%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU359+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:53:00 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 141 ( 12 unt; 9 def)
% Number of atoms : 621 ( 46 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 767 ( 287 ~; 386 |; 46 &)
% ( 15 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 130 ( 0 sgn 119 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( ex_sup_of_relstr_set(X0,X1)
=> ( X2 = join_on_relstr(X0,X1)
<=> ( 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',d9_yellow_0) ).
fof(f2,axiom,
! [X0,X1] :
( rel_str(X0)
=> element(join_on_relstr(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(f10,axiom,
! [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(f11,conjecture,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
=> ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) ) )
& ( ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) )
=> ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).
fof(f12,negated_conjecture,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
=> ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) ) )
& ( ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) )
=> ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
=> ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) ) )
& ( ( relstr_set_smaller(X0,X2,X1)
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X4)
=> related(X0,X1,X4) ) ) )
=> ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) ) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f16,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = join_on_relstr(X0,X1)
<=> ( 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)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = join_on_relstr(X0,X1)
<=> ( 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)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f19,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,[],[f10]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ( ~ relstr_set_smaller(X0,X2,X1)
| ? [X3] :
( ~ related(X0,X1,X3)
& relstr_set_smaller(X0,X2,X3)
& element(X3,the_carrier(X0)) ) )
& X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
| ( ( join_on_relstr(X0,X2) != X1
| ~ ex_sup_of_relstr_set(X0,X2) )
& relstr_set_smaller(X0,X2,X1)
& ! [X4] :
( related(X0,X1,X4)
| ~ relstr_set_smaller(X0,X2,X4)
| ~ element(X4,the_carrier(X0)) ) ) )
& element(X1,the_carrier(X0)) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f22,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ( ~ relstr_set_smaller(X0,X2,X1)
| ? [X3] :
( ~ related(X0,X1,X3)
& relstr_set_smaller(X0,X2,X3)
& element(X3,the_carrier(X0)) ) )
& X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
| ( ( join_on_relstr(X0,X2) != X1
| ~ ex_sup_of_relstr_set(X0,X2) )
& relstr_set_smaller(X0,X2,X1)
& ! [X4] :
( related(X0,X1,X4)
| ~ relstr_set_smaller(X0,X2,X4)
| ~ element(X4,the_carrier(X0)) ) ) )
& element(X1,the_carrier(X0)) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| element(sK0(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| relstr_set_smaller(X0,X1,sK0(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ related(X0,X2,sK0(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3)
| join_on_relstr(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( ~ rel_str(X0)
| element(join_on_relstr(X0,X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| element(sK4(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| relstr_set_smaller(X0,X1,sK4(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ related(X0,X2,sK4(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| sK6 != join_on_relstr(sK5,sK7)
| element(sK8,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK6) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| sK6 != join_on_relstr(sK5,sK7)
| relstr_set_smaller(sK5,sK7,sK8)
| ~ relstr_set_smaller(sK5,sK7,sK6) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| sK6 != join_on_relstr(sK5,sK7)
| ~ related(sK5,sK6,sK8)
| ~ relstr_set_smaller(sK5,sK7,sK6) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X4] :
( ~ element(X4,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X4)
| related(sK5,sK6,X4)
| sK6 = join_on_relstr(sK5,sK7) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X4] :
( ~ element(X4,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X4)
| related(sK5,sK6,X4)
| ex_sup_of_relstr_set(sK5,sK7) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| ex_sup_of_relstr_set(sK5,sK7) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
element(sK6,the_carrier(sK5)),
inference(cnf_transformation,[],[f22]) ).
fof(f48,plain,
rel_str(sK5),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
antisymmetric_relstr(sK5),
inference(cnf_transformation,[],[f22]) ).
fof(f50,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| relstr_set_smaller(X0,X1,join_on_relstr(X0,X1)) ),
inference(equality_resolution,[],[f27]) ).
fof(f51,plain,
! [X3,X0,X1] :
( ~ rel_str(X0)
| ~ element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,join_on_relstr(X0,X1),X3) ),
inference(equality_resolution,[],[f26]) ).
