%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU293+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:12 PM UTC 2026
% Result : Theorem 4.91s 1.69s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 13 unt; 3 def)
% Number of atoms : 343 ( 60 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 403 ( 148 ~; 155 |; 68 &)
% ( 18 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 128 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f20,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f27,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) )
& ( X1 = empty_set
=> ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f120,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f196,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f201,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(f325,conjecture,
! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(X4,X0)
& in(apply(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f326,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(X4,X0)
& in(apply(X3,X4),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f325]) ).
fof(f418,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f432,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f433,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f432]) ).
fof(f441,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f442,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f441]) ).
fof(f501,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f120]) ).
fof(f558,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f196]) ).
fof(f715,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(X4,X0)
& in(apply(X3,X4),X2) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(ennf_transformation,[],[f326]) ).
fof(f716,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(X4,X0)
& in(apply(X3,X4),X2) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f715]) ).
fof(f834,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f433]) ).
fof(f835,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f834]) ).
fof(f836,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f835]) ).
fof(f837,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),X2) )
& ( ( in(sK21(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK21(X0,X1,X2)),X1) )
| in(sK21(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X3,sK21(X0,X1,X2))],[f836]) ).
fof(f853,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( X0 = relation_dom_as_subset(X0,X1,X2)
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| ~ quasi_total(X2,X0,X1) ) )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f442]) ).
fof(f1023,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,[],[f201]) ).
fof(f1158,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(apply(X3,X4),X2)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(X4,X0)
& in(apply(X3,X4),X2) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(nnf_transformation,[],[f716]) ).
fof(f1159,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(apply(X3,X4),X2)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(X4,X0)
& in(apply(X3,X4),X2) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f1158]) ).
fof(f1160,plain,
( ( ~ in(sK259,sK255)
| ~ in(apply(sK258,sK259),sK257)
| ~ in(sK259,relation_inverse_image(sK258,sK257)) )
& ( ( in(sK259,sK255)
& in(apply(sK258,sK259),sK257) )
| in(sK259,relation_inverse_image(sK258,sK257)) )
& empty_set != sK256
& function(sK258)
& quasi_total(sK258,sK255,sK256)
& relation_of2_as_subset(sK258,sK255,sK256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255,sK256,sK257,sK258,sK259]),skolemize(X0,sK255),skolemize(X1,sK256),skolemize(X2,sK257),skolemize(X3,sK258),skolemize(X4,sK259)],[f1159]) ).
fof(f1190,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f418]) ).
fof(f1233,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f837]) ).
fof(f1234,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f837]) ).
fof(f1235,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f837]) ).
fof(f1269,plain,
! [X2,X0,X1] :
( ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f853]) ).
fof(f1511,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f1667,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f558]) ).
fof(f1672,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1023]) ).
fof(f2035,plain,
relation_of2_as_subset(sK258,sK255,sK256),
inference(cnf_transformation,[],[f1160]) ).
fof(f2036,plain,
quasi_total(sK258,sK255,sK256),
inference(cnf_transformation,[],[f1160]) ).
fof(f2037,plain,
function(sK258),
inference(cnf_transformation,[],[f1160]) ).
fof(f2038,plain,
empty_set != sK256,
inference(cnf_transformation,[],[f1160]) ).
fof(f2039,plain,
( in(apply(sK258,sK259),sK257)
| in(sK259,relation_inverse_image(sK258,sK257)) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f2040,plain,
( in(sK259,sK255)
| in(sK259,relation_inverse_image(sK258,sK257)) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f2041,plain,
( ~ in(sK259,sK255)
| ~ in(apply(sK258,sK259),sK257)
| ~ in(sK259,relation_inverse_image(sK258,sK257)) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f2447,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| in(X4,relation_inverse_image(X0,X1))
| ~ function(X0) ),
inference(equality_resolution,[],[f1235]) ).
fof(f2448,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f1234]) ).
fof(f2449,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1)
| ~ function(X0) ),
inference(equality_resolution,[],[f1233]) ).
fof(f2610,definition,
( spl269_1
<=> in(sK259,relation_inverse_image(sK258,sK257)) ),
introduced(definition,[new_symbols(definition,[spl269_1])],[avatar_definition]) ).
fof(f2611,plain,
( in(sK259,relation_inverse_image(sK258,sK257))
| ~ spl269_1 ),
inference(avatar_component_clause,[],[f2610]) ).
fof(f2613,definition,
( spl269_2
<=> in(apply(sK258,sK259),sK257) ),
introduced(definition,[new_symbols(definition,[spl269_2])],[avatar_definition]) ).
