%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU357+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 : n004.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 12:48:31 PM UTC 2026
% Result : Theorem 10.35s 2.38s
% Output : Refutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 141 ( 11 unt; 10 def)
% Number of atoms : 749 ( 33 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1047 ( 439 ~; 470 |; 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(f153,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) )
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( relstr_element_smaller(X0,X1,X3)
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X4)
=> related(X0,X4,X3) ) ) )
=> X3 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_0) ).
fof(f507,conjecture,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).
fof(f508,negated_conjecture,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f507]) ).
fof(f543,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(f681,plain,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) )
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( ( relstr_element_smaller(X0,X1,X4)
& ! [X5] :
( element(X5,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X5)
=> related(X0,X5,X4) ) ) )
=> X2 = X4 ) ) ) ) ),
inference(rectify,[],[f153]) ).
fof(f924,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_element_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X5,X4)
& relstr_element_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f681]) ).
fof(f925,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_element_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X5,X4)
& relstr_element_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(flattening,[],[f924]) ).
fof(f1314,plain,
? [X0] :
( ? [X1] :
( ex_inf_of_relstr_set(X0,X1)
<~> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f508]) ).
fof(f1315,plain,
? [X0] :
( ? [X1] :
( ex_inf_of_relstr_set(X0,X1)
<~> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f1314]) ).
fof(f1366,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,[],[f543]) ).
fof(f1367,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,[],[f1366]) ).
fof(f1540,definition,
! [X2,X1,X0] :
( sP6(X2,X1,X0)
<=> ! [X4] :
( X2 = X4
| ~ relstr_element_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X5,X4)
& relstr_element_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f1541,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& sP6(X2,X1,X0) ) )
| ~ rel_str(X0) ),
inference(definition_folding,[],[f925,f1540]) ).
fof(f1854,plain,
! [X2,X1,X0] :
( ( sP6(X2,X1,X0)
| ? [X4] :
( X2 != X4
& relstr_element_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& element(X4,the_carrier(X0)) ) )
& ( ! [X4] :
( X2 = X4
| ~ relstr_element_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X5,X4)
& relstr_element_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) )
| ~ sP6(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1540]) ).
fof(f1855,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ? [X3] :
( X0 != X3
& relstr_element_smaller(X2,X1,X3)
& ! [X4] :
( related(X2,X4,X3)
| ~ relstr_element_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(X3,the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_element_smaller(X2,X1,X5)
| ? [X6] :
( ~ related(X2,X6,X5)
& relstr_element_smaller(X2,X1,X6)
& element(X6,the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f1854]) ).
fof(f1856,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ( sK173(X0,X1,X2) != X0
& relstr_element_smaller(X2,X1,sK173(X0,X1,X2))
& ! [X4] :
( related(X2,X4,sK173(X0,X1,X2))
| ~ relstr_element_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(sK173(X0,X1,X2),the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_element_smaller(X2,X1,X5)
| ( ~ related(X2,sK174(X1,X2,X5),X5)
& relstr_element_smaller(X2,X1,sK174(X1,X2,X5))
& element(sK174(X1,X2,X5),the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP6(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173,sK174]),skolemize(X3,sK173(X0,X1,X2)),skolemize(X6,sK174(X1,X2,X5))],[f1855]) ).
fof(f1857,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ sP6(X2,X1,X0) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& sP6(X2,X1,X0) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f1541]) ).
fof(f1858,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ sP6(X2,X1,X0) ) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_element_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP6(X4,X1,X0) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(rectify,[],[f1857]) ).
fof(f1859,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ( ~ related(X0,sK175(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK175(X0,X1,X2))
& element(sK175(X0,X1,X2),the_carrier(X0)) )
| ~ sP6(X2,X1,X0) ) )
& ( ( element(sK176(X0,X1),the_carrier(X0))
& relstr_element_smaller(X0,X1,sK176(X0,X1))
& ! [X5] :
( related(X0,X5,sK176(X0,X1))
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP6(sK176(X0,X1),X1,X0) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175,sK176]),skolemize(X3,sK175(X0,X1,X2)),skolemize(X4,sK176(X0,X1))],[f1858]) ).
fof(f2216,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_inf_of_relstr_set(X0,X1) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_element_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) )
| ex_inf_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(nnf_transformation,[],[f1315]) ).
fof(f2217,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_inf_of_relstr_set(X0,X1) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_element_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ex_inf_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(rectify,[],[f2216]) ).
fof(f2218,plain,
( ( ! [X2] :
( ~ element(X2,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X2)
| ( ~ related(sK487,sK489(X2),X2)
& relstr_element_smaller(sK487,sK488,sK489(X2))
& element(sK489(X2),the_carrier(sK487)) ) )
| ~ ex_inf_of_relstr_set(sK487,sK488) )
& ( ( element(sK490,the_carrier(sK487))
& relstr_element_smaller(sK487,sK488,sK490)
& ! [X5] :
( related(sK487,X5,sK490)
| ~ relstr_element_smaller(sK487,sK488,X5)
| ~ element(X5,the_carrier(sK487)) ) )
| ex_inf_of_relstr_set(sK487,sK488) )
& antisymmetric_relstr(sK487)
& rel_str(sK487) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK487,sK488,sK489,sK490]),skolemize(X0,sK487),skolemize(X1,sK488),skolemize(X3,sK489(X2)),skolemize(X4,sK490)],[f2217]) ).
