TSTP Solution File: SEU368+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU368+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.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 : 300s
% DateTime : Tue Apr 30 15:31:47 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 172 ( 40 unt; 0 def)
% Number of atoms : 417 ( 78 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 396 ( 151 ~; 139 |; 72 &)
% ( 16 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 16 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 172 ( 159 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1122,plain,
$false,
inference(avatar_sat_refutation,[],[f263,f275,f441,f450,f574,f652,f658,f676,f691,f1042,f1121]) ).
fof(f1121,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f1120]) ).
fof(f1120,plain,
( $false
| spl15_2 ),
inference(equality_resolution,[],[f1095]) ).
fof(f1095,plain,
( ! [X0] : incl_POSet(X0) != incl_POSet(sK1)
| spl15_2 ),
inference(subsumption_resolution,[],[f1054,f632]) ).
fof(f632,plain,
! [X0,X1] :
( inclusion_relation(X0) = inclusion_relation(X1)
| incl_POSet(X0) != incl_POSet(X1) ),
inference(superposition,[],[f596,f222]) ).
fof(f222,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_relation(X0)),
inference(forward_demodulation,[],[f129,f128]) ).
fof(f128,plain,
! [X0] : inclusion_relation(X0) = inclusion_order(X0),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] : inclusion_relation(X0) = inclusion_order(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
fof(f129,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f596,plain,
! [X2,X0,X1] :
( incl_POSet(X0) != rel_str_of(X1,X2)
| inclusion_relation(X0) = X2 ),
inference(subsumption_resolution,[],[f587,f243]) ).
fof(f243,plain,
! [X0] : relation_of2(inclusion_relation(X0),X0,X0),
inference(resolution,[],[f185,f215]) ).
fof(f215,plain,
! [X0] : relation_of2_as_subset(inclusion_relation(X0),X0,X0),
inference(forward_demodulation,[],[f134,f128]) ).
fof(f134,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( relation_of2_as_subset(inclusion_order(X0),X0,X0)
& v1_partfun1(inclusion_order(X0),X0,X0)
& transitive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& reflexive(inclusion_order(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f587,plain,
! [X2,X0,X1] :
( incl_POSet(X0) != rel_str_of(X1,X2)
| inclusion_relation(X0) = X2
| ~ relation_of2(inclusion_relation(X0),X0,X0) ),
inference(superposition,[],[f170,f222]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f1054,plain,
( ! [X0] :
( inclusion_relation(X0) != inclusion_relation(sK1)
| incl_POSet(X0) != incl_POSet(sK1) )
| spl15_2 ),
inference(superposition,[],[f262,f636]) ).
fof(f636,plain,
! [X0,X1] :
( the_InternalRel(incl_POSet(X0)) = inclusion_relation(X1)
| incl_POSet(X0) != incl_POSet(X1) ),
inference(superposition,[],[f596,f345]) ).
fof(f345,plain,
! [X0] : incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0))),
inference(subsumption_resolution,[],[f339,f140]) ).
fof(f140,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( rel_str(incl_POSet(X0))
& strict_rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(f339,plain,
! [X0] :
( incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0)))
| ~ rel_str(incl_POSet(X0)) ),
inference(resolution,[],[f151,f135]) ).
fof(f135,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( antisymmetric_relstr(incl_POSet(X0))
& transitive_relstr(incl_POSet(X0))
& reflexive_relstr(incl_POSet(X0))
& strict_rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).
fof(f151,plain,
! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f262,plain,
( the_InternalRel(incl_POSet(sK1)) != inclusion_relation(sK1)
| spl15_2 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f260,plain,
( spl15_2
<=> the_InternalRel(incl_POSet(sK1)) = inclusion_relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f1042,plain,
( spl15_14
| ~ spl15_15 ),
inference(avatar_split_clause,[],[f1031,f1039,f1035]) ).
fof(f1035,plain,
( spl15_14
<=> empty(the_carrier(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f1039,plain,
( spl15_15
<=> empty_carrier(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f1031,plain,
( ~ empty_carrier(sK14)
| empty(the_carrier(sK14)) ),
inference(subsumption_resolution,[],[f1026,f200]) ).
