%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU356+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 : n015.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 12:48:30 PM UTC 2026
% Result : Theorem 10.11s 2.11s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 141 ( 11 unt; 10 def)
% Number of atoms : 747 ( 33 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1044 ( 438 ~; 468 |; 96 &)
% ( 16 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 185 ( 0 sgn 153 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f143,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( relstr_set_smaller(X0,X1,X3)
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X4)
=> related(X0,X3,X4) ) ) )
=> X3 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_yellow_0) ).
fof(f499,conjecture,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
fof(f500,negated_conjecture,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f499]) ).
fof(f541,axiom,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X1) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
fof(f678,plain,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( ( relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( element(X5,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X5)
=> related(X0,X4,X5) ) ) )
=> X2 = X4 ) ) ) ) ),
inference(rectify,[],[f143]) ).
fof(f904,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f678]) ).
fof(f905,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(flattening,[],[f904]) ).
fof(f1300,plain,
? [X0] :
( ? [X1] :
( ex_sup_of_relstr_set(X0,X1)
<~> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f500]) ).
fof(f1301,plain,
? [X0] :
( ? [X1] :
( ex_sup_of_relstr_set(X0,X1)
<~> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f1300]) ).
fof(f1359,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X1 = X2
| ~ related(X0,X1,X2)
| ~ related(X0,X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f541]) ).
fof(f1360,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X1 = X2
| ~ related(X0,X1,X2)
| ~ related(X0,X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f1359]) ).
fof(f1531,definition,
! [X2,X1,X0] :
( sP5(X2,X1,X0)
<=> ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f1532,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& sP5(X2,X1,X0) ) )
| ~ rel_str(X0) ),
inference(definition_folding,[],[f905,f1531]) ).
fof(f1819,plain,
! [X2,X1,X0] :
( ( sP5(X2,X1,X0)
| ? [X4] :
( X2 != X4
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& element(X4,the_carrier(X0)) ) )
& ( ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) )
| ~ sP5(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1531]) ).
fof(f1820,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ? [X3] :
( X0 != X3
& relstr_set_smaller(X2,X1,X3)
& ! [X4] :
( related(X2,X3,X4)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(X3,the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_set_smaller(X2,X1,X5)
| ? [X6] :
( ~ related(X2,X5,X6)
& relstr_set_smaller(X2,X1,X6)
& element(X6,the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f1819]) ).
fof(f1821,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ( sK155(X0,X1,X2) != X0
& relstr_set_smaller(X2,X1,sK155(X0,X1,X2))
& ! [X4] :
( related(X2,sK155(X0,X1,X2),X4)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(sK155(X0,X1,X2),the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_set_smaller(X2,X1,X5)
| ( ~ related(X2,X5,sK156(X1,X2,X5))
& relstr_set_smaller(X2,X1,sK156(X1,X2,X5))
& element(sK156(X1,X2,X5),the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP5(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155,sK156]),skolemize(X3,sK155(X0,X1,X2)),skolemize(X6,sK156(X1,X2,X5))],[f1820]) ).
fof(f1822,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ sP5(X2,X1,X0) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& sP5(X2,X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f1532]) ).
fof(f1823,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ sP5(X2,X1,X0) ) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP5(X4,X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(rectify,[],[f1822]) ).
fof(f1824,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK157(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK157(X0,X1,X2))
& element(sK157(X0,X1,X2),the_carrier(X0)) )
| ~ sP5(X2,X1,X0) ) )
& ( ( element(sK158(X0,X1),the_carrier(X0))
& relstr_set_smaller(X0,X1,sK158(X0,X1))
& ! [X5] :
( related(X0,sK158(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP5(sK158(X0,X1),X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157,sK158]),skolemize(X3,sK157(X0,X1,X2)),skolemize(X4,sK158(X0,X1))],[f1823]) ).
fof(f2192,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) )
| ex_sup_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(nnf_transformation,[],[f1301]) ).
fof(f2193,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ex_sup_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(rectify,[],[f2192]) ).
fof(f2194,plain,
( ( ! [X2] :
( ~ element(X2,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X2)
| ( ~ related(sK479,X2,sK481(X2))
& relstr_set_smaller(sK479,sK480,sK481(X2))
& element(sK481(X2),the_carrier(sK479)) ) )
| ~ ex_sup_of_relstr_set(sK479,sK480) )
& ( ( element(sK482,the_carrier(sK479))
& relstr_set_smaller(sK479,sK480,sK482)
& ! [X5] :
( related(sK479,sK482,X5)
| ~ relstr_set_smaller(sK479,sK480,X5)
| ~ element(X5,the_carrier(sK479)) ) )
| ex_sup_of_relstr_set(sK479,sK480) )
& antisymmetric_relstr(sK479)
& rel_str(sK479) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK479,sK480,sK481,sK482]),skolemize(X0,sK479),skolemize(X1,sK480),skolemize(X3,sK481(X2)),skolemize(X4,sK482)],[f2193]) ).