fof(f2824,plain,
! [X2,X0,X1] :
( element(sK173(X0,X1,X2),the_carrier(X2))
| sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1856]) ).
fof(f2825,plain,
! [X2,X0,X1,X4] :
( related(X2,X4,sK173(X0,X1,X2))
| sP6(X0,X1,X2)
| ~ relstr_element_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) ),
inference(cnf_transformation,[],[f1856]) ).
fof(f2826,plain,
! [X2,X0,X1] :
( relstr_element_smaller(X2,X1,sK173(X0,X1,X2))
| sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1856]) ).
fof(f2827,plain,
! [X2,X0,X1] :
( sK173(X0,X1,X2) != X0
| sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1856]) ).
fof(f2829,plain,
! [X0,X1,X5] :
( related(X0,X5,sK176(X0,X1))
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0))
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f2830,plain,
! [X0,X1] :
( relstr_element_smaller(X0,X1,sK176(X0,X1))
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f2831,plain,
! [X0,X1] :
( element(sK176(X0,X1),the_carrier(X0))
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f2832,plain,
! [X2,X0,X1] :
( element(sK175(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ sP6(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f2833,plain,
! [X2,X0,X1] :
( relstr_element_smaller(X0,X1,sK175(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ sP6(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f2834,plain,
! [X2,X0,X1] :
( ~ related(X0,sK175(X0,X1,X2),X2)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ex_inf_of_relstr_set(X0,X1)
| ~ sP6(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f3902,plain,
rel_str(sK487),
inference(cnf_transformation,[],[f2218]) ).
fof(f3903,plain,
antisymmetric_relstr(sK487),
inference(cnf_transformation,[],[f2218]) ).
fof(f3904,plain,
! [X5] :
( related(sK487,X5,sK490)
| ~ relstr_element_smaller(sK487,sK488,X5)
| ~ element(X5,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3905,plain,
( relstr_element_smaller(sK487,sK488,sK490)
| ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3906,plain,
( element(sK490,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3907,plain,
! [X2] :
( ~ element(X2,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X2)
| element(sK489(X2),the_carrier(sK487))
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3908,plain,
! [X2] :
( ~ element(X2,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X2)
| relstr_element_smaller(sK487,sK488,sK489(X2))
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3909,plain,
! [X2] :
( ~ element(X2,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X2)
| ~ related(sK487,sK489(X2),X2)
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3956,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,[],[f1367]) ).
fof(f5156,definition,
sF518 = the_carrier(sK487),
introduced(definition,[new_symbols(definition,[sF518])],[function_definition]) ).
fof(f5157,plain,
the_carrier(sK487) = sF518,
inference(reorient_equations,[],[f5156]) ).
fof(f5158,plain,
! [X2] :
( ~ element(X2,sF518)
| ~ relstr_element_smaller(sK487,sK488,X2)
| ~ related(sK487,sK489(X2),X2)
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(definition_folding,[],[f3909,f5157]) ).
fof(f5159,plain,
! [X2] :
( ~ element(X2,sF518)
| ~ relstr_element_smaller(sK487,sK488,X2)
| relstr_element_smaller(sK487,sK488,sK489(X2))
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(definition_folding,[],[f3908,f5157]) ).
fof(f5160,plain,
! [X2] :
( ~ element(X2,sF518)
| ~ relstr_element_smaller(sK487,sK488,X2)
| element(sK489(X2),sF518)
| ~ ex_inf_of_relstr_set(sK487,sK488) ),
inference(definition_folding,[],[f3907,f5157,f5157]) ).
fof(f5161,plain,
( element(sK490,sF518)
| ex_inf_of_relstr_set(sK487,sK488) ),
inference(definition_folding,[],[f3906,f5157]) ).
fof(f5162,plain,
! [X5] :
( related(sK487,X5,sK490)
| ~ relstr_element_smaller(sK487,sK488,X5)
| ~ element(X5,sF518)
| ex_inf_of_relstr_set(sK487,sK488) ),
inference(definition_folding,[],[f3904,f5157]) ).
fof(f5202,definition,
( spl519_5
<=> ex_inf_of_relstr_set(sK487,sK488) ),
introduced(definition,[new_symbols(definition,[spl519_5])],[avatar_definition]) ).
fof(f5203,plain,
( ~ ex_inf_of_relstr_set(sK487,sK488)
| spl519_5 ),
inference(avatar_component_clause,[],[f5202]) ).
fof(f5204,plain,
( ex_inf_of_relstr_set(sK487,sK488)
| ~ spl519_5 ),
inference(avatar_component_clause,[],[f5202]) ).
