TSTP Solution File: LCL022-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:48:50 EDT 2022
% Result : Unsatisfiable 0.68s 0.88s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 24 unt; 0 nHn; 13 RR)
% Number of literals : 57 ( 0 equ; 19 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(yql,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
cnf(prove_ec_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11)))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))),bind(Y,$fot(equivalent(equivalent(X_8,X_9),X_11)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(equivalent(X_1422,X_1423),equivalent(equivalent(X_1422,equivalent(X_1423,X_1421)),equivalent(equivalent(X_1421,X_1422),X_1422))))
| is_a_theorem(equivalent(equivalent(equivalent(X_1421,X_1422),equivalent(X_1423,X_1421)),equivalent(X_1422,X_1423))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_1422)),bind(X_11,$fot(equivalent(X_1422,X_1423))),bind(X_8,$fot(equivalent(X_1421,X_1422))),bind(X_9,$fot(equivalent(X_1423,X_1421)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)),equivalent(equivalent(equivalent(X_297,X_295),X_297),equivalent(X_8,equivalent(X_297,X_295)))))
| is_a_theorem(equivalent(equivalent(X_8,X_297),equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(equivalent(X_297,X_295))),bind(X_11,$fot(equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)))),bind(X_9,$fot(X_297))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_194,X_192),X_194),equivalent(equivalent(X_192,X_193),X_193)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_192,X_193),X_193)),equivalent(equivalent(equivalent(X_194,X_192),X_194),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(equivalent(X_194,X_192),X_194))),bind(Y,$fot(equivalent(equivalent(X_192,X_193),X_193)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_188,X_189),X_189),equivalent(equivalent(equivalent(X_188,X_189),X_190),equivalent(equivalent(X_190,X_188),equivalent(X_188,X_189)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_190,X_188),X_190),equivalent(equivalent(X_188,X_189),X_189))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(equivalent(X_188,X_189))),bind(X_11,$fot(equivalent(equivalent(X_188,X_189),X_189))),bind(X_8,$fot(equivalent(X_190,X_188))),bind(X_9,$fot(X_190))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))),equivalent(equivalent(X_183,X_182),equivalent(X_8,X_183))))
| is_a_theorem(equivalent(equivalent(X_8,X_182),equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_183)),bind(X_11,$fot(equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))))),bind(X_9,$fot(X_182))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))))
| is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))),equivalent(equivalent(X_23,X_22),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_23,X_22))),bind(Y,$fot(equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19))))
| is_a_theorem(equivalent(equivalent(X_8,X_20),equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_19)),bind(X_11,$fot(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_16,X_17)),equivalent(equivalent(X_16,X_17),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_16,X_17))),bind(Y,$fot(equivalent(X_16,X_17)))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))),
inference(subst,[],[yql:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12))))
| is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(X_14,X_15))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_12)),bind(X_11,$fot(equivalent(X_14,X_15))),bind(X_8,$fot(X_14)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(X_14,X_15))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17))),
inference(subst,[],[refute_0_17:[bind(X_14,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_16,X_17)),equivalent(equivalent(X_16,X_17),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17))) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19)))),
inference(subst,[],[refute_0_19:[bind(Z,$fot(equivalent(X_8,X_19))),bind(X_16,$fot(X_19)),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_8,X_20),equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19)))) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22)))),
inference(subst,[],[refute_0_21:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22)),bind(X_8,$fot(X_23))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))),equivalent(equivalent(X_23,X_22),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22)))) )],[refute_0_22,refute_0_12]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))),equivalent(equivalent(X_183,X_182),equivalent(X_8,X_183)))),
inference(subst,[],[refute_0_23:[bind(Z,$fot(equivalent(X_8,X_183))),bind(X_21,$fot(X_181)),bind(X_22,$fot(X_182)),bind(X_23,$fot(X_183))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(equivalent(X_8,X_182),equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_183),equivalent(equivalent(X_183,X_181),equivalent(X_181,X_182))),equivalent(equivalent(X_183,X_182),equivalent(X_8,X_183)))) )],[refute_0_24,refute_0_11]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_188,X_189),X_189),equivalent(equivalent(equivalent(X_188,X_189),X_190),equivalent(equivalent(X_190,X_188),equivalent(X_188,X_189))))),
inference(subst,[],[refute_0_25:[bind(X_181,$fot(X_188)),bind(X_182,$fot(X_189)),bind(X_183,$fot(X_190)),bind(X_8,$fot(equivalent(X_188,X_189)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_190,X_188),X_190),equivalent(equivalent(X_188,X_189),X_189))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_188,X_189),X_189),equivalent(equivalent(equivalent(X_188,X_189),X_190),equivalent(equivalent(X_190,X_188),equivalent(X_188,X_189))))) )],[refute_0_26,refute_0_10]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_194,X_192),X_194),equivalent(equivalent(X_192,X_193),X_193))),
inference(subst,[],[refute_0_27:[bind(X_188,$fot(X_192)),bind(X_189,$fot(X_193)),bind(X_190,$fot(X_194))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(equivalent(X_192,X_193),X_193)),equivalent(equivalent(equivalent(X_194,X_192),X_194),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_194,X_192),X_194),equivalent(equivalent(X_192,X_193),X_193))) )],[refute_0_28,refute_0_9]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)),equivalent(equivalent(equivalent(X_297,X_295),X_297),equivalent(X_8,equivalent(X_297,X_295))))),
inference(subst,[],[refute_0_29:[bind(Z,$fot(equivalent(X_8,equivalent(X_297,X_295)))),bind(X_192,$fot(X_295)),bind(X_193,$fot(X_296)),bind(X_194,$fot(X_297))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(equivalent(X_8,X_297),equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,equivalent(X_297,X_295)),equivalent(equivalent(X_295,X_296),X_296)),equivalent(equivalent(equivalent(X_297,X_295),X_297),equivalent(X_8,equivalent(X_297,X_295))))) )],[refute_0_30,refute_0_8]) ).
cnf(refute_0_32,plain,
is_a_theorem(equivalent(equivalent(X_1422,X_1423),equivalent(equivalent(X_1422,equivalent(X_1423,X_1421)),equivalent(equivalent(X_1421,X_1422),X_1422)))),
inference(subst,[],[refute_0_31:[bind(X_295,$fot(X_1421)),bind(X_296,$fot(X_1422)),bind(X_297,$fot(X_1423)),bind(X_8,$fot(X_1422))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1421,X_1422),equivalent(X_1423,X_1421)),equivalent(X_1422,X_1423))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_1422,X_1423),equivalent(equivalent(X_1422,equivalent(X_1423,X_1421)),equivalent(equivalent(X_1421,X_1422),X_1422)))) )],[refute_0_32,refute_0_7]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(subst,[],[refute_0_33:[bind(X_1421,$fot(a)),bind(X_1422,$fot(b)),bind(X_1423,$fot(c))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))) )],[refute_0_34,prove_ec_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jul 4 15:48:46 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.68/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.88
% 0.68/0.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.68/0.88
%------------------------------------------------------------------------------