fof(f2757,plain,
! [X2,X0,X1] :
( element(sK155(X0,X1,X2),the_carrier(X2))
| sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
fof(f2758,plain,
! [X2,X0,X1,X4] :
( related(X2,sK155(X0,X1,X2),X4)
| sP5(X0,X1,X2)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) ),
inference(cnf_transformation,[],[f1821]) ).
fof(f2759,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X2,X1,sK155(X0,X1,X2))
| sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
fof(f2760,plain,
! [X2,X0,X1] :
( sK155(X0,X1,X2) != X0
| sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
fof(f2762,plain,
! [X0,X1,X5] :
( related(X0,sK158(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f2763,plain,
! [X0,X1] :
( relstr_set_smaller(X0,X1,sK158(X0,X1))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f2764,plain,
! [X0,X1] :
( element(sK158(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f2765,plain,
! [X2,X0,X1] :
( element(sK157(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP5(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f2766,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,sK157(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP5(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f2767,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK157(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP5(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1824]) ).
fof(f3852,plain,
rel_str(sK479),
inference(cnf_transformation,[],[f2194]) ).
fof(f3853,plain,
antisymmetric_relstr(sK479),
inference(cnf_transformation,[],[f2194]) ).
fof(f3854,plain,
! [X5] :
( related(sK479,sK482,X5)
| ~ relstr_set_smaller(sK479,sK480,X5)
| ~ element(X5,the_carrier(sK479))
| ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3855,plain,
( relstr_set_smaller(sK479,sK480,sK482)
| ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3856,plain,
( element(sK482,the_carrier(sK479))
| ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3857,plain,
! [X2] :
( ~ element(X2,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X2)
| element(sK481(X2),the_carrier(sK479))
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3858,plain,
! [X2] :
( ~ element(X2,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X2)
| relstr_set_smaller(sK479,sK480,sK481(X2))
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3859,plain,
! [X2] :
( ~ element(X2,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X2)
| ~ related(sK479,X2,sK481(X2))
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(cnf_transformation,[],[f2194]) ).
fof(f3918,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,X1)
| ~ related(X0,X1,X2)
| X1 = X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1360]) ).
fof(f5118,definition,
sF511 = the_carrier(sK479),
introduced(definition,[new_symbols(definition,[sF511])],[function_definition]) ).
fof(f5119,plain,
the_carrier(sK479) = sF511,
inference(reorient_equations,[],[f5118]) ).
fof(f5120,plain,
! [X2] :
( ~ element(X2,sF511)
| ~ relstr_set_smaller(sK479,sK480,X2)
| ~ related(sK479,X2,sK481(X2))
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(definition_folding,[],[f3859,f5119]) ).
fof(f5121,plain,
! [X2] :
( ~ element(X2,sF511)
| ~ relstr_set_smaller(sK479,sK480,X2)
| relstr_set_smaller(sK479,sK480,sK481(X2))
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(definition_folding,[],[f3858,f5119]) ).
fof(f5122,plain,
! [X2] :
( ~ element(X2,sF511)
| ~ relstr_set_smaller(sK479,sK480,X2)
| element(sK481(X2),sF511)
| ~ ex_sup_of_relstr_set(sK479,sK480) ),
inference(definition_folding,[],[f3857,f5119,f5119]) ).
fof(f5123,plain,
( element(sK482,sF511)
| ex_sup_of_relstr_set(sK479,sK480) ),
inference(definition_folding,[],[f3856,f5119]) ).
fof(f5124,plain,
! [X5] :
( related(sK479,sK482,X5)
| ~ relstr_set_smaller(sK479,sK480,X5)
| ~ element(X5,sF511)
| ex_sup_of_relstr_set(sK479,sK480) ),
inference(definition_folding,[],[f3854,f5119]) ).
fof(f5165,definition,
( spl512_5
<=> ex_sup_of_relstr_set(sK479,sK480) ),
introduced(definition,[new_symbols(definition,[spl512_5])],[avatar_definition]) ).
fof(f5166,plain,
( ~ ex_sup_of_relstr_set(sK479,sK480)
| spl512_5 ),
inference(avatar_component_clause,[],[f5165]) ).
fof(f5167,plain,
( ex_sup_of_relstr_set(sK479,sK480)
| ~ spl512_5 ),
inference(avatar_component_clause,[],[f5165]) ).
fof(f5169,definition,
( spl512_6
<=> ! [X5] :
( related(sK479,sK482,X5)
| ~ element(X5,sF511)
| ~ relstr_set_smaller(sK479,sK480,X5) ) ),
introduced(definition,[new_symbols(definition,[spl512_6])],[avatar_definition]) ).
fof(f5170,plain,
( ! [X5] :
( ~ relstr_set_smaller(sK479,sK480,X5)
| ~ element(X5,sF511)
| related(sK479,sK482,X5) )
| ~ spl512_6 ),
inference(avatar_component_clause,[],[f5169]) ).