fof(f5206,definition,
( spl519_6
<=> ! [X5] :
( related(sK487,X5,sK490)
| ~ element(X5,sF518)
| ~ relstr_element_smaller(sK487,sK488,X5) ) ),
introduced(definition,[new_symbols(definition,[spl519_6])],[avatar_definition]) ).
fof(f5207,plain,
( ! [X5] :
( ~ relstr_element_smaller(sK487,sK488,X5)
| ~ element(X5,sF518)
| related(sK487,X5,sK490) )
| ~ spl519_6 ),
inference(avatar_component_clause,[],[f5206]) ).
fof(f5208,plain,
( spl519_5
| spl519_6 ),
inference(avatar_split_clause,[],[f5162,f5206,f5202]) ).
fof(f5210,definition,
( spl519_7
<=> relstr_element_smaller(sK487,sK488,sK490) ),
introduced(definition,[new_symbols(definition,[spl519_7])],[avatar_definition]) ).
fof(f5212,plain,
( relstr_element_smaller(sK487,sK488,sK490)
| ~ spl519_7 ),
inference(avatar_component_clause,[],[f5210]) ).
fof(f5213,plain,
( spl519_5
| spl519_7 ),
inference(avatar_split_clause,[],[f3905,f5210,f5202]) ).
fof(f5215,definition,
( spl519_8
<=> element(sK490,sF518) ),
introduced(definition,[new_symbols(definition,[spl519_8])],[avatar_definition]) ).
fof(f5217,plain,
( element(sK490,sF518)
| ~ spl519_8 ),
inference(avatar_component_clause,[],[f5215]) ).
fof(f5218,plain,
( spl519_5
| spl519_8 ),
inference(avatar_split_clause,[],[f5161,f5215,f5202]) ).
fof(f5220,definition,
( spl519_9
<=> ! [X2] :
( ~ element(X2,sF518)
| element(sK489(X2),sF518)
| ~ relstr_element_smaller(sK487,sK488,X2) ) ),
introduced(definition,[new_symbols(definition,[spl519_9])],[avatar_definition]) ).
fof(f5221,plain,
( ! [X2] :
( ~ relstr_element_smaller(sK487,sK488,X2)
| element(sK489(X2),sF518)
| ~ element(X2,sF518) )
| ~ spl519_9 ),
inference(avatar_component_clause,[],[f5220]) ).
fof(f5222,plain,
( ~ spl519_5
| spl519_9 ),
inference(avatar_split_clause,[],[f5160,f5220,f5202]) ).
fof(f5224,definition,
( spl519_10
<=> ! [X2] :
( ~ element(X2,sF518)
| relstr_element_smaller(sK487,sK488,sK489(X2))
| ~ relstr_element_smaller(sK487,sK488,X2) ) ),
introduced(definition,[new_symbols(definition,[spl519_10])],[avatar_definition]) ).
fof(f5225,plain,
( ! [X2] :
( relstr_element_smaller(sK487,sK488,sK489(X2))
| ~ element(X2,sF518)
| ~ relstr_element_smaller(sK487,sK488,X2) )
| ~ spl519_10 ),
inference(avatar_component_clause,[],[f5224]) ).
fof(f5226,plain,
( ~ spl519_5
| spl519_10 ),
inference(avatar_split_clause,[],[f5159,f5224,f5202]) ).
fof(f5228,definition,
( spl519_11
<=> ! [X2] :
( ~ element(X2,sF518)
| ~ related(sK487,sK489(X2),X2)
| ~ relstr_element_smaller(sK487,sK488,X2) ) ),
introduced(definition,[new_symbols(definition,[spl519_11])],[avatar_definition]) ).
fof(f5229,plain,
( ! [X2] :
( ~ related(sK487,sK489(X2),X2)
| ~ element(X2,sF518)
| ~ relstr_element_smaller(sK487,sK488,X2) )
| ~ spl519_11 ),
inference(avatar_component_clause,[],[f5228]) ).
fof(f5230,plain,
( ~ spl519_5
| spl519_11 ),
inference(avatar_split_clause,[],[f5158,f5228,f5202]) ).
fof(f5553,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X0)
| ex_inf_of_relstr_set(sK487,sK488)
| ~ sP6(X0,sK488,sK487)
| ~ rel_str(sK487)
| ~ element(sK175(sK487,sK488,X0),sF518)
| related(sK487,sK175(sK487,sK488,X0),sK490) )
| ~ spl519_6 ),
inference(resolution,[],[f2833,f5207]) ).
fof(f5557,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X0)
| ~ sP6(X0,sK488,sK487)
| ~ rel_str(sK487)
| ~ element(sK175(sK487,sK488,X0),sF518)
| related(sK487,sK175(sK487,sK488,X0),sK490) )
| spl519_5
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5553,f5203]) ).
fof(f5558,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,X0)
| ~ sP6(X0,sK488,sK487)
| ~ element(sK175(sK487,sK488,X0),sF518)
| related(sK487,sK175(sK487,sK488,X0),sK490) )
| spl519_5
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5557,f3902]) ).
