%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU360+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 : n007.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 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 115 ( 16 unt; 6 def)
% Number of atoms : 446 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 581 ( 250 ~; 261 |; 35 &)
% ( 17 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 7 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 141 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ( lower_bounded_relstr(X0)
<=> ? [X1] :
( element(X1,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f13,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f19,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(f20,axiom,
! [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(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ( ex_sup_of_relstr_set(X0,empty_set)
& ex_inf_of_relstr_set(X0,the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ( ex_sup_of_relstr_set(X0,empty_set)
& ex_inf_of_relstr_set(X0,the_carrier(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f26,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f32,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
<=> ? [X1] :
( element(X1,the_carrier(X0))
& relstr_element_smaller(X0,the_carrier(X0),X1) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f36]) ).
fof(f38,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,[],[f19]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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,[],[f20]) ).
fof(f41,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,[],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
? [X0] :
( ( ~ ex_sup_of_relstr_set(X0,empty_set)
| ~ ex_inf_of_relstr_set(X0,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f46,plain,
? [X0] :
( ( ~ ex_sup_of_relstr_set(X0,empty_set)
| ~ ex_inf_of_relstr_set(X0,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f52,plain,
! [X0] :
( ~ lower_bounded_relstr(X0)
| relstr_element_smaller(X0,the_carrier(X0),sK0(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X0] :
( ~ lower_bounded_relstr(X0)
| element(sK0(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( related(X0,X2,X3)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ relstr_set_smaller(X0,X1,X2)
| ~ antisymmetric_relstr(X0)
| element(sK10(X0,X1,X2),the_carrier(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK10(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(cnf_transformation,[],[f39]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| element(sK12(X0,X1,X2),the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| relstr_element_smaller(X0,X1,sK12(X0,X1,X2))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ related(X0,sK12(X0,X1,X2),X2)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1] :
( in(X0,X1)
| ~ element(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f84,plain,
( ~ ex_inf_of_relstr_set(sK13,the_carrier(sK13))
| ~ ex_sup_of_relstr_set(sK13,empty_set) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
rel_str(sK13),
inference(cnf_transformation,[],[f46]) ).
fof(f86,plain,
lower_bounded_relstr(sK13),
inference(cnf_transformation,[],[f46]) ).
fof(f87,plain,
antisymmetric_relstr(sK13),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
~ empty_carrier(sK13),
inference(cnf_transformation,[],[f46]) ).
fof(f91,plain,
! [X0,X1] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f95,definition,
( spl14_1
<=> ex_sup_of_relstr_set(sK13,empty_set) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f97,plain,
( ~ ex_sup_of_relstr_set(sK13,empty_set)
| spl14_1 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl14_2
<=> ex_inf_of_relstr_set(sK13,the_carrier(sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f101,plain,
( ~ ex_inf_of_relstr_set(sK13,the_carrier(sK13))
| spl14_2 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f84,f99,f95]) ).
fof(f106,plain,
( ~ one_sorted_str(sK13)
| ~ empty(the_carrier(sK13)) ),
inference(resolution,[],[f63,f88]) ).
fof(f110,definition,
( spl14_3
<=> empty(the_carrier(sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f112,plain,
( ~ empty(the_carrier(sK13))
| spl14_3 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,definition,
( spl14_4
<=> one_sorted_str(sK13) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f116,plain,
( ~ one_sorted_str(sK13)
| spl14_4 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f106,f114,f110]) ).
fof(f128,plain,
( element(sK0(sK13),the_carrier(sK13))
| ~ rel_str(sK13) ),
inference(resolution,[],[f53,f86]) ).
fof(f129,plain,
element(sK0(sK13),the_carrier(sK13)),
inference(forward_subsumption_resolution,[],[f128,f85]) ).
fof(f130,plain,
( relstr_element_smaller(sK13,the_carrier(sK13),sK0(sK13))
| ~ rel_str(sK13) ),
inference(resolution,[],[f52,f86]) ).
