TSTP Solution File: LCL110-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL110-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:49:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of clauses : 57 ( 32 unt; 0 nHn; 20 RR)
% Number of literals : 89 ( 0 equ; 33 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 : 151 ( 31 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(mv_1,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(mv_2,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(mv_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) ).
cnf(mv_5,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(prove_mv_24,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(not(X_351)),implies(X_352,X_351)))
| is_a_theorem(implies(implies(implies(X_352,X_351),Z),implies(not(not(X_351)),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(X_351)))),bind(Y,$fot(implies(X_352,X_351)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(not(X_162),implies(X_162,X_161)))
| is_a_theorem(implies(implies(implies(X_162,X_161),Z),implies(not(X_162),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(X_162))),bind(Y,$fot(implies(X_162,X_161)))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(X_70,X_71),X_72))
| ~ is_a_theorem(implies(implies(implies(X_70,X_71),X_72),implies(X_71,X_72)))
| is_a_theorem(implies(X_71,X_72)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_70,X_71),X_72))),bind(Y,$fot(implies(X_71,X_72)))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(X_67,implies(Y,X_67))),
inference(subst,[],[mv_1:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X_67,implies(Y,X_67)))
| is_a_theorem(implies(implies(implies(Y,X_67),X_69),implies(X_67,X_69))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_67)),bind(Y,$fot(implies(Y,X_67))),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(implies(Y,X_67),X_69),implies(X_67,X_69))),
inference(resolve,[$cnf( is_a_theorem(implies(X_67,implies(Y,X_67))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(X_70,X_71),X_72),implies(X_71,X_72))),
inference(subst,[],[refute_0_7:[bind(Y,$fot(X_70)),bind(X_67,$fot(X_71)),bind(X_69,$fot(X_72))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(X_70,X_71),X_72))
| is_a_theorem(implies(X_71,X_72)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_70,X_71),X_72),implies(X_71,X_72))) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(not(Y),implies(Y,X))) ),
inference(subst,[],[refute_0_9:[bind(X_70,$fot(not(X))),bind(X_71,$fot(not(Y))),bind(X_72,$fot(implies(Y,X)))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(not(Y),implies(Y,X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(not(X_162),implies(X_162,X_161))),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_161)),bind(Y,$fot(X_162))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(X_162,X_161),Z),implies(not(X_162),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_162),implies(X_162,X_161))) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(not(X_348),not(X_349)),implies(X_349,X_348)),implies(not(not(X_348)),implies(X_349,X_348)))),
inference(subst,[],[refute_0_13:[bind(Z,$fot(implies(X_349,X_348))),bind(X_161,$fot(not(X_349))),bind(X_162,$fot(not(X_348)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42),X_42))
| ~ is_a_theorem(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42))
| is_a_theorem(X_42) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42))),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_9,implies(Y,X_9))),
inference(subst,[],[mv_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_9)
| ~ is_a_theorem(implies(X_9,implies(Y,X_9)))
| is_a_theorem(implies(Y,X_9)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_9)),bind(Y,$fot(implies(Y,X_9)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_9)
| is_a_theorem(implies(Y,X_9)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_9,implies(Y,X_9))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_32,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(subst,[],[refute_0_20:[bind(X_11,$fot(implies(X_32,implies(implies(not(X),not(Y)),implies(Y,X)))))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Y))),bind(Y,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(X_32,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X))))
| is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_32),X_32)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_32)),bind(Y,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_32),X_32)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42),X_42)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_40)),bind(Y,$fot(X_41)),bind(X_32,$fot(X_42))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42))
| is_a_theorem(X_42) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_40),not(X_41)),implies(X_41,X_40)),X_42),X_42)) )],[refute_0_26,refute_0_15]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_348),not(X_349)),implies(X_349,X_348)),implies(not(not(X_348)),implies(X_349,X_348))))
| is_a_theorem(implies(not(not(X_348)),implies(X_349,X_348))) ),
inference(subst,[],[refute_0_27:[bind(X_40,$fot(X_348)),bind(X_41,$fot(X_349)),bind(X_42,$fot(implies(not(not(X_348)),implies(X_349,X_348))))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(not(not(X_348)),implies(X_349,X_348))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_348),not(X_349)),implies(X_349,X_348)),implies(not(not(X_348)),implies(X_349,X_348)))) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(not(not(X_351)),implies(X_352,X_351))),
inference(subst,[],[refute_0_29:[bind(X_348,$fot(X_351)),bind(X_349,$fot(X_352))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_352,X_351),Z),implies(not(not(X_351)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_351)),implies(X_352,X_351))) )],[refute_0_30,refute_0_2]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(implies(X_622,implies(X_623,X_622)),X_624),X_624),implies(not(not(X_624)),X_624))),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_624)),bind(X_351,$fot(X_624)),bind(X_352,$fot(implies(X_622,implies(X_623,X_622))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434),X_434))
| is_a_theorem(X_434) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434))),bind(Y,$fot(X_434))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(X,implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)),implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)))
| is_a_theorem(implies(implies(implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99),X),X)) ),
inference(subst,[],[refute_0_23:[bind(Y,$fot(implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36))
| is_a_theorem(implies(Y,implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36))) ),
inference(subst,[],[refute_0_18:[bind(X_9,$fot(implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36)))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(X,implies(Y,X)))
| is_a_theorem(implies(X_11,implies(X,implies(Y,X)))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_11,implies(X,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X,implies(Y,X))) )],[mv_1,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_32,implies(X,implies(Y,X))),implies(X,implies(Y,X)))),
inference(subst,[],[refute_0_37:[bind(X_11,$fot(implies(X_32,implies(X,implies(Y,X)))))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(X_32,implies(X,implies(Y,X))),implies(X,implies(Y,X))))
| is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_32),X_32)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_32)),bind(Y,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_32),X_32)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,implies(X,implies(Y,X))),implies(X,implies(Y,X)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36)),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_34)),bind(Y,$fot(X_35)),bind(X_32,$fot(X_36))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(Y,implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_34,implies(X_35,X_34)),X_36),X_36)) )],[refute_0_41,refute_0_35]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X,implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)),implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(implies(X,implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)))),bind(X_34,$fot(X_97)),bind(X_35,$fot(X_98)),bind(X_36,$fot(X_99))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99)),implies(implies(implies(X_97,implies(X_98,X_97)),X_99),X_99))) )],[refute_0_43,refute_0_34]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434),X_434)),
inference(subst,[],[refute_0_44:[bind(X,$fot(X_434)),bind(X_97,$fot(X_435)),bind(X_98,$fot(X_436)),bind(X_99,$fot(X_437))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434))
| is_a_theorem(X_434) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_435,implies(X_436,X_435)),X_437),X_437),X_434),X_434)) )],[refute_0_45,refute_0_33]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_622,implies(X_623,X_622)),X_624),X_624),implies(not(not(X_624)),X_624)))
| is_a_theorem(implies(not(not(X_624)),X_624)) ),
inference(subst,[],[refute_0_46:[bind(X_434,$fot(implies(not(not(X_624)),X_624))),bind(X_435,$fot(X_622)),bind(X_436,$fot(X_623)),bind(X_437,$fot(X_624))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(not(not(X_624)),X_624)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_622,implies(X_623,X_622)),X_624),X_624),implies(not(not(X_624)),X_624))) )],[refute_0_32,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(not(not(a)),a)),
inference(subst,[],[refute_0_48:[bind(X_624,$fot(a))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(not(not(a)),a)) )],[refute_0_49,prove_mv_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL110-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 18:40:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------