fof(f5559,plain,
( ! [X0] :
( related(sK487,sK175(sK487,sK488,X0),sK490)
| ~ relstr_element_smaller(sK487,sK488,X0)
| ~ sP6(X0,sK488,sK487)
| ~ element(sK175(sK487,sK488,X0),sF518)
| ~ element(X0,sF518) )
| spl519_5
| ~ spl519_6 ),
inference(forward_demodulation,[],[f5558,f5157]) ).
fof(f5587,plain,
! [X0,X1] :
( element(sK175(sK487,X0,X1),sF518)
| ~ element(X1,sF518)
| ~ relstr_element_smaller(sK487,X0,X1)
| ex_inf_of_relstr_set(sK487,X0)
| ~ sP6(X1,X0,sK487)
| ~ rel_str(sK487) ),
inference(superposition,[],[f2832,f5157]) ).
fof(f5588,plain,
! [X0,X1] :
( element(sK175(sK487,X0,X1),sF518)
| ~ element(X1,sF518)
| ~ relstr_element_smaller(sK487,X0,X1)
| ex_inf_of_relstr_set(sK487,X0)
| ~ sP6(X1,X0,sK487) ),
inference(forward_subsumption_resolution,[],[f5587,f3902]) ).
fof(f5600,plain,
( ~ relstr_element_smaller(sK487,sK488,sK490)
| ~ sP6(sK490,sK488,sK487)
| ~ element(sK175(sK487,sK488,sK490),sF518)
| ~ element(sK490,sF518)
| ~ element(sK490,the_carrier(sK487))
| ~ relstr_element_smaller(sK487,sK488,sK490)
| ex_inf_of_relstr_set(sK487,sK488)
| ~ sP6(sK490,sK488,sK487)
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6 ),
inference(resolution,[],[f5559,f2834]) ).
fof(f5603,plain,
( ~ relstr_element_smaller(sK487,sK488,sK490)
| ~ sP6(sK490,sK488,sK487)
| ~ element(sK175(sK487,sK488,sK490),sF518)
| ~ element(sK490,sF518)
| ~ element(sK490,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488)
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6 ),
inference(duplicate_literal_removal,[],[f5600]) ).
fof(f5606,plain,
( ~ relstr_element_smaller(sK487,sK488,sK490)
| ~ sP6(sK490,sK488,sK487)
| ~ element(sK490,sF518)
| ~ element(sK490,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488)
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5603,f5588]) ).
fof(f5608,plain,
( ~ sP6(sK490,sK488,sK487)
| ~ element(sK490,sF518)
| ~ element(sK490,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488)
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7 ),
inference(forward_subsumption_resolution,[],[f5606,f5212]) ).
fof(f5611,plain,
( ~ sP6(sK490,sK488,sK487)
| ~ element(sK490,the_carrier(sK487))
| ex_inf_of_relstr_set(sK487,sK488)
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5608,f5217]) ).
fof(f5613,plain,
( ~ sP6(sK490,sK488,sK487)
| ~ element(sK490,the_carrier(sK487))
| ~ rel_str(sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5611,f5203]) ).
fof(f5615,plain,
( ~ sP6(sK490,sK488,sK487)
| ~ element(sK490,the_carrier(sK487))
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5613,f3902]) ).
fof(f5616,plain,
( ~ element(sK490,sF518)
| ~ sP6(sK490,sK488,sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_demodulation,[],[f5615,f5157]) ).
fof(f5617,plain,
( ~ sP6(sK490,sK488,sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5616,f5217]) ).
fof(f5659,plain,
! [X0] :
( element(sK176(sK487,X0),sF518)
| ~ ex_inf_of_relstr_set(sK487,X0)
| ~ rel_str(sK487) ),
inference(superposition,[],[f2831,f5157]) ).
fof(f5660,plain,
! [X0] :
( element(sK176(sK487,X0),sF518)
| ~ ex_inf_of_relstr_set(sK487,X0) ),
inference(forward_subsumption_resolution,[],[f5659,f3902]) ).
fof(f5673,plain,
( ! [X0] :
( related(sK487,sK173(X0,sK488,sK487),sK490)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487) )
| ~ spl519_6 ),
inference(resolution,[],[f2826,f5207]) ).
fof(f5679,plain,
( ! [X0] :
( ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sK490 = sK173(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),the_carrier(sK487))
| ~ element(sK490,the_carrier(sK487))
| ~ antisymmetric_relstr(sK487)
| ~ rel_str(sK487) )
| ~ spl519_6 ),
inference(resolution,[],[f5673,f3956]) ).
fof(f5681,plain,
( ! [X0] :
( ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sK490 = sK173(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),the_carrier(sK487))
| ~ element(sK490,the_carrier(sK487))
| ~ rel_str(sK487) )
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5679,f3903]) ).
fof(f5682,plain,
( ! [X0] :
( ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sK490 = sK173(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),the_carrier(sK487))
| ~ element(sK490,the_carrier(sK487)) )
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5681,f3902]) ).
