TSTP Solution File: LCL077-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL077-2 : 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 12:49:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of clauses : 65 ( 36 unt; 0 nHn; 25 RR)
% Number of literals : 103 ( 0 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 137 ( 28 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_39,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)) ).
cnf(refute_0_0,plain,
is_a_theorem(implies(X_28,implies(Y,X_28))),
inference(subst,[],[cn_18:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X_28,implies(Y,X_28)))
| ~ is_a_theorem(implies(implies(Y,X_28),X_30))
| is_a_theorem(implies(X_28,X_30)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(X_28)),bind(X2,$fot(implies(Y,X_28))),bind(X3,$fot(X_30))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(Y,X_28),X_30))
| is_a_theorem(implies(X_28,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_28,implies(Y,X_28))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(not(X_581),not(X_581)))),not(not(X_581))),X_581))
| is_a_theorem(implies(not(not(X_581)),X_581)) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(not(not(implies(not(X_581),not(X_581)))))),bind(X_28,$fot(not(not(X_581)))),bind(X_30,$fot(X_581))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_120,implies(X_120,X_121)))
| ~ is_a_theorem(implies(implies(X_120,implies(X_120,X_121)),implies(X_120,X_121)))
| is_a_theorem(implies(X_120,X_121)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_120,implies(X_120,X_121)))),bind(Y,$fot(implies(X_120,X_121)))]]) ).
cnf(refute_0_5,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_6,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) )],[cn_35,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_105,implies(implies(X_105,X_106),X_106)))
| is_a_theorem(implies(implies(X_105,implies(X_105,X_106)),implies(X_105,X_106))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_105)),bind(Y,$fot(implies(X_105,X_106))),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(X_58,X_59),implies(X_58,X_59)))
| is_a_theorem(implies(implies(implies(X_58,X_59),X_58),implies(implies(X_58,X_59),X_59))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X_58,X_59))),bind(Y,$fot(X_58)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_56,implies(X_57,X_57)))
| is_a_theorem(implies(implies(X_56,X_57),implies(X_56,X_57))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_57))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(X_7,implies(Y,X_7))),
inference(subst,[],[cn_18:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X_7)
| ~ is_a_theorem(implies(X_7,implies(Y,X_7)))
| is_a_theorem(implies(Y,X_7)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_7)),bind(Y,$fot(implies(Y,X_7)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(X_7)
| is_a_theorem(implies(Y,X_7)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_7,implies(Y,X_7))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X,implies(Y,X)))
| is_a_theorem(implies(X_9,implies(X,implies(Y,X)))) ),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_9)),bind(X_7,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(X_9,implies(X,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X,implies(Y,X))) )],[cn_18,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(X_28,implies(X,implies(Y,X)))),
inference(subst,[],[refute_0_14:[bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(X_28,implies(X,implies(Y,X))))
| ~ is_a_theorem(implies(implies(X,implies(Y,X)),X_30))
| is_a_theorem(implies(X_28,X_30)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(X_28)),bind(X2,$fot(implies(X,implies(Y,X)))),bind(X3,$fot(X_30))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(X,implies(Y,X)),X_30))
| is_a_theorem(implies(X_28,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_28,implies(X,implies(Y,X)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_53,implies(Y,X_53)),implies(X_53,X_53)))
| is_a_theorem(implies(X_28,implies(X_53,X_53))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_53)),bind(X_30,$fot(implies(X_53,X_53)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(X_48,implies(X_47,X_48))),
inference(subst,[],[cn_18:[bind(X,$fot(X_48)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(X_48,implies(X_47,X_48)))
| is_a_theorem(implies(implies(X_48,X_47),implies(X_48,X_48))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_48)),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_48,X_47),implies(X_48,X_48))),
inference(resolve,[$cnf( is_a_theorem(implies(X_48,implies(X_47,X_48))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_53,implies(Y,X_53)),implies(X_53,X_53))),
inference(subst,[],[refute_0_21:[bind(X_47,$fot(implies(Y,X_53))),bind(X_48,$fot(X_53))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_28,implies(X_53,X_53))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_53,implies(Y,X_53)),implies(X_53,X_53))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(X_56,implies(X_57,X_57))),
inference(subst,[],[refute_0_23:[bind(X_28,$fot(X_56)),bind(X_53,$fot(X_57))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_56,X_57),implies(X_56,X_57))),
inference(resolve,[$cnf( is_a_theorem(implies(X_56,implies(X_57,X_57))) )],[refute_0_24,refute_0_9]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_58,X_59),implies(X_58,X_59))),
inference(subst,[],[refute_0_25:[bind(X_56,$fot(X_58)),bind(X_57,$fot(X_59))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(X_58,X_59),X_58),implies(implies(X_58,X_59),X_59))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_58,X_59),implies(X_58,X_59))) )],[refute_0_26,refute_0_8]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(X_101,X_59),X_101),implies(implies(X_101,X_59),X_59))),
inference(subst,[],[refute_0_27:[bind(X_58,$fot(X_101))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(X_101,X_59),X_101),implies(implies(X_101,X_59),X_59)))
| is_a_theorem(implies(X_101,implies(implies(X_101,X_59),X_59))) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(implies(X_101,X_59))),bind(X_28,$fot(X_101)),bind(X_30,$fot(implies(implies(X_101,X_59),X_59)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(X_101,implies(implies(X_101,X_59),X_59))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_101,X_59),X_101),implies(implies(X_101,X_59),X_59))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(X_105,implies(implies(X_105,X_106),X_106))),