fof(f5171,plain,
( spl512_5
| spl512_6 ),
inference(avatar_split_clause,[],[f5124,f5169,f5165]) ).
fof(f5173,definition,
( spl512_7
<=> relstr_set_smaller(sK479,sK480,sK482) ),
introduced(definition,[new_symbols(definition,[spl512_7])],[avatar_definition]) ).
fof(f5175,plain,
( relstr_set_smaller(sK479,sK480,sK482)
| ~ spl512_7 ),
inference(avatar_component_clause,[],[f5173]) ).
fof(f5176,plain,
( spl512_5
| spl512_7 ),
inference(avatar_split_clause,[],[f3855,f5173,f5165]) ).
fof(f5178,definition,
( spl512_8
<=> element(sK482,sF511) ),
introduced(definition,[new_symbols(definition,[spl512_8])],[avatar_definition]) ).
fof(f5180,plain,
( element(sK482,sF511)
| ~ spl512_8 ),
inference(avatar_component_clause,[],[f5178]) ).
fof(f5181,plain,
( spl512_5
| spl512_8 ),
inference(avatar_split_clause,[],[f5123,f5178,f5165]) ).
fof(f5183,definition,
( spl512_9
<=> ! [X2] :
( ~ element(X2,sF511)
| element(sK481(X2),sF511)
| ~ relstr_set_smaller(sK479,sK480,X2) ) ),
introduced(definition,[new_symbols(definition,[spl512_9])],[avatar_definition]) ).
fof(f5184,plain,
( ! [X2] :
( ~ relstr_set_smaller(sK479,sK480,X2)
| element(sK481(X2),sF511)
| ~ element(X2,sF511) )
| ~ spl512_9 ),
inference(avatar_component_clause,[],[f5183]) ).
fof(f5185,plain,
( ~ spl512_5
| spl512_9 ),
inference(avatar_split_clause,[],[f5122,f5183,f5165]) ).
fof(f5187,definition,
( spl512_10
<=> ! [X2] :
( ~ element(X2,sF511)
| relstr_set_smaller(sK479,sK480,sK481(X2))
| ~ relstr_set_smaller(sK479,sK480,X2) ) ),
introduced(definition,[new_symbols(definition,[spl512_10])],[avatar_definition]) ).
fof(f5188,plain,
( ! [X2] :
( relstr_set_smaller(sK479,sK480,sK481(X2))
| ~ element(X2,sF511)
| ~ relstr_set_smaller(sK479,sK480,X2) )
| ~ spl512_10 ),
inference(avatar_component_clause,[],[f5187]) ).
fof(f5189,plain,
( ~ spl512_5
| spl512_10 ),
inference(avatar_split_clause,[],[f5121,f5187,f5165]) ).
fof(f5191,definition,
( spl512_11
<=> ! [X2] :
( ~ element(X2,sF511)
| ~ related(sK479,X2,sK481(X2))
| ~ relstr_set_smaller(sK479,sK480,X2) ) ),
introduced(definition,[new_symbols(definition,[spl512_11])],[avatar_definition]) ).
fof(f5192,plain,
( ! [X2] :
( ~ related(sK479,X2,sK481(X2))
| ~ element(X2,sF511)
| ~ relstr_set_smaller(sK479,sK480,X2) )
| ~ spl512_11 ),
inference(avatar_component_clause,[],[f5191]) ).
fof(f5193,plain,
( ~ spl512_5
| spl512_11 ),
inference(avatar_split_clause,[],[f5120,f5191,f5165]) ).
fof(f5518,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X0)
| ex_sup_of_relstr_set(sK479,sK480)
| ~ sP5(X0,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK157(sK479,sK480,X0),sF511)
| related(sK479,sK482,sK157(sK479,sK480,X0)) )
| ~ spl512_6 ),
inference(resolution,[],[f2766,f5170]) ).
fof(f5522,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X0)
| ~ sP5(X0,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK157(sK479,sK480,X0),sF511)
| related(sK479,sK482,sK157(sK479,sK480,X0)) )
| spl512_5
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5518,f5166]) ).
fof(f5523,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,X0)
| ~ sP5(X0,sK480,sK479)
| ~ element(sK157(sK479,sK480,X0),sF511)
| related(sK479,sK482,sK157(sK479,sK480,X0)) )
| spl512_5
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5522,f3852]) ).
fof(f5524,plain,
( ! [X0] :
( related(sK479,sK482,sK157(sK479,sK480,X0))
| ~ relstr_set_smaller(sK479,sK480,X0)
| ~ sP5(X0,sK480,sK479)
| ~ element(sK157(sK479,sK480,X0),sF511)
| ~ element(X0,sF511) )
| spl512_5
| ~ spl512_6 ),
inference(forward_demodulation,[],[f5523,f5119]) ).