fof(f5683,plain,
( ! [X0] :
( ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sK490 = sK173(X0,sK488,sK487)
| ~ element(sK490,the_carrier(sK487)) )
| ~ spl519_6 ),
inference(forward_subsumption_resolution,[],[f5682,f2824]) ).
fof(f5684,plain,
( ! [X0] :
( ~ element(sK490,sF518)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6 ),
inference(forward_demodulation,[],[f5683,f5157]) ).
fof(f5685,plain,
( ! [X0] :
( ~ related(sK487,sK490,sK173(X0,sK488,sK487))
| sP6(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5684,f5217]) ).
fof(f5687,plain,
( ! [X0] :
( sP6(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sK490 = sK173(X0,sK488,sK487)
| sP6(X0,sK488,sK487)
| ~ relstr_element_smaller(sK487,sK488,sK490)
| ~ element(sK490,the_carrier(sK487)) )
| ~ spl519_6
| ~ spl519_8 ),
inference(resolution,[],[f5685,f2825]) ).
fof(f5688,plain,
( ! [X0] :
( sP6(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sK490 = sK173(X0,sK488,sK487)
| ~ relstr_element_smaller(sK487,sK488,sK490)
| ~ element(sK490,the_carrier(sK487)) )
| ~ spl519_6
| ~ spl519_8 ),
inference(duplicate_literal_removal,[],[f5687]) ).
fof(f5690,plain,
( ! [X0] :
( sP6(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sK490 = sK173(X0,sK488,sK487)
| ~ element(sK490,the_carrier(sK487)) )
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5688,f5212]) ).
fof(f5691,plain,
( ! [X0] :
( ~ element(sK490,sF518)
| sP6(X0,sK488,sK487)
| ~ element(sK173(X0,sK488,sK487),sF518)
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_demodulation,[],[f5690,f5157]) ).
fof(f5692,plain,
( ! [X0] :
( ~ element(sK173(X0,sK488,sK487),sF518)
| sP6(X0,sK488,sK487)
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5691,f5217]) ).
fof(f5715,plain,
! [X0,X1] :
( element(sK173(X0,X1,sK487),sF518)
| sP6(X0,X1,sK487) ),
inference(superposition,[],[f2824,f5157]) ).
fof(f5956,plain,
( ! [X0] :
( sP6(X0,sK488,sK487)
| sP6(X0,sK488,sK487)
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(resolution,[],[f5715,f5692]) ).
fof(f5958,plain,
( ! [X0] :
( sP6(X0,sK488,sK487)
| sK490 = sK173(X0,sK488,sK487) )
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(duplicate_literal_removal,[],[f5956]) ).
fof(f5961,plain,
( sK490 = sK173(sK490,sK488,sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(resolution,[],[f5958,f5617]) ).
fof(f5969,plain,
( sK490 != sK490
| sP6(sK490,sK488,sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(superposition,[],[f2827,f5961]) ).
fof(f5973,plain,
( sP6(sK490,sK488,sK487)
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(trivial_inequality_removal,[],[f5969]) ).
fof(f5976,plain,
( $false
| spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(forward_subsumption_resolution,[],[f5973,f5617]) ).
fof(f5977,plain,
( spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(avatar_contradiction_clause,[],[f5976]) ).
fof(f5990,definition,
( spl519_79
<=> element(sK176(sK487,sK488),sF518) ),
introduced(definition,[new_symbols(definition,[spl519_79])],[avatar_definition]) ).
fof(f5991,plain,
( element(sK176(sK487,sK488),sF518)
| ~ spl519_79 ),
inference(avatar_component_clause,[],[f5990]) ).
fof(f5992,plain,
( ~ element(sK176(sK487,sK488),sF518)
| spl519_79 ),
inference(avatar_component_clause,[],[f5990]) ).
fof(f6011,plain,
( ! [X0] :
( ~ element(sK176(sK487,X0),sF518)
| ~ relstr_element_smaller(sK487,sK488,sK176(sK487,X0))
| ~ relstr_element_smaller(sK487,X0,sK489(sK176(sK487,X0)))
| ~ element(sK489(sK176(sK487,X0)),the_carrier(sK487))
| ~ ex_inf_of_relstr_set(sK487,X0)
| ~ rel_str(sK487) )
| ~ spl519_11 ),
inference(resolution,[],[f5229,f2829]) ).
fof(f6014,plain,
( ! [X0] :
( ~ element(sK176(sK487,X0),sF518)
| ~ relstr_element_smaller(sK487,sK488,sK176(sK487,X0))
| ~ relstr_element_smaller(sK487,X0,sK489(sK176(sK487,X0)))
| ~ element(sK489(sK176(sK487,X0)),the_carrier(sK487))
| ~ ex_inf_of_relstr_set(sK487,X0) )
| ~ spl519_11 ),
inference(forward_subsumption_resolution,[],[f6011,f3902]) ).
fof(f6016,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,X0))
| ~ relstr_element_smaller(sK487,X0,sK489(sK176(sK487,X0)))
| ~ element(sK489(sK176(sK487,X0)),the_carrier(sK487))
| ~ ex_inf_of_relstr_set(sK487,X0) )
| ~ spl519_11 ),
inference(forward_subsumption_resolution,[],[f6014,f5660]) ).