fof(f200,plain,
rel_str(sK14),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( strict_rel_str(sK14)
& rel_str(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f44,f123]) ).
fof(f123,plain,
( ? [X0] :
( strict_rel_str(X0)
& rel_str(X0) )
=> ( strict_rel_str(sK14)
& rel_str(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] :
( strict_rel_str(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_orders_2) ).
fof(f1026,plain,
( ~ empty_carrier(sK14)
| empty(the_carrier(sK14))
| ~ rel_str(sK14) ),
inference(superposition,[],[f305,f350]) ).
fof(f350,plain,
sK14 = rel_str_of(the_carrier(sK14),the_InternalRel(sK14)),
inference(subsumption_resolution,[],[f344,f200]) ).
fof(f344,plain,
( sK14 = rel_str_of(the_carrier(sK14),the_InternalRel(sK14))
| ~ rel_str(sK14) ),
inference(resolution,[],[f151,f201]) ).
fof(f201,plain,
strict_rel_str(sK14),
inference(cnf_transformation,[],[f124]) ).
fof(f305,plain,
! [X0] :
( ~ empty_carrier(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| empty(the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[],[f172,f264]) ).
fof(f264,plain,
! [X0] :
( relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[],[f150,f185]) ).
fof(f150,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f172,plain,
! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| ~ empty_carrier(rel_str_of(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| empty(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| empty(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation_of2(X1,X0,X0)
& ~ empty(X0) )
=> ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_2) ).
fof(f691,plain,
( ~ spl15_11
| ~ spl15_12
| ~ spl15_13
| spl15_10 ),
inference(avatar_split_clause,[],[f678,f673,f688,f684,f680]) ).
fof(f680,plain,
( spl15_11
<=> reflexive_relstr(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f684,plain,
( spl15_12
<=> transitive_relstr(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f688,plain,
( spl15_13
<=> antisymmetric_relstr(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f673,plain,
( spl15_10
<=> transitive(the_InternalRel(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f678,plain,
( ~ antisymmetric_relstr(sK14)
| ~ transitive_relstr(sK14)
| ~ reflexive_relstr(sK14)
| spl15_10 ),
inference(subsumption_resolution,[],[f677,f200]) ).
fof(f677,plain,
( ~ rel_str(sK14)
| ~ antisymmetric_relstr(sK14)
| ~ transitive_relstr(sK14)
| ~ reflexive_relstr(sK14)
| spl15_10 ),
inference(resolution,[],[f674,f158]) ).
fof(f158,plain,
! [X0] :
( transitive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) ) ),
inference(pure_predicate_removal,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0))
& relation(the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_orders_2) ).
fof(f674,plain,
( ~ transitive(the_InternalRel(sK14))
| spl15_10 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f676,plain,
( spl15_9
| spl15_10 ),
inference(avatar_split_clause,[],[f660,f673,f670]) ).
fof(f670,plain,
( spl15_9
<=> ! [X0] : incl_POSet(X0) != sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f660,plain,
! [X0] :
( transitive(the_InternalRel(sK14))
| incl_POSet(X0) != sK14 ),
inference(superposition,[],[f211,f635]) ).
fof(f635,plain,
! [X0] :
( inclusion_relation(X0) = the_InternalRel(sK14)
| incl_POSet(X0) != sK14 ),
inference(superposition,[],[f596,f350]) ).
fof(f211,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(superposition,[],[f132,f128]) ).
fof(f132,plain,
! [X0] : transitive(inclusion_order(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f658,plain,
spl15_8,
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f657,plain,
( $false
| spl15_8 ),
inference(subsumption_resolution,[],[f656,f197]) ).
fof(f197,plain,
reflexive_relstr(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( antisymmetric_relstr(sK13)
& transitive_relstr(sK13)
& reflexive_relstr(sK13)
& strict_rel_str(sK13)
& ~ empty_carrier(sK13)
& rel_str(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f6,f121]) ).
fof(f121,plain,
( ? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( antisymmetric_relstr(sK13)
& transitive_relstr(sK13)
& reflexive_relstr(sK13)
& strict_rel_str(sK13)
& ~ empty_carrier(sK13)
& rel_str(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f6,axiom,
? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_orders_2) ).