fof(f52,plain,
! [X0,X1] :
( rel_str(X0)
| element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| relstr_set_smaller(X0,X1,join_on_relstr(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f53,plain,
! [X3,X0,X1] :
( rel_str(X0)
| element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,join_on_relstr(X0,X1),X3) ),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ ex_sup_of_relstr_set(X0,X1)
| element(X2,the_carrier(X0))
| rel_str(X0)
| ~ related(X0,X2,sK0(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f55,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,sK0(X0,X1,X2))
| element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ element(sK0(X0,X1,X2),the_carrier(X0))
| element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| join_on_relstr(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(join_on_relstr(X0,X1),the_carrier(X0))
| rel_str(X0) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK4(X0,X1,X2))
| antisymmetric_relstr(X0)
| rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f64,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,sK4(X0,X1,X2))
| antisymmetric_relstr(X0)
| rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ element(sK4(X0,X1,X2),the_carrier(X0))
| antisymmetric_relstr(X0)
| rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f66,plain,
~ antisymmetric_relstr(sK5),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f67,plain,
~ rel_str(sK5),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f68,plain,
~ element(sK6,the_carrier(sK5)),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f69,plain,
! [X4] :
( element(X4,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X4)
| related(sK5,sK6,X4)
| ex_sup_of_relstr_set(sK5,sK7) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f70,plain,
! [X4] :
( element(X4,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X4)
| related(sK5,sK6,X4)
| sK6 = join_on_relstr(sK5,sK7) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f74,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| sK6 != join_on_relstr(sK5,sK7)
| ~ element(sK8,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK6) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f76,definition,
( spl9_1
<=> relstr_set_smaller(sK5,sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f77,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl9_2
<=> element(sK8,the_carrier(sK5)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f84,definition,
( spl9_3
<=> sK6 = join_on_relstr(sK5,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f85,plain,
( sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( sK6 != join_on_relstr(sK5,sK7)
| spl9_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl9_4
<=> ex_sup_of_relstr_set(sK5,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f89,plain,
( ex_sup_of_relstr_set(sK5,sK7)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f74,f88,f84,f80,f76]) ).
fof(f93,definition,
( spl9_5
<=> relstr_set_smaller(sK5,sK7,sK8) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f95,plain,
( relstr_set_smaller(sK5,sK7,sK8)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( ~ spl9_1
| spl9_5
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f38,f88,f84,f93,f76]) ).
fof(f98,definition,
( spl9_6
<=> related(sK5,sK6,sK8) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f100,plain,
( ~ related(sK5,sK6,sK8)
| spl9_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( ~ spl9_1
| ~ spl9_6
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f39,f88,f84,f98,f76]) ).
fof(f103,definition,
( spl9_7
<=> ! [X4] :
( element(X4,the_carrier(sK5))
| related(sK5,sK6,X4)
| ~ relstr_set_smaller(sK5,sK7,X4) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f104,plain,
( ! [X4] :
( related(sK5,sK6,X4)
| element(X4,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X4) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f108,plain,
( spl9_3
| spl9_7 ),
inference(avatar_split_clause,[],[f70,f103,f84]) ).
fof(f109,plain,
( spl9_4
| spl9_7 ),
inference(avatar_split_clause,[],[f69,f103,f88]) ).
fof(f110,plain,
( spl9_4
| spl9_1 ),
inference(avatar_split_clause,[],[f45,f76,f88]) ).
fof(f111,plain,
( spl9_3
| spl9_1 ),
inference(avatar_split_clause,[],[f46,f76,f84]) ).
fof(f113,plain,
! [X0,X1] :
( relstr_set_smaller(X0,X1,join_on_relstr(X0,X1))
| ~ ex_sup_of_relstr_set(X0,X1)
| rel_str(X0) ),
inference(forward_subsumption_resolution,[],[f52,f57]) ).
fof(f114,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| ~ ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| ~ spl9_3 ),
inference(superposition,[],[f113,f85]) ).
fof(f119,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| rel_str(sK5)
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f114,f89]) ).
fof(f120,plain,
( relstr_set_smaller(sK5,sK7,sK6)
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f119,f67]) ).
fof(f121,plain,
( spl9_1
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f120,f88,f84,f76]) ).
fof(f125,plain,
! [X3,X0,X1] :
( ~ ex_sup_of_relstr_set(X0,X1)
| rel_str(X0)
| element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,join_on_relstr(X0,X1),X3) ),
inference(forward_subsumption_resolution,[],[f53,f57]) ).
fof(f126,plain,
( ! [X0] :
( rel_str(sK5)
| element(X0,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X0)
| related(sK5,join_on_relstr(sK5,sK7),X0) )
| ~ spl9_4 ),
inference(resolution,[],[f125,f89]) ).
fof(f127,plain,
( ! [X0] :
( related(sK5,join_on_relstr(sK5,sK7),X0)
| ~ relstr_set_smaller(sK5,sK7,X0)
| element(X0,the_carrier(sK5)) )
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f126,f67]) ).
fof(f128,plain,
( ! [X0] :
( related(sK5,sK6,X0)
| element(X0,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X0) )
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_demodulation,[],[f127,f85]) ).
fof(f129,plain,
( spl9_7
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f128,f88,f84,f103]) ).
fof(f130,plain,
( element(sK8,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK8)
| spl9_6
| ~ spl9_7 ),
inference(resolution,[],[f104,f100]) ).