fof(f131,plain,
relstr_element_smaller(sK13,the_carrier(sK13),sK0(sK13)),
inference(forward_subsumption_resolution,[],[f130,f85]) ).
fof(f238,plain,
! [X0,X1] :
( ~ antisymmetric_relstr(X0)
| element(sK10(X0,empty_set,X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ex_sup_of_relstr_set(X0,empty_set)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[],[f70,f91]) ).
fof(f241,plain,
! [X0,X1] :
( ex_sup_of_relstr_set(X0,empty_set)
| element(sK10(X0,empty_set,X1),the_carrier(X0))
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ antisymmetric_relstr(X0) ),
inference(duplicate_literal_removal,[],[f238]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(sK10(X0,X1,X2),the_carrier(X0))
| ~ in(sK10(X0,X1,X2),X3)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X3,X2) ),
inference(resolution,[],[f72,f55]) ).
fof(f259,plain,
! [X2,X3,X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ element(sK10(X0,X1,X2),the_carrier(X0))
| ~ in(sK10(X0,X1,X2),X3)
| ~ relstr_element_smaller(X0,X3,X2) ),
inference(duplicate_literal_removal,[],[f256]) ).
fof(f261,plain,
! [X2,X3,X0,X1] :
( ~ relstr_set_smaller(X0,X1,X2)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ in(sK10(X0,X1,X2),X3)
| ~ relstr_element_smaller(X0,X3,X2) ),
inference(forward_subsumption_resolution,[],[f259,f70]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1)
| ~ element(sK12(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ in(X2,X3)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X3,sK12(X0,X1,X2)) ),
inference(resolution,[],[f78,f55]) ).
fof(f295,plain,
! [X2,X3,X0,X1] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1)
| ~ element(sK12(X0,X1,X2),the_carrier(X0))
| ~ in(X2,X3)
| ~ relstr_element_smaller(X0,X3,sK12(X0,X1,X2)) ),
inference(duplicate_literal_removal,[],[f292]) ).
fof(f297,plain,
! [X2,X3,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ in(X2,X3)
| ~ relstr_element_smaller(X0,X3,sK12(X0,X1,X2)) ),
inference(forward_subsumption_resolution,[],[f295,f76]) ).
fof(f389,plain,
( ! [X0] :
( ~ antisymmetric_relstr(sK13)
| relstr_element_smaller(sK13,the_carrier(sK13),sK12(sK13,the_carrier(sK13),X0))
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13))
| ~ rel_str(sK13) )
| spl14_2 ),
inference(resolution,[],[f101,f77]) ).
fof(f392,plain,
( ! [X0] :
( relstr_element_smaller(sK13,the_carrier(sK13),sK12(sK13,the_carrier(sK13),X0))
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13))
| ~ rel_str(sK13) )
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f389,f87]) ).
fof(f394,plain,
( ! [X0] :
( relstr_element_smaller(sK13,the_carrier(sK13),sK12(sK13,the_carrier(sK13),X0))
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13)) )
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f392,f85]) ).
fof(f537,plain,
( ~ rel_str(sK13)
| spl14_4 ),
inference(resolution,[],[f116,f59]) ).
fof(f538,plain,
( $false
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f537,f85]) ).
fof(f539,plain,
spl14_4,
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f558,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ element(X1,the_carrier(X0))
| ex_sup_of_relstr_set(X0,empty_set)
| ~ in(sK10(X0,empty_set,X1),X2)
| ~ relstr_element_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[],[f261,f91]) ).
fof(f563,plain,
! [X2,X0,X1] :
( ex_sup_of_relstr_set(X0,empty_set)
| ~ antisymmetric_relstr(X0)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ in(sK10(X0,empty_set,X1),X2)
| ~ relstr_element_smaller(X0,X2,X1) ),
inference(duplicate_literal_removal,[],[f558]) ).