fof(f656,plain,
( ~ reflexive_relstr(sK13)
| spl15_8 ),
inference(subsumption_resolution,[],[f655,f198]) ).
fof(f198,plain,
transitive_relstr(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f655,plain,
( ~ transitive_relstr(sK13)
| ~ reflexive_relstr(sK13)
| spl15_8 ),
inference(subsumption_resolution,[],[f654,f199]) ).
fof(f199,plain,
antisymmetric_relstr(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f654,plain,
( ~ antisymmetric_relstr(sK13)
| ~ transitive_relstr(sK13)
| ~ reflexive_relstr(sK13)
| spl15_8 ),
inference(subsumption_resolution,[],[f653,f194]) ).
fof(f194,plain,
rel_str(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f653,plain,
( ~ rel_str(sK13)
| ~ antisymmetric_relstr(sK13)
| ~ transitive_relstr(sK13)
| ~ reflexive_relstr(sK13)
| spl15_8 ),
inference(resolution,[],[f650,f158]) ).
fof(f650,plain,
( ~ transitive(the_InternalRel(sK13))
| spl15_8 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f649,plain,
( spl15_8
<=> transitive(the_InternalRel(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f652,plain,
( spl15_7
| spl15_8 ),
inference(avatar_split_clause,[],[f637,f649,f646]) ).
fof(f646,plain,
( spl15_7
<=> ! [X0] : incl_POSet(X0) != sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f637,plain,
! [X0] :
( transitive(the_InternalRel(sK13))
| incl_POSet(X0) != sK13 ),
inference(superposition,[],[f211,f634]) ).
fof(f634,plain,
! [X0] :
( inclusion_relation(X0) = the_InternalRel(sK13)
| incl_POSet(X0) != sK13 ),
inference(superposition,[],[f596,f349]) ).
fof(f349,plain,
sK13 = rel_str_of(the_carrier(sK13),the_InternalRel(sK13)),
inference(subsumption_resolution,[],[f343,f194]) ).
fof(f343,plain,
( sK13 = rel_str_of(the_carrier(sK13),the_InternalRel(sK13))
| ~ rel_str(sK13) ),
inference(resolution,[],[f151,f196]) ).
fof(f196,plain,
strict_rel_str(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f574,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f573,plain,
( $false
| spl15_1 ),
inference(trivial_inequality_removal,[],[f562]) ).
fof(f562,plain,
( sK1 != sK1
| spl15_1 ),
inference(superposition,[],[f258,f561]) ).
fof(f561,plain,
! [X0] : the_carrier(incl_POSet(X0)) = X0,
inference(equality_resolution,[],[f551]) ).
fof(f551,plain,
! [X0,X1] :
( incl_POSet(X0) != incl_POSet(X1)
| the_carrier(incl_POSet(X0)) = X1 ),
inference(superposition,[],[f538,f345]) ).
fof(f538,plain,
! [X2,X0,X1] :
( incl_POSet(X0) != rel_str_of(X1,X2)
| X0 = X1 ),
inference(subsumption_resolution,[],[f529,f243]) ).
fof(f529,plain,
! [X2,X0,X1] :
( incl_POSet(X0) != rel_str_of(X1,X2)
| X0 = X1
| ~ relation_of2(inclusion_relation(X0),X0,X0) ),
inference(superposition,[],[f169,f222]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f258,plain,
( sK1 != the_carrier(incl_POSet(sK1))
| spl15_1 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f256,plain,
( spl15_1
<=> sK1 = the_carrier(incl_POSet(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f450,plain,
~ spl15_5,
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f449,plain,
( $false
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f442,f127]) ).
fof(f127,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f442,plain,
( empty(powerset(empty_set))
| ~ spl15_5 ),
inference(resolution,[],[f436,f148]) ).
fof(f148,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f62,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f436,plain,
( empty(sK2(powerset(empty_set)))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f434,plain,
( spl15_5
<=> empty(sK2(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f441,plain,
( spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f396,f438,f434]) ).
fof(f438,plain,
( spl15_6
<=> in(empty_set,sK2(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f396,plain,
( in(empty_set,sK2(powerset(empty_set)))
| empty(sK2(powerset(empty_set))) ),
inference(superposition,[],[f231,f383]) ).