fof(f2614,plain,
( in(apply(sK258,sK259),sK257)
| ~ spl269_2 ),
inference(avatar_component_clause,[],[f2613]) ).
fof(f2615,plain,
( spl269_1
| spl269_2 ),
inference(avatar_split_clause,[],[f2039,f2613,f2610]) ).
fof(f2617,definition,
( spl269_3
<=> in(sK259,sK255) ),
introduced(definition,[new_symbols(definition,[spl269_3])],[avatar_definition]) ).
fof(f2618,plain,
( in(sK259,sK255)
| ~ spl269_3 ),
inference(avatar_component_clause,[],[f2617]) ).
fof(f2619,plain,
( spl269_1
| spl269_3 ),
inference(avatar_split_clause,[],[f2040,f2617,f2610]) ).
fof(f2620,plain,
( ~ in(sK259,relation_inverse_image(sK258,sK257))
| spl269_1 ),
inference(avatar_component_clause,[],[f2610]) ).
fof(f2621,plain,
( ~ in(apply(sK258,sK259),sK257)
| spl269_2 ),
inference(avatar_component_clause,[],[f2613]) ).
fof(f2622,plain,
( ~ in(sK259,sK255)
| spl269_3 ),
inference(avatar_component_clause,[],[f2617]) ).
fof(f2623,plain,
( ~ spl269_1
| ~ spl269_2
| ~ spl269_3 ),
inference(avatar_split_clause,[],[f2041,f2617,f2613,f2610]) ).
fof(f2728,plain,
( sK255 = relation_dom_as_subset(sK255,sK256,sK258)
| empty_set = sK256
| ~ relation_of2_as_subset(sK258,sK255,sK256) ),
inference(resolution,[],[f1269,f2036]) ).
fof(f2729,plain,
( sK255 = relation_dom_as_subset(sK255,sK256,sK258)
| ~ relation_of2_as_subset(sK258,sK255,sK256) ),
inference(forward_subsumption_resolution,[],[f2728,f2038]) ).
fof(f2730,plain,
sK255 = relation_dom_as_subset(sK255,sK256,sK258),
inference(forward_subsumption_resolution,[],[f2729,f2035]) ).
fof(f2735,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(resolution,[],[f1667,f1672]) ).
fof(f2736,plain,
relation_dom_as_subset(sK255,sK256,sK258) = relation_dom(sK258),
inference(resolution,[],[f2735,f2035]) ).
fof(f2737,plain,
sK255 = relation_dom(sK258),
inference(forward_demodulation,[],[f2736,f2730]) ).
fof(f2746,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f1190,f1511]) ).
fof(f2747,plain,
relation(sK258),
inference(resolution,[],[f2746,f2035]) ).
fof(f2751,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK258))
| ~ in(apply(sK258,X0),X1)
| in(X0,relation_inverse_image(sK258,X1))
| ~ function(sK258) ),
inference(resolution,[],[f2747,f2447]) ).
fof(f2752,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK258,X1))
| in(X0,relation_dom(sK258))
| ~ function(sK258) ),
inference(resolution,[],[f2747,f2448]) ).
fof(f2761,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK258,X1))
| in(X0,relation_dom(sK258)) ),
inference(forward_subsumption_resolution,[],[f2752,f2037]) ).
fof(f2762,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK258))
| ~ in(apply(sK258,X0),X1)
| in(X0,relation_inverse_image(sK258,X1)) ),
inference(forward_subsumption_resolution,[],[f2751,f2037]) ).
fof(f2766,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK258,X1))
| in(X0,sK255) ),
inference(forward_demodulation,[],[f2761,f2737]) ).
fof(f2767,plain,
! [X0,X1] :
( ~ in(X0,sK255)
| ~ in(apply(sK258,X0),X1)
| in(X0,relation_inverse_image(sK258,X1)) ),
inference(forward_demodulation,[],[f2762,f2737]) ).
fof(f2768,plain,
( $false
| spl269_1
| ~ spl269_2
| ~ spl269_3 ),
inference(unit_resulting_resolution,[],[f2767,f2618,f2620,f2614]) ).
fof(f2771,plain,
( spl269_1
| ~ spl269_2
| ~ spl269_3 ),
inference(avatar_contradiction_clause,[],[f2768]) ).
fof(f2772,plain,
( in(sK259,sK255)
| ~ spl269_1 ),
inference(resolution,[],[f2611,f2766]) ).
fof(f2773,plain,
( $false
| ~ spl269_1
| spl269_3 ),
inference(forward_subsumption_resolution,[],[f2772,f2622]) ).
fof(f2774,plain,
( ~ spl269_1
| spl269_3 ),
inference(avatar_contradiction_clause,[],[f2773]) ).