fof(f6017,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK487,X0,sK489(sK176(sK487,X0)))
| ~ relstr_element_smaller(sK487,sK488,sK176(sK487,X0))
| ~ element(sK489(sK176(sK487,X0)),sF518)
| ~ ex_inf_of_relstr_set(sK487,X0) )
| ~ spl519_11 ),
inference(forward_demodulation,[],[f6016,f5157]) ).
fof(f6059,plain,
( ~ ex_inf_of_relstr_set(sK487,sK488)
| spl519_79 ),
inference(resolution,[],[f5992,f5660]) ).
fof(f6060,plain,
( $false
| ~ spl519_5
| spl519_79 ),
inference(forward_subsumption_resolution,[],[f6059,f5204]) ).
fof(f6061,plain,
( ~ spl519_5
| spl519_79 ),
inference(avatar_contradiction_clause,[],[f6060]) ).
fof(f6118,plain,
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ element(sK489(sK176(sK487,sK488)),sF518)
| ~ ex_inf_of_relstr_set(sK487,sK488)
| ~ element(sK176(sK487,sK488),sF518)
| ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ spl519_10
| ~ spl519_11 ),
inference(resolution,[],[f6017,f5225]) ).
fof(f6121,plain,
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ element(sK489(sK176(sK487,sK488)),sF518)
| ~ ex_inf_of_relstr_set(sK487,sK488)
| ~ element(sK176(sK487,sK488),sF518)
| ~ spl519_10
| ~ spl519_11 ),
inference(duplicate_literal_removal,[],[f6118]) ).
fof(f6135,plain,
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ ex_inf_of_relstr_set(sK487,sK488)
| ~ element(sK176(sK487,sK488),sF518)
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11 ),
inference(forward_subsumption_resolution,[],[f6121,f5221]) ).
fof(f6136,plain,
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ element(sK176(sK487,sK488),sF518)
| ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11 ),
inference(forward_subsumption_resolution,[],[f6135,f5204]) ).
fof(f6137,plain,
( ~ relstr_element_smaller(sK487,sK488,sK176(sK487,sK488))
| ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(forward_subsumption_resolution,[],[f6136,f5991]) ).
fof(f6138,plain,
( ~ ex_inf_of_relstr_set(sK487,sK488)
| ~ rel_str(sK487)
| ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(resolution,[],[f6137,f2830]) ).
fof(f6139,plain,
( ~ rel_str(sK487)
| ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(forward_subsumption_resolution,[],[f6138,f5204]) ).
fof(f6140,plain,
( $false
| ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(forward_subsumption_resolution,[],[f6139,f3902]) ).
fof(f6141,plain,
( ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(avatar_contradiction_clause,[],[f6140]) ).
cnf(s3,plain,
( spl519_5
| spl519_6 ),
inference(sat_conversion,[],[f5208]) ).
cnf(s4,plain,
( spl519_5
| spl519_7 ),
inference(sat_conversion,[],[f5213]) ).
cnf(s5,plain,
( spl519_5
| spl519_8 ),
inference(sat_conversion,[],[f5218]) ).
cnf(s6,plain,
( ~ spl519_5
| spl519_9 ),
inference(sat_conversion,[],[f5222]) ).
cnf(s7,plain,
( ~ spl519_5
| spl519_10 ),
inference(sat_conversion,[],[f5226]) ).
cnf(s8,plain,
( ~ spl519_5
| spl519_11 ),
inference(sat_conversion,[],[f5230]) ).
cnf(s62,plain,
( spl519_5
| ~ spl519_6
| ~ spl519_7
| ~ spl519_8 ),
inference(sat_conversion,[],[f5977]) ).
cnf(s65,plain,
( ~ spl519_5
| spl519_79 ),
inference(sat_conversion,[],[f6061]) ).
cnf(s69,plain,
( ~ spl519_5
| ~ spl519_9
| ~ spl519_10
| ~ spl519_11
| ~ spl519_79 ),
inference(sat_conversion,[],[f6141]) ).
cnf(s70,plain,
spl519_5,
inference(rat,[],[s62,s3,s4,s5]) ).
cnf(s71,plain,
spl519_79,
inference(rat,[],[s65,s70]) ).
cnf(s72,plain,
spl519_11,
inference(rat,[],[s8,s70]) ).
cnf(s73,plain,
spl519_10,
inference(rat,[],[s7,s70]) ).
cnf(s74,plain,
spl519_9,
inference(rat,[],[s6,s70]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s69,s71,s72,s70,s73,s74]) ).
fof(f6142,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU357+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.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 04:53:52 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 10.35/2.38 % (4159345)Detected formulas, will run a generic FOF schedule.