fof(f5549,plain,
! [X0,X1] :
( element(sK157(sK479,X0,X1),sF511)
| ~ element(X1,sF511)
| ~ relstr_set_smaller(sK479,X0,X1)
| ex_sup_of_relstr_set(sK479,X0)
| ~ sP5(X1,X0,sK479)
| ~ rel_str(sK479) ),
inference(superposition,[],[f2765,f5119]) ).
fof(f5550,plain,
! [X0,X1] :
( element(sK157(sK479,X0,X1),sF511)
| ~ element(X1,sF511)
| ~ relstr_set_smaller(sK479,X0,X1)
| ex_sup_of_relstr_set(sK479,X0)
| ~ sP5(X1,X0,sK479) ),
inference(forward_subsumption_resolution,[],[f5549,f3852]) ).
fof(f5567,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ex_sup_of_relstr_set(sK479,sK480)
| ~ sP5(sK482,sK480,sK479)
| ~ rel_str(sK479)
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ~ sP5(sK482,sK480,sK479)
| ~ element(sK157(sK479,sK480,sK482),sF511)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6 ),
inference(resolution,[],[f2767,f5524]) ).
fof(f5570,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ex_sup_of_relstr_set(sK479,sK480)
| ~ sP5(sK482,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK157(sK479,sK480,sK482),sF511)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6 ),
inference(duplicate_literal_removal,[],[f5567]) ).
fof(f5572,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ex_sup_of_relstr_set(sK479,sK480)
| ~ sP5(sK482,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5570,f5550]) ).
fof(f5574,plain,
( ~ element(sK482,the_carrier(sK479))
| ex_sup_of_relstr_set(sK479,sK480)
| ~ sP5(sK482,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6
| ~ spl512_7 ),
inference(forward_subsumption_resolution,[],[f5572,f5175]) ).
fof(f5575,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ sP5(sK482,sK480,sK479)
| ~ rel_str(sK479)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6
| ~ spl512_7 ),
inference(forward_subsumption_resolution,[],[f5574,f5166]) ).
fof(f5576,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ sP5(sK482,sK480,sK479)
| ~ element(sK482,sF511)
| spl512_5
| ~ spl512_6
| ~ spl512_7 ),
inference(forward_subsumption_resolution,[],[f5575,f3852]) ).
fof(f5577,plain,
( ~ element(sK482,the_carrier(sK479))
| ~ sP5(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5576,f5180]) ).
fof(f5578,plain,
( ~ element(sK482,sF511)
| ~ sP5(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_demodulation,[],[f5577,f5119]) ).
fof(f5579,plain,
( ~ sP5(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5578,f5180]) ).
fof(f5580,plain,
! [X0] :
( element(sK158(sK479,X0),sF511)
| ~ ex_sup_of_relstr_set(sK479,X0)
| ~ rel_str(sK479) ),
inference(superposition,[],[f2764,f5119]) ).
fof(f5581,plain,
! [X0] :
( element(sK158(sK479,X0),sF511)
| ~ ex_sup_of_relstr_set(sK479,X0) ),
inference(forward_subsumption_resolution,[],[f5580,f3852]) ).
fof(f5635,plain,
( ! [X0] :
( related(sK479,sK482,sK155(X0,sK480,sK479))
| ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479) )
| ~ spl512_6 ),
inference(resolution,[],[f2759,f5170]) ).
fof(f5641,plain,
( ! [X0] :
( ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sK482 = sK155(X0,sK480,sK479)
| ~ element(sK482,the_carrier(sK479))
| ~ element(sK155(X0,sK480,sK479),the_carrier(sK479))
| ~ antisymmetric_relstr(sK479)
| ~ rel_str(sK479) )
| ~ spl512_6 ),
inference(resolution,[],[f5635,f3918]) ).
fof(f5643,plain,
( ! [X0] :
( ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sK482 = sK155(X0,sK480,sK479)
| ~ element(sK482,the_carrier(sK479))
| ~ element(sK155(X0,sK480,sK479),the_carrier(sK479))
| ~ rel_str(sK479) )
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5641,f3853]) ).
fof(f5644,plain,
( ! [X0] :
( ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sK482 = sK155(X0,sK480,sK479)
| ~ element(sK482,the_carrier(sK479))
| ~ element(sK155(X0,sK480,sK479),the_carrier(sK479)) )
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5643,f3852]) ).
fof(f5645,plain,
( ! [X0] :
( ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sK482 = sK155(X0,sK480,sK479)
| ~ element(sK482,the_carrier(sK479)) )
| ~ spl512_6 ),
inference(forward_subsumption_resolution,[],[f5644,f2757]) ).
fof(f5646,plain,
( ! [X0] :
( ~ element(sK482,sF511)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6 ),
inference(forward_demodulation,[],[f5645,f5119]) ).
fof(f5647,plain,
( ! [X0] :
( ~ related(sK479,sK155(X0,sK480,sK479),sK482)
| sP5(X0,sK480,sK479)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5646,f5180]) ).