fof(f131,plain,
( ! [X0] :
( element(sK4(sK5,X0,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK4(sK5,X0,sK6))
| antisymmetric_relstr(sK5)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,X0,sK6)
| element(sK6,the_carrier(sK5))
| ex_sup_of_relstr_set(sK5,X0) )
| ~ spl9_7 ),
inference(resolution,[],[f104,f63]) ).
fof(f132,plain,
( ! [X0] :
( element(sK4(sK5,X0,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK4(sK5,X0,sK6))
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,X0,sK6)
| element(sK6,the_carrier(sK5))
| ex_sup_of_relstr_set(sK5,X0) )
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f131,f66]) ).
fof(f134,plain,
( ! [X0] :
( element(sK4(sK5,X0,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK4(sK5,X0,sK6))
| ~ relstr_set_smaller(sK5,X0,sK6)
| element(sK6,the_carrier(sK5))
| ex_sup_of_relstr_set(sK5,X0) )
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f132,f67]) ).
fof(f137,plain,
( ! [X0] :
( ~ relstr_set_smaller(sK5,sK7,sK4(sK5,X0,sK6))
| element(sK4(sK5,X0,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,X0,sK6)
| ex_sup_of_relstr_set(sK5,X0) )
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f134,f68]) ).
fof(f138,plain,
( element(sK8,the_carrier(sK5))
| ~ spl9_5
| spl9_6
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f130,f95]) ).
fof(f139,plain,
( spl9_2
| ~ spl9_5
| spl9_6
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f138,f103,f98,f93,f80]) ).
fof(f151,plain,
( element(sK4(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK6)
| ex_sup_of_relstr_set(sK5,sK7)
| antisymmetric_relstr(sK5)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| element(sK6,the_carrier(sK5))
| ex_sup_of_relstr_set(sK5,sK7)
| ~ spl9_7 ),
inference(resolution,[],[f137,f64]) ).
fof(f152,plain,
( element(sK4(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK6)
| ex_sup_of_relstr_set(sK5,sK7)
| antisymmetric_relstr(sK5)
| rel_str(sK5)
| element(sK6,the_carrier(sK5))
| ~ spl9_7 ),
inference(duplicate_literal_removal,[],[f151]) ).
fof(f153,plain,
( ! [X0] :
( element(X0,the_carrier(sK5))
| rel_str(sK5)
| ~ related(sK5,X0,sK0(sK5,sK7,X0))
| ~ relstr_set_smaller(sK5,sK7,X0)
| join_on_relstr(sK5,sK7) = X0 )
| ~ spl9_4 ),
inference(resolution,[],[f54,f89]) ).
fof(f154,plain,
( ! [X0] :
( ~ related(sK5,X0,sK0(sK5,sK7,X0))
| element(X0,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,X0)
| join_on_relstr(sK5,sK7) = X0 )
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f153,f67]) ).
fof(f155,plain,
( element(sK6,the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| element(sK0(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6))
| ~ spl9_4
| ~ spl9_7 ),
inference(resolution,[],[f154,f104]) ).
fof(f159,plain,
( ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| element(sK0(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6))
| ~ spl9_4
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f155,f68]) ).
fof(f161,plain,
( sK6 = join_on_relstr(sK5,sK7)
| element(sK0(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6))
| ~ spl9_1
| ~ spl9_4
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f159,f77]) ).
fof(f162,plain,
( element(sK0(sK5,sK7,sK6),the_carrier(sK5))
| ~ relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6))
| ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f161,f86]) ).
fof(f164,definition,
( spl9_10
<=> relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f166,plain,
( ~ relstr_set_smaller(sK5,sK7,sK0(sK5,sK7,sK6))
| spl9_10 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl9_11
<=> element(sK0(sK5,sK7,sK6),the_carrier(sK5)) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f170,plain,
( element(sK0(sK5,sK7,sK6),the_carrier(sK5))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( ~ spl9_10
| spl9_11
| ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f162,f103,f88,f84,f76,f168,f164]) ).
fof(f175,plain,
( element(sK6,the_carrier(sK5))
| ~ ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| spl9_10 ),
inference(resolution,[],[f166,f55]) ).
fof(f176,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f175,f68]) ).
fof(f177,plain,
( rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_4
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f176,f89]) ).
fof(f178,plain,
( ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_4
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f177,f67]) ).
fof(f179,plain,
( sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_1
| ~ spl9_4
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f178,f77]) ).
fof(f180,plain,
( $false
| ~ spl9_1
| spl9_3
| ~ spl9_4
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f179,f86]) ).
fof(f181,plain,
( ~ spl9_1
| spl9_3
| ~ spl9_4
| spl9_10 ),
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f182,plain,
( element(sK6,the_carrier(sK5))
| ~ ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_11 ),
inference(resolution,[],[f170,f56]) ).
fof(f183,plain,
( ~ ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f182,f68]) ).