fof(f2776,plain,
( $false
| ~ spl269_1
| spl269_2 ),
inference(unit_resulting_resolution,[],[f2449,f2037,f2747,f2611,f2621]) ).
fof(f2777,plain,
( ~ spl269_1
| spl269_2 ),
inference(avatar_contradiction_clause,[],[f2776]) ).
cnf(s1,plain,
( spl269_1
| spl269_2 ),
inference(sat_conversion,[],[f2615]) ).
cnf(s2,plain,
( spl269_1
| spl269_3 ),
inference(sat_conversion,[],[f2619]) ).
cnf(s3,plain,
( ~ spl269_1
| ~ spl269_2
| ~ spl269_3 ),
inference(sat_conversion,[],[f2623]) ).
cnf(s14,plain,
( spl269_1
| ~ spl269_2
| ~ spl269_3 ),
inference(sat_conversion,[],[f2771]) ).
cnf(s15,plain,
( ~ spl269_1
| spl269_3 ),
inference(sat_conversion,[],[f2774]) ).
cnf(s16,plain,
( ~ spl269_1
| spl269_2 ),
inference(sat_conversion,[],[f2777]) ).
cnf(s17,plain,
spl269_1,
inference(rat,[],[s14,s1,s2]) ).
cnf(s18,plain,
spl269_2,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
spl269_3,
inference(rat,[],[s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s3,s18,s19,s17]) ).
fof(f2778,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU293+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 04:27:36 UTC 2026
% 0.16/0.38 % CPUTime :
% 0.16/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/1.69 % (3201624)Detected formulas, will run a generic FOF schedule.
% 4.91/1.69 % (3201630)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1269017579:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.91/1.69 % (3201632)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=950513792:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.91/1.69 % (3201629)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3794470867:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.91/1.69 % (3201631)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1137782102:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.91/1.69 % (3201633)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2001931057:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.91/1.69 % (3201634)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1189614519:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.91/1.69 % (3201635)dis-21_1_sil=8000:lcm=predicate:random_seed=3535371626:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.91/1.69 % (3201634)Instruction limit reached!
% 4.91/1.69 % (3201634)------------------------------
% 4.91/1.69 % (3201634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201634)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201634)Termination reason: Instruction limit
% 4.91/1.69 % (3201634)Termination phase: Saturation
% 4.91/1.69 % (3201634)Time elapsed: 0.059 s
% 4.91/1.69 % (3201634)Peak memory usage: 90 MB
% 4.91/1.69 % (3201634)Instructions burned: 140 (million)
% 4.91/1.69 % (3201632)Instruction limit reached!
% 4.91/1.69 % (3201632)------------------------------
% 4.91/1.69 % (3201632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201632)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201632)Termination reason: Instruction limit
% 4.91/1.69 % (3201632)Termination phase: Saturation
% 4.91/1.69 % (3201632)Time elapsed: 0.063 s
% 4.91/1.69 % (3201632)Peak memory usage: 91 MB
% 4.91/1.69 % (3201632)Instructions burned: 110 (million)
% 4.91/1.69 % (3201635)Instruction limit reached!
% 4.91/1.69 % (3201635)------------------------------
% 4.91/1.69 % (3201635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201635)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201635)Termination reason: Instruction limit
% 4.91/1.69 % (3201635)Termination phase: Saturation
% 4.91/1.69 % (3201635)Time elapsed: 0.063 s
% 4.91/1.69 % (3201635)Peak memory usage: 90 MB
% 4.91/1.69 % (3201635)Instructions burned: 129 (million)
% 4.91/1.69 % (3201633)Instruction limit reached!
% 4.91/1.69 % (3201633)------------------------------
% 4.91/1.69 % (3201633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201633)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201633)Termination reason: Instruction limit
% 4.91/1.69 % (3201633)Termination phase: Saturation
% 4.91/1.69 % (3201633)Time elapsed: 0.078 s
% 4.91/1.69 % (3201633)Peak memory usage: 90 MB
% 4.91/1.69 % (3201633)Instructions burned: 120 (million)
% 4.91/1.69 % (3201644)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1515803915:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.91/1.69 % (3201643)lrs+10_1_sil=8000:sp=occurrence:random_seed=1407397731:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.91/1.69 % (3201645)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1825191423:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.91/1.69 % (3201646)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2876935365:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.91/1.69 % (3201644)Instruction limit reached!