fof(f611,plain,
( ! [X0,X1] :
( ~ rel_str(sK13)
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13))
| ~ antisymmetric_relstr(sK13)
| ~ in(X0,X1)
| ~ relstr_element_smaller(sK13,X1,sK12(sK13,the_carrier(sK13),X0)) )
| spl14_2 ),
inference(resolution,[],[f297,f101]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13))
| ~ antisymmetric_relstr(sK13)
| ~ in(X0,X1)
| ~ relstr_element_smaller(sK13,X1,sK12(sK13,the_carrier(sK13),X0)) )
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f611,f85]) ).
fof(f615,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ element(X0,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ relstr_element_smaller(sK13,X1,sK12(sK13,the_carrier(sK13),X0)) )
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f614,f87]) ).
fof(f655,plain,
( ! [X0,X1] :
( empty(X1)
| ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ relstr_element_smaller(sK13,X1,sK12(sK13,the_carrier(sK13),X0))
| ~ element(X0,X1)
| ~ element(X0,the_carrier(sK13)) )
| spl14_2 ),
inference(resolution,[],[f615,f83]) ).
fof(f905,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ relstr_element_smaller(sK13,the_carrier(sK13),sK12(sK13,the_carrier(sK13),X0))
| ~ element(X0,the_carrier(sK13))
| ~ element(X0,the_carrier(sK13)) )
| spl14_2
| spl14_3 ),
inference(resolution,[],[f655,f112]) ).
fof(f908,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ relstr_element_smaller(sK13,the_carrier(sK13),sK12(sK13,the_carrier(sK13),X0))
| ~ element(X0,the_carrier(sK13)) )
| spl14_2
| spl14_3 ),
inference(duplicate_literal_removal,[],[f905]) ).
fof(f909,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13)) )
| spl14_2
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f908,f394]) ).
fof(f919,plain,
( ~ element(sK0(sK13),the_carrier(sK13))
| spl14_2
| spl14_3 ),
inference(resolution,[],[f909,f131]) ).
fof(f935,plain,
( $false
| spl14_2
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f919,f129]) ).
fof(f936,plain,
( spl14_2
| spl14_3 ),
inference(avatar_contradiction_clause,[],[f935]) ).
fof(f957,definition,
( spl14_70
<=> ! [X0] :
( ~ element(X0,the_carrier(sK13))
| element(sK10(sK13,empty_set,X0),the_carrier(sK13)) ) ),
introduced(definition,[new_symbols(definition,[spl14_70])],[avatar_definition]) ).
fof(f958,plain,
( ! [X0] :
( element(sK10(sK13,empty_set,X0),the_carrier(sK13))
| ~ element(X0,the_carrier(sK13)) )
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f961,definition,
( spl14_71
<=> ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13)) ) ),
introduced(definition,[new_symbols(definition,[spl14_71])],[avatar_definition]) ).
fof(f962,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13)) )
| ~ spl14_71 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f968,plain,
( ! [X0,X1] :
( ~ antisymmetric_relstr(sK13)
| ~ element(X0,the_carrier(sK13))
| ~ rel_str(sK13)
| ~ in(sK10(sK13,empty_set,X0),X1)
| ~ relstr_element_smaller(sK13,X1,X0) )
| spl14_1 ),
inference(resolution,[],[f97,f563]) ).
fof(f970,plain,
( ! [X0] :
( element(sK10(sK13,empty_set,X0),the_carrier(sK13))
| ~ rel_str(sK13)
| ~ element(X0,the_carrier(sK13))
| ~ antisymmetric_relstr(sK13) )
| spl14_1 ),
inference(resolution,[],[f97,f241]) ).
fof(f971,plain,
( ! [X0] :
( element(sK10(sK13,empty_set,X0),the_carrier(sK13))
| ~ element(X0,the_carrier(sK13))
| ~ antisymmetric_relstr(sK13) )
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f970,f85]) ).
fof(f973,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(sK13))
| ~ rel_str(sK13)
| ~ in(sK10(sK13,empty_set,X0),X1)
| ~ relstr_element_smaller(sK13,X1,X0) )
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f968,f87]) ).