% 10.35/2.38 % (4159354)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=354738655:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.35/2.38 % (4159356)dis-21_1_sil=8000:lcm=predicate:random_seed=649451094: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)
% 10.35/2.38 % (4159353)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1421492919:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.35/2.38 % (4159352)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=3616344030:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.35/2.38 % (4159350)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=2871545475:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.35/2.38 % (4159351)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=1909723110:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.35/2.38 % (4159355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=403129767:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.35/2.38 % (4159354)Instruction limit reached!
% 10.35/2.38 % (4159354)------------------------------
% 10.35/2.38 % (4159354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159354)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159354)Termination reason: Instruction limit
% 10.35/2.38 % (4159354)Termination phase: Saturation
% 10.35/2.38 % (4159354)Time elapsed: 0.041 s
% 10.35/2.38 % (4159354)Peak memory usage: 91 MB
% 10.35/2.38 % (4159354)Instructions burned: 120 (million)
% 10.35/2.38 % (4159353)Instruction limit reached!
% 10.35/2.38 % (4159353)------------------------------
% 10.35/2.38 % (4159353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159353)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159353)Termination reason: Instruction limit
% 10.35/2.38 % (4159353)Termination phase: Saturation
% 10.35/2.38 % (4159353)Time elapsed: 0.060 s
% 10.35/2.38 % (4159353)Peak memory usage: 91 MB
% 10.35/2.38 % (4159353)Instructions burned: 110 (million)
% 10.35/2.38 % (4159356)Instruction limit reached!
% 10.35/2.38 % (4159356)------------------------------
% 10.35/2.38 % (4159356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159356)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159356)Termination reason: Instruction limit
% 10.35/2.38 % (4159356)Termination phase: Saturation
% 10.35/2.38 % (4159356)Time elapsed: 0.065 s
% 10.35/2.38 % (4159356)Peak memory usage: 91 MB
% 10.35/2.38 % (4159356)Instructions burned: 129 (million)
% 10.35/2.38 % (4159355)Instruction limit reached!
% 10.35/2.38 % (4159355)------------------------------
% 10.35/2.38 % (4159355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159355)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159355)Termination reason: Instruction limit
% 10.35/2.38 % (4159355)Termination phase: Saturation
% 10.35/2.38 % (4159355)Time elapsed: 0.087 s
% 10.35/2.38 % (4159355)Peak memory usage: 92 MB
% 10.35/2.38 % (4159355)Instructions burned: 139 (million)
% 10.35/2.38 % (4159364)lrs+10_1_sil=8000:sp=occurrence:random_seed=4115680985:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.35/2.38 % (4159365)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1547358704:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.35/2.38 % (4159365)Refutation not found, incomplete strategy
% 10.35/2.38 % (4159365)------------------------------
% 10.35/2.38 % (4159365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159365)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159365)Termination reason: Refutation not found, incomplete strategy
% 10.35/2.38 % (4159365)Time elapsed: 0.005 s
% 10.35/2.38 % (4159365)Peak memory usage: 90 MB
% 10.35/2.38 % (4159365)Instructions burned: 12 (million)
% 10.35/2.38 % (4159366)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1328873656:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.35/2.38 % (4159367)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=3977476019:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.35/2.38 % (4159365)------------------------------
% 10.35/2.38 % (4159365)------------------------------
% 10.35/2.38 % (4159364)Instruction limit reached!
% 10.35/2.38 % (4159364)------------------------------
% 10.35/2.38 % (4159364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159364)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159364)Termination reason: Instruction limit
% 10.35/2.38 % (4159364)Termination phase: Saturation
% 10.35/2.38 % (4159364)Time elapsed: 0.200 s
% 10.35/2.38 % (4159364)Peak memory usage: 95 MB
% 10.35/2.38 % (4159364)Instructions burned: 286 (million)
% 10.35/2.38 % (4159367)Instruction limit reached!
% 10.35/2.38 % (4159367)------------------------------
% 10.35/2.38 % (4159367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159367)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159367)Termination reason: Instruction limit
% 10.35/2.38 % (4159367)Termination phase: Saturation
% 10.35/2.38 % (4159367)Time elapsed: 0.146 s
% 10.35/2.38 % (4159367)Peak memory usage: 94 MB
% 10.35/2.38 % (4159367)Instructions burned: 250 (million)
% 10.35/2.38 % (4159372)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3059432001:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.35/2.38 % (4159366)Instruction limit reached!
% 10.35/2.38 % (4159366)------------------------------
% 10.35/2.38 % (4159366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159366)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159366)Termination reason: Instruction limit
% 10.35/2.38 % (4159366)Termination phase: Saturation
% 10.35/2.38 % (4159366)Time elapsed: 0.218 s
% 10.35/2.38 % (4159366)Peak memory usage: 95 MB
% 10.35/2.38 % (4159366)Instructions burned: 325 (million)
% 10.35/2.38 % (4159373)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=853707092:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 10.35/2.38 % (4159372)Instruction limit reached!