fof(f5649,plain,
( ! [X0] :
( sP5(X0,sK480,sK479)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sK482 = sK155(X0,sK480,sK479)
| sP5(X0,sK480,sK479)
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ~ element(sK482,the_carrier(sK479)) )
| ~ spl512_6
| ~ spl512_8 ),
inference(resolution,[],[f5647,f2758]) ).
fof(f5650,plain,
( ! [X0] :
( sP5(X0,sK480,sK479)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sK482 = sK155(X0,sK480,sK479)
| ~ relstr_set_smaller(sK479,sK480,sK482)
| ~ element(sK482,the_carrier(sK479)) )
| ~ spl512_6
| ~ spl512_8 ),
inference(duplicate_literal_removal,[],[f5649]) ).
fof(f5652,plain,
( ! [X0] :
( sP5(X0,sK480,sK479)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sK482 = sK155(X0,sK480,sK479)
| ~ element(sK482,the_carrier(sK479)) )
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5650,f5175]) ).
fof(f5653,plain,
( ! [X0] :
( ~ element(sK482,sF511)
| sP5(X0,sK480,sK479)
| ~ element(sK155(X0,sK480,sK479),sF511)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_demodulation,[],[f5652,f5119]) ).
fof(f5654,plain,
( ! [X0] :
( ~ element(sK155(X0,sK480,sK479),sF511)
| sP5(X0,sK480,sK479)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5653,f5180]) ).
fof(f5669,plain,
! [X0,X1] :
( element(sK155(X0,X1,sK479),sF511)
| sP5(X0,X1,sK479) ),
inference(superposition,[],[f2757,f5119]) ).
fof(f5820,plain,
( ! [X0] :
( sP5(X0,sK480,sK479)
| sP5(X0,sK480,sK479)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(resolution,[],[f5669,f5654]) ).
fof(f5822,plain,
( ! [X0] :
( sP5(X0,sK480,sK479)
| sK482 = sK155(X0,sK480,sK479) )
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(duplicate_literal_removal,[],[f5820]) ).
fof(f5825,plain,
( sK482 = sK155(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(resolution,[],[f5822,f5579]) ).
fof(f5829,plain,
( sK482 != sK482
| sP5(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(superposition,[],[f2760,f5825]) ).
fof(f5833,plain,
( sP5(sK482,sK480,sK479)
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(trivial_inequality_removal,[],[f5829]) ).
fof(f5836,plain,
( $false
| spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(forward_subsumption_resolution,[],[f5833,f5579]) ).
fof(f5837,plain,
( spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(avatar_contradiction_clause,[],[f5836]) ).
fof(f5850,definition,
( spl512_79
<=> element(sK158(sK479,sK480),sF511) ),
introduced(definition,[new_symbols(definition,[spl512_79])],[avatar_definition]) ).
fof(f5851,plain,
( element(sK158(sK479,sK480),sF511)
| ~ spl512_79 ),
inference(avatar_component_clause,[],[f5850]) ).
fof(f5852,plain,
( ~ element(sK158(sK479,sK480),sF511)
| spl512_79 ),
inference(avatar_component_clause,[],[f5850]) ).
fof(f5871,plain,
( ! [X0] :
( ~ element(sK158(sK479,X0),sF511)
| ~ relstr_set_smaller(sK479,sK480,sK158(sK479,X0))
| ~ relstr_set_smaller(sK479,X0,sK481(sK158(sK479,X0)))
| ~ element(sK481(sK158(sK479,X0)),the_carrier(sK479))
| ~ ex_sup_of_relstr_set(sK479,X0)
| ~ rel_str(sK479) )
| ~ spl512_11 ),
inference(resolution,[],[f5192,f2762]) ).
fof(f5874,plain,
( ! [X0] :
( ~ element(sK158(sK479,X0),sF511)
| ~ relstr_set_smaller(sK479,sK480,sK158(sK479,X0))
| ~ relstr_set_smaller(sK479,X0,sK481(sK158(sK479,X0)))
| ~ element(sK481(sK158(sK479,X0)),the_carrier(sK479))
| ~ ex_sup_of_relstr_set(sK479,X0) )
| ~ spl512_11 ),
inference(forward_subsumption_resolution,[],[f5871,f3852]) ).
fof(f5876,plain,
( ! [X0] :
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,X0))
| ~ relstr_set_smaller(sK479,X0,sK481(sK158(sK479,X0)))
| ~ element(sK481(sK158(sK479,X0)),the_carrier(sK479))
| ~ ex_sup_of_relstr_set(sK479,X0) )
| ~ spl512_11 ),
inference(forward_subsumption_resolution,[],[f5874,f5581]) ).