fof(f974,plain,
( ! [X0] :
( element(sK10(sK13,empty_set,X0),the_carrier(sK13))
| ~ element(X0,the_carrier(sK13)) )
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f971,f87]) ).
fof(f976,plain,
( ! [X0,X1] :
( ~ in(sK10(sK13,empty_set,X0),X1)
| ~ element(X0,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X1,X0) )
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f973,f85]) ).
fof(f977,plain,
( spl14_70
| spl14_1 ),
inference(avatar_split_clause,[],[f974,f95,f957]) ).
fof(f1110,plain,
( ! [X0,X1] :
( empty(X1)
| ~ relstr_element_smaller(sK13,X1,X0)
| ~ element(sK10(sK13,empty_set,X0),X1)
| ~ element(X0,the_carrier(sK13)) )
| spl14_1 ),
inference(resolution,[],[f976,f83]) ).
fof(f1119,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(sK10(sK13,empty_set,X0),the_carrier(sK13))
| ~ element(X0,the_carrier(sK13)) )
| spl14_1
| spl14_3 ),
inference(resolution,[],[f1110,f112]) ).
fof(f1122,plain,
( ! [X0] :
( ~ relstr_element_smaller(sK13,the_carrier(sK13),X0)
| ~ element(X0,the_carrier(sK13)) )
| spl14_1
| spl14_3
| ~ spl14_70 ),
inference(forward_subsumption_resolution,[],[f1119,f958]) ).
fof(f1123,plain,
( spl14_71
| spl14_1
| spl14_3
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1122,f957,f110,f95,f961]) ).
fof(f1131,plain,
( ~ element(sK0(sK13),the_carrier(sK13))
| ~ spl14_71 ),
inference(resolution,[],[f962,f131]) ).
fof(f1149,plain,
( $false
| ~ spl14_71 ),
inference(forward_subsumption_resolution,[],[f1131,f129]) ).
fof(f1150,plain,
~ spl14_71,
inference(avatar_contradiction_clause,[],[f1149]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f102]) ).
cnf(s2,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f117]) ).
cnf(s44,plain,
spl14_4,
inference(sat_conversion,[],[f539]) ).
cnf(s64,plain,
( spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f936]) ).
cnf(s69,plain,
( spl14_1
| spl14_70 ),
inference(sat_conversion,[],[f977]) ).
cnf(s86,plain,
( spl14_1
| spl14_3
| ~ spl14_70
| spl14_71 ),
inference(sat_conversion,[],[f1123]) ).
cnf(s88,plain,
~ spl14_71,
inference(sat_conversion,[],[f1150]) ).
cnf(s92,plain,
( spl14_1
| spl14_3
| ~ spl14_70 ),
inference(rat,[],[s86,s88]) ).
cnf(s94,plain,
~ spl14_3,
inference(rat,[],[s2,s44]) ).
cnf(s95,plain,
spl14_2,
inference(rat,[],[s64,s94]) ).
cnf(s96,plain,
~ spl14_1,
inference(rat,[],[s1,s95]) ).
cnf(s97,plain,
~ spl14_70,
inference(rat,[],[s92,s94,s96]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s69,s97,s96]) ).
fof(f1153,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:52:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.47 % (2031648)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2031657)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2921714071:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2031654)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2031653)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=823495399_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (2031654)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1595638680:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2031655)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2619888703:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2031656)dis+10_1_sil=32000:sp=arity:random_seed=1187187698:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2031659)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=90994216:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (2031658)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3220165053:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (2031657) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2031648-2031657"...
% 0.16/0.47 % (2031657)...printing done.
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (2031657)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2031657)------------------------------
% 0.16/0.47 % (2031657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2031657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2031657)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2031657)Termination reason: Refutation
% 0.16/0.47 % (2031657)Time elapsed: 0.017 s
% 0.16/0.47 % (2031657)Peak memory usage: 13 MB
% 0.16/0.47 % (2031657)Instructions burned: 44 (million)
% 0.16/0.47 % (2031648)Success in time 0.047 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------