theorem(implies(X_253,X_253)) ),
inference(subst,[],[refute_0_35:[bind(X_93,$fot(implies(implies(implies(implies(X_97,X_98),X_97),implies(X_97,X_98)),implies(implies(implies(X_97,X_98),X_97),X_98)))),bind(X_94,$fot(X_253))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_253,X_253)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_97,X_98),X_97),implies(X_97,X_98)),implies(implies(implies(X_97,X_98),X_97),X_98))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(X_254,X_254)),
inference(subst,[],[refute_0_37:[bind(X_253,$fot(X_254))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(not(X_130),not(implies(X_254,X_254))),X_130)),
inference(resolve,[$cnf( is_a_theorem(implies(X_254,X_254)) )],[refute_0_38,refute_0_18]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(not(X_336),not(implies(X_254,X_254))),X_336)),
inference(subst,[],[refute_0_39:[bind(X_130,$fot(X_336))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(Y,X),X_25))
| ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(implies(not(X),not(Y)),X_25)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(implies(not(X),not(Y)))),bind(X2,$fot(implies(Y,X))),bind(X3,$fot(X_25))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(Y,X),X_25))
| is_a_theorem(implies(implies(not(X),not(Y)),X_25)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(not(X_336),not(implies(X_254,X_254))),X_336))
| is_a_theorem(implies(implies(not(not(implies(X_254,X_254))),not(not(X_336))),X_336)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(not(implies(X_254,X_254)))),bind(Y,$fot(not(X_336))),bind(X_25,$fot(X_336))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(not(not(implies(X_254,X_254))),not(not(X_336))),X_336)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_336),not(implies(X_254,X_254))),X_336)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(not(not(implies(X_368,X_368))),not(not(X_369))),X_369)),
inference(subst,[],[refute_0_44:[bind(X_254,$fot(X_368)),bind(X_336,$fot(X_369))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(not(not(X_369)),X_369)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(X_368,X_368))),not(not(X_369))),X_369)) )],[refute_0_45,refute_0_6]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(not(not(not(Y))),not(Y))),
inference(subst,[],[refute_0_46:[bind(X_369,$fot(not(Y)))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(Y,not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),not(Y))) )],[refute_0_47,refute_0_2]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(a,not(not(a)))),
inference(subst,[],[refute_0_48:[bind(Y,$fot(a))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_49,prove_cn_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL076-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 02:07:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------