fof(f5877,plain,
( ! [X0] :
( ~ relstr_set_smaller(sK479,X0,sK481(sK158(sK479,X0)))
| ~ relstr_set_smaller(sK479,sK480,sK158(sK479,X0))
| ~ element(sK481(sK158(sK479,X0)),sF511)
| ~ ex_sup_of_relstr_set(sK479,X0) )
| ~ spl512_11 ),
inference(forward_demodulation,[],[f5876,f5119]) ).
fof(f5919,plain,
( ~ ex_sup_of_relstr_set(sK479,sK480)
| spl512_79 ),
inference(resolution,[],[f5852,f5581]) ).
fof(f5920,plain,
( $false
| ~ spl512_5
| spl512_79 ),
inference(forward_subsumption_resolution,[],[f5919,f5167]) ).
fof(f5921,plain,
( ~ spl512_5
| spl512_79 ),
inference(avatar_contradiction_clause,[],[f5920]) ).
fof(f5969,plain,
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ element(sK481(sK158(sK479,sK480)),sF511)
| ~ ex_sup_of_relstr_set(sK479,sK480)
| ~ element(sK158(sK479,sK480),sF511)
| ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ spl512_10
| ~ spl512_11 ),
inference(resolution,[],[f5877,f5188]) ).
fof(f5972,plain,
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ element(sK481(sK158(sK479,sK480)),sF511)
| ~ ex_sup_of_relstr_set(sK479,sK480)
| ~ element(sK158(sK479,sK480),sF511)
| ~ spl512_10
| ~ spl512_11 ),
inference(duplicate_literal_removal,[],[f5969]) ).
fof(f5986,plain,
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ ex_sup_of_relstr_set(sK479,sK480)
| ~ element(sK158(sK479,sK480),sF511)
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11 ),
inference(forward_subsumption_resolution,[],[f5972,f5184]) ).
fof(f5987,plain,
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ element(sK158(sK479,sK480),sF511)
| ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11 ),
inference(forward_subsumption_resolution,[],[f5986,f5167]) ).
fof(f5988,plain,
( ~ relstr_set_smaller(sK479,sK480,sK158(sK479,sK480))
| ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(forward_subsumption_resolution,[],[f5987,f5851]) ).
fof(f5989,plain,
( ~ ex_sup_of_relstr_set(sK479,sK480)
| ~ rel_str(sK479)
| ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(resolution,[],[f5988,f2763]) ).
fof(f5990,plain,
( ~ rel_str(sK479)
| ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(forward_subsumption_resolution,[],[f5989,f5167]) ).
fof(f5991,plain,
( $false
| ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(forward_subsumption_resolution,[],[f5990,f3852]) ).
fof(f5992,plain,
( ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(avatar_contradiction_clause,[],[f5991]) ).
cnf(s3,plain,
( spl512_5
| spl512_6 ),
inference(sat_conversion,[],[f5171]) ).
cnf(s4,plain,
( spl512_5
| spl512_7 ),
inference(sat_conversion,[],[f5176]) ).
cnf(s5,plain,
( spl512_5
| spl512_8 ),
inference(sat_conversion,[],[f5181]) ).
cnf(s6,plain,
( ~ spl512_5
| spl512_9 ),
inference(sat_conversion,[],[f5185]) ).
cnf(s7,plain,
( ~ spl512_5
| spl512_10 ),
inference(sat_conversion,[],[f5189]) ).
cnf(s8,plain,
( ~ spl512_5
| spl512_11 ),
inference(sat_conversion,[],[f5193]) ).
cnf(s62,plain,
( spl512_5
| ~ spl512_6
| ~ spl512_7
| ~ spl512_8 ),
inference(sat_conversion,[],[f5837]) ).
cnf(s65,plain,
( ~ spl512_5
| spl512_79 ),
inference(sat_conversion,[],[f5921]) ).
cnf(s69,plain,
( ~ spl512_5
| ~ spl512_9
| ~ spl512_10
| ~ spl512_11
| ~ spl512_79 ),
inference(sat_conversion,[],[f5992]) ).
cnf(s70,plain,
spl512_5,
inference(rat,[],[s62,s3,s4,s5]) ).
cnf(s71,plain,
spl512_79,
inference(rat,[],[s65,s70]) ).
cnf(s72,plain,
spl512_11,
inference(rat,[],[s8,s70]) ).
cnf(s73,plain,
spl512_10,
inference(rat,[],[s7,s70]) ).
cnf(s74,plain,
spl512_9,
inference(rat,[],[s6,s70]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s69,s71,s72,s70,s73,s74]) ).
fof(f5993,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU356+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:56:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 10.11/2.11 % (2265339)Detected formulas, will run a generic FOF schedule.
% 10.11/2.11 % (2265350)dis-21_1_sil=8000:lcm=predicate:random_seed=2842970407: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)
% 10.11/2.11 % (2265348)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1707397615:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.11/2.11 % (2265347)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3432532825:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.11/2.11 % (2265344)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=2433356557:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.11/2.11 % (2265346)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=2336972413:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.11/2.11 % (2265345)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=720514428:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.11/2.11 % (2265349)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2183551358:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.11/2.11 % (2265347)Instruction limit reached!