fof(f383,plain,
empty_set = sK4(sK2(powerset(empty_set))),
inference(resolution,[],[f376,f126]) ).
fof(f126,plain,
empty(empty_set),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f376,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK4(sK2(powerset(X0))) ),
inference(resolution,[],[f370,f152]) ).
fof(f152,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f370,plain,
! [X0] :
( empty(sK4(sK2(powerset(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f362,f231]) ).
fof(f362,plain,
! [X0,X1] :
( ~ in(X1,sK4(sK2(powerset(X0))))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f359,f127]) ).
fof(f359,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK4(sK2(powerset(X0)))) ),
inference(resolution,[],[f338,f187]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f338,plain,
! [X0] :
( element(sK4(sK2(X0)),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f337,f148]) ).
fof(f337,plain,
! [X0] :
( element(sK4(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) ),
inference(resolution,[],[f328,f231]) ).
fof(f328,plain,
! [X0,X1] :
( ~ in(X0,sK2(X1))
| element(X0,X1)
| empty(X1) ),
inference(resolution,[],[f184,f147]) ).
fof(f147,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f231,plain,
! [X0] :
( in(sK4(X0),X0)
| empty(X0) ),
inference(resolution,[],[f166,f160]) ).
fof(f160,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f102]) ).
fof(f102,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f166,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f275,plain,
( spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f266,f273,f270]) ).
fof(f270,plain,
( spl15_3
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f273,plain,
( spl15_4
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f266,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,empty_set) ),
inference(resolution,[],[f187,f221]) ).
fof(f221,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f161,f218]) ).
fof(f218,plain,
! [X0] : empty_set = sK5(X0),
inference(resolution,[],[f152,f162]) ).
fof(f162,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f16,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f161,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f105]) ).
fof(f263,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f254,f260,f256]) ).
fof(f254,plain,
( the_InternalRel(incl_POSet(sK1)) != inclusion_relation(sK1)
| sK1 != the_carrier(incl_POSet(sK1)) ),
inference(forward_demodulation,[],[f125,f128]) ).
fof(f125,plain,
( inclusion_order(sK1) != the_InternalRel(incl_POSet(sK1))
| sK1 != the_carrier(incl_POSet(sK1)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( inclusion_order(sK1) != the_InternalRel(incl_POSet(sK1))
| sK1 != the_carrier(incl_POSet(sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f60,f95]) ).
fof(f95,plain,
( ? [X0] :
( inclusion_order(X0) != the_InternalRel(incl_POSet(X0))
| the_carrier(incl_POSet(X0)) != X0 )
=> ( inclusion_order(sK1) != the_InternalRel(incl_POSet(sK1))
| sK1 != the_carrier(incl_POSet(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0] :
( inclusion_order(X0) != the_InternalRel(incl_POSet(X0))
| the_carrier(incl_POSet(X0)) != X0 ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,negated_conjecture,
~ ! [X0] :
( inclusion_order(X0) = the_InternalRel(incl_POSet(X0))
& the_carrier(incl_POSet(X0)) = X0 ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
! [X0] :
( inclusion_order(X0) = the_InternalRel(incl_POSet(X0))
& the_carrier(incl_POSet(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU368+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:58:58 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (15634)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (15639)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (15641)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 % (15640)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (15637)WARNING: value z3 for option sas not known
% 0.21/0.38 % (15636)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (15635)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (15637)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (15638)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.40 TRYING [4]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.41 TRYING [3]
% 0.21/0.42 % (15637)First to succeed.
% 0.21/0.42 TRYING [5]
% 0.21/0.42 % (15637)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42 % (15637)------------------------------
% 0.21/0.42 % (15637)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.42 % (15637)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (15637)Memory used [KB]: 1229
% 0.21/0.42 % (15637)Time elapsed: 0.040 s
% 0.21/0.42 % (15637)Instructions burned: 60 (million)
% 0.21/0.42 % (15637)------------------------------
% 0.21/0.42 % (15637)------------------------------
% 0.21/0.42 % (15634)Success in time 0.067 s
%------------------------------------------------------------------------------