% 4.91/1.69 % (3201644)------------------------------
% 4.91/1.69 % (3201644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201644)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201644)Termination reason: Instruction limit
% 4.91/1.69 % (3201644)Termination phase: Saturation
% 4.91/1.69 % (3201644)Time elapsed: 0.086 s
% 4.91/1.69 % (3201644)Peak memory usage: 91 MB
% 4.91/1.69 % (3201644)Instructions burned: 157 (million)
% 4.91/1.69 % (3201646)Instruction limit reached!
% 4.91/1.69 % (3201646)------------------------------
% 4.91/1.69 % (3201646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201646)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201646)Termination reason: Instruction limit
% 4.91/1.69 % (3201646)Termination phase: Saturation
% 4.91/1.69 % (3201646)Time elapsed: 0.138 s
% 4.91/1.69 % (3201646)Peak memory usage: 92 MB
% 4.91/1.69 % (3201646)Instructions burned: 248 (million)
% 4.91/1.69 % (3201643)Instruction limit reached!
% 4.91/1.69 % (3201643)------------------------------
% 4.91/1.69 % (3201643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201643)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201643)Termination reason: Instruction limit
% 4.91/1.69 % (3201643)Termination phase: Saturation
% 4.91/1.69 % (3201643)Time elapsed: 0.188 s
% 4.91/1.69 % (3201643)Peak memory usage: 94 MB
% 4.91/1.69 % (3201643)Instructions burned: 285 (million)
% 4.91/1.69 % (3201651)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2986703324:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.91/1.69 % (3201645)Instruction limit reached!
% 4.91/1.69 % (3201645)------------------------------
% 4.91/1.69 % (3201645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201645)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201645)Termination reason: Instruction limit
% 4.91/1.69 % (3201645)Termination phase: Saturation
% 4.91/1.69 % (3201645)Time elapsed: 0.232 s
% 4.91/1.69 % (3201645)Peak memory usage: 94 MB
% 4.91/1.69 % (3201645)Instructions burned: 326 (million)
% 4.91/1.69 % (3201652)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=545424363:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.91/1.69 % (3201653)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2500589850:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.91/1.69 % (3201630)First to succeed.
% 4.91/1.69 % (3201630)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3201624"
% 4.91/1.69 % (3201655)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3967494358:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.91/1.69 % (3201653)Instruction limit reached!
% 4.91/1.69 % (3201653)------------------------------
% 4.91/1.69 % (3201653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201653)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201653)Termination reason: Instruction limit
% 4.91/1.69 % (3201653)Termination phase: Saturation
% 4.91/1.69 % (3201653)Time elapsed: 0.071 s
% 4.91/1.69 % (3201653)Peak memory usage: 91 MB
% 4.91/1.69 % (3201653)Instructions burned: 114 (million)
% 4.91/1.69 % (3201651)Instruction limit reached!
% 4.91/1.69 % (3201651)------------------------------
% 4.91/1.69 % (3201651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201651)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201651)Termination reason: Instruction limit
% 4.91/1.69 % (3201651)Termination phase: Saturation
% 4.91/1.69 % (3201651)Time elapsed: 0.191 s
% 4.91/1.69 % (3201651)Peak memory usage: 92 MB
% 4.91/1.69 % (3201651)Instructions burned: 295 (million)
% 4.91/1.69 % (3201655)Instruction limit reached!
% 4.91/1.69 % (3201655)------------------------------
% 4.91/1.69 % (3201655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.69 % (3201655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.69 % (3201655)CaDiCaL version: 2.1.3
% 4.91/1.69 % (3201655)Termination reason: Instruction limit
% 4.91/1.69 % (3201655)Termination phase: Saturation
% 4.91/1.69 % (3201655)Time elapsed: 0.072 s
% 4.91/1.69 % (3201655)Peak memory usage: 91 MB
% 4.91/1.69 % (3201655)Instructions burned: 129 (million)
% 4.91/1.69 % (3201630)Refutation found. Thanks to Tanya!
% 4.91/1.69 % SZS status Theorem for theBenchmark
% 4.91/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 6.34/1.88 % (3201630)------------------------------
% 6.34/1.88 % (3201630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.88 % (3201630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.88 % (3201630)CaDiCaL version: 2.1.3
% 6.34/1.88 % (3201630)Termination reason: Refutation
% 6.34/1.88 % (3201630)Time elapsed: 0.552 s
% 6.34/1.88 % (3201630)Peak memory usage: 142 MB
% 6.34/1.88 % (3201630)Instructions burned: 1322 (million)
% 6.34/1.88 % (3201630)------------------------------
% 6.34/1.88 % (3201630)------------------------------
% 6.34/1.88 % (3201624)Success in time 0.831 s
% 6.34/1.88 % Vampire exiting
%------------------------------------------------------------------------------