% 10.11/2.11 % (2265347)------------------------------
% 10.11/2.11 % (2265347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265347)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265347)Termination reason: Instruction limit
% 10.11/2.11 % (2265347)Termination phase: Saturation
% 10.11/2.11 % (2265347)Time elapsed: 0.058 s
% 10.11/2.11 % (2265347)Peak memory usage: 91 MB
% 10.11/2.11 % (2265347)Instructions burned: 110 (million)
% 10.11/2.11 % (2265350)Instruction limit reached!
% 10.11/2.11 % (2265350)------------------------------
% 10.11/2.11 % (2265350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265350)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265350)Termination reason: Instruction limit
% 10.11/2.11 % (2265350)Termination phase: Saturation
% 10.11/2.11 % (2265350)Time elapsed: 0.066 s
% 10.11/2.11 % (2265350)Peak memory usage: 91 MB
% 10.11/2.11 % (2265350)Instructions burned: 131 (million)
% 10.11/2.11 % (2265348)Instruction limit reached!
% 10.11/2.11 % (2265348)------------------------------
% 10.11/2.11 % (2265348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265348)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265348)Termination reason: Instruction limit
% 10.11/2.11 % (2265348)Termination phase: Saturation
% 10.11/2.11 % (2265348)Time elapsed: 0.073 s
% 10.11/2.11 % (2265348)Peak memory usage: 91 MB
% 10.11/2.11 % (2265348)Instructions burned: 119 (million)
% 10.11/2.11 % (2265349)Instruction limit reached!
% 10.11/2.11 % (2265349)------------------------------
% 10.11/2.11 % (2265349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265349)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265349)Termination reason: Instruction limit
% 10.11/2.11 % (2265349)Termination phase: Saturation
% 10.11/2.11 % (2265349)Time elapsed: 0.087 s
% 10.11/2.11 % (2265349)Peak memory usage: 92 MB
% 10.11/2.11 % (2265349)Instructions burned: 139 (million)
% 10.11/2.11 % (2265359)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1848457965:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.11/2.11 % (2265358)lrs+10_1_sil=8000:sp=occurrence:random_seed=4005608451:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.11/2.11 % (2265359)Refutation not found, incomplete strategy
% 10.11/2.11 % (2265359)------------------------------
% 10.11/2.11 % (2265359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265359)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265359)Termination reason: Refutation not found, incomplete strategy
% 10.11/2.11 % (2265359)Time elapsed: 0.010 s
% 10.11/2.11 % (2265359)Peak memory usage: 89 MB
% 10.11/2.11 % (2265359)Instructions burned: 14 (million)
% 10.11/2.11 % (2265360)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2837231251:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.11/2.11 % (2265361)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=2532433526:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.11/2.11 % (2265361)Instruction limit reached!
% 10.11/2.11 % (2265361)------------------------------
% 10.11/2.11 % (2265361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265361)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265361)Termination reason: Instruction limit
% 10.11/2.11 % (2265361)Termination phase: Saturation
% 10.11/2.11 % (2265361)Time elapsed: 0.099 s
% 10.11/2.11 % (2265361)Peak memory usage: 95 MB
% 10.11/2.11 % (2265361)Instructions burned: 250 (million)
% 10.11/2.11 % (2265358)Instruction limit reached!
% 10.11/2.11 % (2265358)------------------------------
% 10.11/2.11 % (2265358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265358)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265358)Termination reason: Instruction limit
% 10.11/2.11 % (2265358)Termination phase: Saturation
% 10.11/2.11 % (2265358)Time elapsed: 0.183 s
% 10.11/2.11 % (2265358)Peak memory usage: 95 MB
% 10.11/2.11 % (2265358)Instructions burned: 285 (million)
% 10.11/2.11 % (2265366)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1196447115:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.11/2.11 % (2265360)Instruction limit reached!
% 10.11/2.11 % (2265360)------------------------------
% 10.11/2.11 % (2265360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265360)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265360)Termination reason: Instruction limit
% 10.11/2.11 % (2265360)Termination phase: Saturation
% 10.11/2.11 % (2265360)Time elapsed: 0.218 s
% 10.11/2.11 % (2265360)Peak memory usage: 95 MB
% 10.11/2.11 % (2265360)Instructions burned: 325 (million)
% 10.11/2.11 % (2265359)------------------------------
% 10.11/2.11 % (2265359)------------------------------
% 10.11/2.11 % (2265366)Instruction limit reached!