% 10.35/2.38 % (4159372)------------------------------
% 10.35/2.38 % (4159372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159372)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159372)Termination reason: Instruction limit
% 10.35/2.38 % (4159372)Termination phase: Saturation
% 10.35/2.38 % (4159372)Time elapsed: 0.100 s
% 10.35/2.38 % (4159372)Peak memory usage: 93 MB
% 10.35/2.38 % (4159372)Instructions burned: 295 (million)
% 10.35/2.38 % (4159374)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2652935998:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.35/2.38 % (4159376)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1093571120:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 10.35/2.38 % (4159374)Instruction limit reached!
% 10.35/2.38 % (4159374)------------------------------
% 10.35/2.38 % (4159374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159374)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159374)Termination reason: Instruction limit
% 10.35/2.38 % (4159374)Termination phase: Saturation
% 10.35/2.38 % (4159374)Time elapsed: 0.064 s
% 10.35/2.38 % (4159374)Peak memory usage: 92 MB
% 10.35/2.38 % (4159374)Instructions burned: 113 (million)
% 10.35/2.38 % (4159378)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2328034908:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.35/2.38 % (4159376)Instruction limit reached!
% 10.35/2.38 % (4159376)------------------------------
% 10.35/2.38 % (4159376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159376)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159376)Termination reason: Instruction limit
% 10.35/2.38 % (4159376)Termination phase: Saturation
% 10.35/2.38 % (4159376)Time elapsed: 0.070 s
% 10.35/2.38 % (4159376)Peak memory usage: 91 MB
% 10.35/2.38 % (4159376)Instructions burned: 127 (million)
% 10.35/2.38 % (4159378)Instruction limit reached!
% 10.35/2.38 % (4159378)------------------------------
% 10.35/2.38 % (4159378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159378)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159378)Termination reason: Instruction limit
% 10.35/2.38 % (4159378)Termination phase: Saturation
% 10.35/2.38 % (4159378)Time elapsed: 0.037 s
% 10.35/2.38 % (4159378)Peak memory usage: 90 MB
% 10.35/2.38 % (4159378)Instructions burned: 115 (million)
% 10.35/2.38 % (4159381)lrs+10_1_sil=8000:sp=occurrence:random_seed=3952059088:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.35/2.38 % (4159384)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1766590042:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 10.35/2.38 % (4159383)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1695097764:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 10.35/2.38 % (4159383)Instruction limit reached!
% 10.35/2.38 % (4159383)------------------------------
% 10.35/2.38 % (4159383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159383)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159383)Termination reason: Instruction limit
% 10.35/2.38 % (4159383)Termination phase: Saturation
% 10.35/2.38 % (4159383)Time elapsed: 0.268 s
% 10.35/2.38 % (4159383)Peak memory usage: 96 MB
% 10.35/2.38 % (4159383)Instructions burned: 438 (million)
% 10.35/2.38 % (4159350)First to succeed.
% 10.35/2.38 % (4159350)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4159345"
% 10.35/2.38 % (4159388)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1978960228:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.35/2.38 % (4159388)Instruction limit reached!
% 10.35/2.38 % (4159388)------------------------------
% 10.35/2.38 % (4159388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159388)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159388)Termination reason: Instruction limit
% 10.35/2.38 % (4159388)Termination phase: Saturation
% 10.35/2.38 % (4159388)Time elapsed: 0.068 s
% 10.35/2.38 % (4159388)Peak memory usage: 92 MB
% 10.35/2.38 % (4159388)Instructions burned: 135 (million)
% 10.35/2.38 % (4159381)Instruction limit reached!
% 10.35/2.38 % (4159381)------------------------------
% 10.35/2.38 % (4159381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.35/2.38 % (4159381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.35/2.38 % (4159381)CaDiCaL version: 2.1.3
% 10.35/2.38 % (4159381)Termination reason: Instruction limit
% 10.35/2.38 % (4159381)Termination phase: Saturation
% 10.35/2.38 % (4159381)Time elapsed: 0.584 s
% 10.35/2.38 % (4159381)Peak memory usage: 104 MB
% 10.35/2.38 % (4159381)Instructions burned: 907 (million)
% 10.35/2.38 % (4159373)Also succeeded, but the first one will report.
% 10.35/2.38 % (4159390)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1970762114:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 10.35/2.38 % (4159350)Refutation found. Thanks to Tanya!
% 10.35/2.38 % SZS status Theorem for theBenchmark
% 10.35/2.38 % SZS output start Proof for theBenchmark
% See solution above
% 11.11/2.57 % (4159350)------------------------------
% 11.11/2.57 % (4159350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.11/2.57 % (4159350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.11/2.57 % (4159350)CaDiCaL version: 2.1.3
% 11.11/2.57 % (4159350)Termination reason: Refutation
% 11.11/2.57 % (4159350)Time elapsed: 1.085 s
% 11.11/2.57 % (4159350)Peak memory usage: 147 MB
% 11.11/2.57 % (4159350)Instructions burned: 1756 (million)
% 11.11/2.57 % (4159350)------------------------------
% 11.11/2.57 % (4159350)------------------------------
% 11.11/2.57 % (4159345)Success in time 1.515 s
% 11.11/2.57 % Vampire exiting
%------------------------------------------------------------------------------