fof(f184,plain,
( rel_str(sK5)
| ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_4
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f183,f89]) ).
fof(f185,plain,
( ~ relstr_set_smaller(sK5,sK7,sK6)
| sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_4
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f184,f67]) ).
fof(f186,plain,
( sK6 = join_on_relstr(sK5,sK7)
| ~ spl9_1
| ~ spl9_4
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f185,f77]) ).
fof(f187,plain,
( $false
| ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f186,f86]) ).
fof(f188,plain,
( ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f189,plain,
( ~ relstr_set_smaller(sK5,sK7,sK6)
| ex_sup_of_relstr_set(sK5,sK7)
| antisymmetric_relstr(sK5)
| rel_str(sK5)
| element(sK6,the_carrier(sK5))
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f152,f65]) ).
fof(f190,plain,
( ex_sup_of_relstr_set(sK5,sK7)
| antisymmetric_relstr(sK5)
| rel_str(sK5)
| element(sK6,the_carrier(sK5))
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f189,f77]) ).
fof(f191,plain,
( ex_sup_of_relstr_set(sK5,sK7)
| rel_str(sK5)
| element(sK6,the_carrier(sK5))
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f190,f66]) ).
fof(f192,plain,
( ex_sup_of_relstr_set(sK5,sK7)
| element(sK6,the_carrier(sK5))
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f191,f67]) ).
fof(f193,plain,
( ex_sup_of_relstr_set(sK5,sK7)
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f192,f68]) ).
fof(f194,plain,
( spl9_4
| ~ spl9_1
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f193,f103,f76,f88]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( ~ spl9_1
| ~ spl9_3
| ~ spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
( ~ spl9_1
| ~ spl9_3
| ~ spl9_4
| ~ spl9_6 ),
inference(sat_conversion,[],[f101]) ).
cnf(s7,plain,
( spl9_3
| spl9_7 ),
inference(sat_conversion,[],[f108]) ).
cnf(s8,plain,
( spl9_4
| spl9_7 ),
inference(sat_conversion,[],[f109]) ).
cnf(s9,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s10,plain,
( spl9_1
| spl9_3 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( spl9_1
| ~ spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f121]) ).
cnf(s13,plain,
( ~ spl9_3
| ~ spl9_4
| spl9_7 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl9_2
| ~ spl9_5
| spl9_6
| ~ spl9_7 ),
inference(sat_conversion,[],[f139]) ).
cnf(s17,plain,
( ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_10
| spl9_11 ),
inference(sat_conversion,[],[f171]) ).
cnf(s18,plain,
( ~ spl9_1
| spl9_3
| ~ spl9_4
| spl9_10 ),
inference(sat_conversion,[],[f181]) ).
cnf(s19,plain,
( ~ spl9_1
| spl9_3
| ~ spl9_4
| ~ spl9_11 ),
inference(sat_conversion,[],[f188]) ).
cnf(s20,plain,
( ~ spl9_1
| spl9_4
| ~ spl9_7 ),
inference(sat_conversion,[],[f194]) ).
cnf(s21,plain,
spl9_1,
inference(rat,[],[s12,s9,s10]) ).
cnf(s22,plain,
( ~ spl9_4
| ~ spl9_3
| spl9_2 ),
inference(rat,[],[s15,s3,s13,s2,s21]) ).
cnf(s23,plain,
spl9_4,
inference(rat,[],[s20,s8,s21]) ).
cnf(s24,plain,
spl9_3,
inference(rat,[],[s17,s7,s18,s19,s21,s23]) ).
cnf(s25,plain,
~ spl9_2,
inference(rat,[],[s1,s23,s21,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s22,s23,s25,s24]) ).
fof(f195,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU359+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:54:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.46 % (4159787)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (4159793)% WARNING: option uhcvi not known.
% 0.11/0.46 % (4159795)dis+10_1_sil=32000:sp=arity:random_seed=1722002083:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (4159792)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1648989074_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (4159798)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4178320492:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (4159794)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4116447575:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (4159796)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1267357902:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (4159797)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4154672185:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (4159793)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=880223484:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % (4159793) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4159787-4159793"...
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % (4159795) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4159787-4159795"...
% 0.11/0.46 % (4159793)...printing done.
% 0.11/0.46 % (4159793)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (4159793)------------------------------
% 0.11/0.46 % (4159793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (4159793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (4159793)CaDiCaL version: 2.1.3
% 0.11/0.46 % (4159793)Termination reason: Refutation
% 0.11/0.46 % (4159793)Time elapsed: 0.004 s
% 0.11/0.46 % (4159793)Peak memory usage: 13 MB
% 0.11/0.46 % (4159793)Instructions burned: 9 (million)
% 0.11/0.46 % (4159787)Success in time 0.038 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------