% 10.11/2.11 % (2265366)------------------------------
% 10.11/2.11 % (2265366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265366)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265366)Termination reason: Instruction limit
% 10.11/2.11 % (2265366)Termination phase: Saturation
% 10.11/2.11 % (2265366)Time elapsed: 0.100 s
% 10.11/2.11 % (2265366)Peak memory usage: 93 MB
% 10.11/2.11 % (2265366)Instructions burned: 295 (million)
% 10.11/2.11 % (2265367)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=757426257:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.11/2.11 % (2265369)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2607589111:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.11/2.11 % (2265370)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2533415836:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 10.11/2.11 % (2265371)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3321197051:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.11/2.11 % (2265369)Instruction limit reached!
% 10.11/2.11 % (2265369)------------------------------
% 10.11/2.11 % (2265369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265369)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265369)Termination reason: Instruction limit
% 10.11/2.11 % (2265369)Termination phase: Saturation
% 10.11/2.11 % (2265369)Time elapsed: 0.065 s
% 10.11/2.11 % (2265369)Peak memory usage: 92 MB
% 10.11/2.11 % (2265369)Instructions burned: 113 (million)
% 10.11/2.11 % (2265371)Instruction limit reached!
% 10.11/2.11 % (2265371)------------------------------
% 10.11/2.11 % (2265371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265371)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265371)Termination reason: Instruction limit
% 10.11/2.11 % (2265371)Termination phase: Saturation
% 10.11/2.11 % (2265371)Time elapsed: 0.036 s
% 10.11/2.11 % (2265371)Peak memory usage: 90 MB
% 10.11/2.11 % (2265371)Instructions burned: 114 (million)
% 10.11/2.11 % (2265370)Instruction limit reached!
% 10.11/2.11 % (2265370)------------------------------
% 10.11/2.11 % (2265370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265370)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265370)Termination reason: Instruction limit
% 10.11/2.11 % (2265370)Termination phase: Saturation
% 10.11/2.11 % (2265370)Time elapsed: 0.071 s
% 10.11/2.11 % (2265370)Peak memory usage: 91 MB
% 10.11/2.11 % (2265370)Instructions burned: 128 (million)
% 10.11/2.11 % (2265376)lrs+10_1_sil=8000:sp=occurrence:random_seed=1109999345:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.11/2.11 % (2265377)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1901251431:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 10.11/2.11 % (2265378)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=542437113:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 10.11/2.11 % (2265376)Instruction limit reached!
% 10.11/2.11 % (2265376)------------------------------
% 10.11/2.11 % (2265376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265376)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265376)Termination reason: Instruction limit
% 10.11/2.11 % (2265376)Termination phase: Saturation
% 10.11/2.11 % (2265376)Time elapsed: 0.313 s
% 10.11/2.11 % (2265376)Peak memory usage: 104 MB
% 10.11/2.11 % (2265376)Instructions burned: 910 (million)
% 10.11/2.11 % (2265377)Instruction limit reached!
% 10.11/2.11 % (2265377)------------------------------
% 10.11/2.11 % (2265377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265377)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265377)Termination reason: Instruction limit
% 10.11/2.11 % (2265377)Termination phase: Saturation
% 10.11/2.11 % (2265377)Time elapsed: 0.269 s
% 10.11/2.11 % (2265377)Peak memory usage: 96 MB
% 10.11/2.11 % (2265377)Instructions burned: 438 (million)
% 10.11/2.11 % (2265344)First to succeed.
% 10.11/2.11 % (2265344)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2265339"
% 10.11/2.11 % (2265382)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=870720170:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.11/2.11 % (2265382)Instruction limit reached!
% 10.11/2.11 % (2265382)------------------------------
% 10.11/2.11 % (2265382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.11 % (2265382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.11 % (2265382)CaDiCaL version: 2.1.3
% 10.11/2.11 % (2265382)Termination reason: Instruction limit
% 10.11/2.11 % (2265382)Termination phase: Saturation
% 10.11/2.11 % (2265382)Time elapsed: 0.038 s
% 10.11/2.11 % (2265382)Peak memory usage: 92 MB
% 10.11/2.11 % (2265382)Instructions burned: 135 (million)
% 10.11/2.11 % (2265383)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2527347418:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 10.11/2.11 % (2265385)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2359927207:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 10.11/2.11 % (2265344)Refutation found. Thanks to Tanya!
% 10.11/2.11 % SZS status Theorem for theBenchmark
% 10.11/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.20 % (2265344)------------------------------
% 0.17/2.20 % (2265344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.20 % (2265344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.20 % (2265344)CaDiCaL version: 2.1.3
% 0.17/2.20 % (2265344)Termination reason: Refutation
% 0.17/2.20 % (2265344)Time elapsed: 1.077 s
% 0.17/2.20 % (2265344)Peak memory usage: 161 MB
% 0.17/2.20 % (2265344)Instructions burned: 1720 (million)
% 0.17/2.20 % (2265344)------------------------------
% 0.17/2.20 % (2265344)------------------------------
% 0.17/2.20 % (2265339)Success in time 1.487 s
% 0.17/2.20 % Vampire exiting
%------------------------------------------------------------------------------