inference(subst,[],[refute_0_30:[bind(X_101,$fot(X_105)),bind(X_59,$fot(X_106))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(X_105,implies(X_105,X_106)),implies(X_105,X_106))),
inference(resolve,[$cnf( is_a_theorem(implies(X_105,implies(implies(X_105,X_106),X_106))) )],[refute_0_31,refute_0_7]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(X_120,implies(X_120,X_121)),implies(X_120,X_121))),
inference(subst,[],[refute_0_32:[bind(X_105,$fot(X_120)),bind(X_106,$fot(X_121))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(X_120,implies(X_120,X_121)))
| is_a_theorem(implies(X_120,X_121)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_120,implies(X_120,X_121)),implies(X_120,X_121))) )],[refute_0_33,refute_0_4]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),X_408)))
| is_a_theorem(implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),X_408)) ),
inference(subst,[],[refute_0_34:[bind(X_120,$fot(implies(not(X_408),not(implies(not(X_408),not(X_408)))))),bind(X_121,$fot(X_408))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(not(X_48),not(X_47)),implies(X_47,X_48))),
inference(subst,[],[cn_49:[bind(X,$fot(X_48)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(not(X_48),not(X_47)),implies(X_47,X_48)))
| is_a_theorem(implies(implies(implies(not(X_48),not(X_47)),X_47),implies(implies(not(X_48),not(X_47)),X_48))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(not(X_48),not(X_47)))),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(X_48),not(X_47)),X_47),implies(implies(not(X_48),not(X_47)),X_48))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_48),not(X_47)),implies(X_47,X_48))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),implies(not(X_48),not(X_48))),implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48))),
inference(subst,[],[refute_0_38:[bind(X_47,$fot(implies(not(X_48),not(X_48))))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(X_37,implies(implies(X_35,X_36),implies(X_35,X_35))))
| ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_35,X_35)),X3))
| is_a_theorem(implies(X_37,X3)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(X_37)),bind(X2,$fot(implies(implies(X_35,X_36),implies(X_35,X_35))))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(X_31,implies(X_32,X_31)),implies(implies(X_31,X_32),implies(X_31,X_31)))),
inference(subst,[],[cn_35:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(X_31,implies(X_32,X_31)),implies(implies(X_31,X_32),implies(X_31,X_31))))
| is_a_theorem(implies(X_33,implies(implies(X_31,X_32),implies(X_31,X_31)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(X_28,$fot(X_33)),bind(X_30,$fot(implies(implies(X_31,X_32),implies(X_31,X_31))))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(X_33,implies(implies(X_31,X_32),implies(X_31,X_31)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31,implies(X_32,X_31)),implies(implies(X_31,X_32),implies(X_31,X_31)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(X_37,implies(implies(X_35,X_36),implies(X_35,X_35)))),
inference(subst,[],[refute_0_43:[bind(X_31,$fot(X_35)),bind(X_32,$fot(X_36)),bind(X_33,$fot(X_37))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_35,X_35)),X3))
| is_a_theorem(implies(X_37,X3)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_37,implies(implies(X_35,X_36),implies(X_35,X_35)))) )],[refute_0_44,refute_0_40]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),implies(not(X_48),not(X_48))),implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48)))
| is_a_theorem(implies(X_406,implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48))) ),
inference(subst,[],[refute_0_45:[bind(X3,$fot(implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48))),bind(X_35,$fot(not(X_48))),bind(X_36,$fot(not(implies(not(X_48),not(X_48))))),bind(X_37,$fot(X_406))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(X_406,implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),implies(not(X_48),not(X_48))),implies(implies(not(X_48),not(implies(not(X_48),not(X_48)))),X_48))) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),X_408))),
inference(subst,[],[refute_0_47:[bind(X_406,$fot(implies(not(X_408),not(implies(not(X_408),not(X_408)))))),bind(X_48,$fot(X_408))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),X_408)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),implies(implies(not(X_408),not(implies(not(X_408),not(X_408)))),X_408))) )],[refute_0_48,refute_0_35]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(not(X_578),not(implies(not(X_578),not(X_578)))),X_578)),
inference(subst,[],[refute_0_49:[bind(X_408,$fot(X_578))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(Y,X),X_30))
| ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(implies(not(X),not(Y)),X_30)) ),
inference(subst,[],[transitivity:[bind(X1,$fot(implies(not(X),not(Y)))),bind(X2,$fot(implies(Y,X))),bind(X3,$fot(X_30))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(Y,X),X_30))
| is_a_theorem(implies(implies(not(X),not(Y)),X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(implies(not(X_578),not(implies(not(X_578),not(X_578)))),X_578))
| is_a_theorem(implies(implies(not(not(implies(not(X_578),not(X_578)))),not(not(X_578))),X_578)) ),
inference(subst,[],[refute_0_52:[bind(X,$fot(not(implies(not(X_578),not(X_578))))),bind(Y,$fot(not(X_578))),bind(X_30,$fot(X_578))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(not(not(implies(not(X_578),not(X_578)))),not(not(X_578))),X_578)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_578),not(implies(not(X_578),not(X_578)))),X_578)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(not(not(implies(not(X_581),not(X_581)))),not(not(X_581))),X_581)),
inference(subst,[],[refute_0_54:[bind(X_578,$fot(X_581))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(not(not(X_581)),X_581)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(not(X_581),not(X_581)))),not(not(X_581))),X_581)) )],[refute_0_55,refute_0_3]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(not(not(a)),a)),
inference(subst,[],[refute_0_56:[bind(X_581,$fot(a))]]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(not(not(a)),a)) )],[refute_0_57,prove_cn_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL077-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 11:05:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.57
% 0.19/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.58
%------------------------------------------------------------------------------