%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU356+1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:30 PM UTC 2026
% Result : Theorem 2.70s 1.29s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 81 ( 7 unt; 1 def)
% Number of atoms : 510 ( 29 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 715 ( 286 ~; 299 |; 96 &)
% ( 8 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 178 ( 146 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( relstr_set_smaller(X0,X1,X3)
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X4)
=> related(X0,X3,X4) ) ) )
=> X3 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_yellow_0) ).
fof(f9,conjecture,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,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(f12,plain,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( ( relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( element(X5,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X5)
=> related(X0,X4,X5) ) ) )
=> X2 = X4 ) ) ) ) ),
inference(rectify,[],[f1]) ).
fof(f13,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(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ) )
| ~ rel_str(X0) ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,definition,
! [X2,X1,X0] :
( sP0(X2,X1,X0)
<=> ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
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)) )
& sP0(X2,X1,X0) ) )
| ~ rel_str(X0) ),
inference(definition_folding,[],[f16,f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) )
| ex_sup_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(nnf_transformation,[],[f14]) ).
fof(f22,plain,
? [X0] :
( ? [X1] :
( ( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) ) )
| ~ ex_sup_of_relstr_set(X0,X1) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) ) )
| ex_sup_of_relstr_set(X0,X1) ) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
( ( ! [X2] :
( ~ element(X2,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK2,X2)
| ( ~ related(sK1,X2,sK3(X2))
& relstr_set_smaller(sK1,sK2,sK3(X2))
& element(sK3(X2),the_carrier(sK1)) ) )
| ~ ex_sup_of_relstr_set(sK1,sK2) )
& ( ( element(sK4,the_carrier(sK1))
& relstr_set_smaller(sK1,sK2,sK4)
& ! [X5] :
( related(sK1,sK4,X5)
| ~ relstr_set_smaller(sK1,sK2,X5)
| ~ element(X5,the_carrier(sK1)) ) )
| ex_sup_of_relstr_set(sK1,sK2) )
& antisymmetric_relstr(sK1)
& rel_str(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X3,sK3(X2)),skolemize(X4,sK4)],[f22]) ).
fof(f25,plain,
! [X2,X1,X0] :
( ( sP0(X2,X1,X0)
| ? [X4] :
( X2 != X4
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& element(X4,the_carrier(X0)) ) )
& ( ! [X4] :
( X2 = X4
| ~ relstr_set_smaller(X0,X1,X4)
| ? [X5] :
( ~ related(X0,X4,X5)
& relstr_set_smaller(X0,X1,X5)
& element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) )
| ~ sP0(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( X0 != X3
& relstr_set_smaller(X2,X1,X3)
& ! [X4] :
( related(X2,X3,X4)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(X3,the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_set_smaller(X2,X1,X5)
| ? [X6] :
( ~ related(X2,X5,X6)
& relstr_set_smaller(X2,X1,X6)
& element(X6,the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( sK6(X0,X1,X2) != X0
& relstr_set_smaller(X2,X1,sK6(X0,X1,X2))
& ! [X4] :
( related(X2,sK6(X0,X1,X2),X4)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) )
& element(sK6(X0,X1,X2),the_carrier(X2)) ) )
& ( ! [X5] :
( X0 = X5
| ~ relstr_set_smaller(X2,X1,X5)
| ( ~ related(X2,X5,sK7(X1,X2,X5))
& relstr_set_smaller(X2,X1,sK7(X1,X2,X5))
& element(sK7(X1,X2,X5),the_carrier(X2)) )
| ~ element(X5,the_carrier(X2)) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X6,sK7(X1,X2,X5))],[f26]) ).
fof(f28,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)) )
| ~ sP0(X2,X1,X0) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& relstr_set_smaller(X0,X1,X2)
& ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& sP0(X2,X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f20]) ).
fof(f29,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)) )
| ~ sP0(X2,X1,X0) ) )
& ( ? [X4] :
( element(X4,the_carrier(X0))
& relstr_set_smaller(X0,X1,X4)
& ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP0(X4,X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK8(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK8(X0,X1,X2))
& element(sK8(X0,X1,X2),the_carrier(X0)) )
| ~ sP0(X2,X1,X0) ) )
& ( ( element(sK9(X0,X1),the_carrier(X0))
& relstr_set_smaller(X0,X1,sK9(X0,X1))
& ! [X5] :
( related(X0,sK9(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& sP0(sK9(X0,X1),X1,X0) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X4,sK9(X0,X1))],[f29]) ).
fof(f32,plain,
rel_str(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
antisymmetric_relstr(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X5] :
( related(sK1,sK4,X5)
| ~ relstr_set_smaller(sK1,sK2,X5)
| ~ element(X5,the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
( relstr_set_smaller(sK1,sK2,sK4)
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
( element(sK4,the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X2] :
( element(sK3(X2),the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK2,X2)
| ~ element(X2,the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
! [X2] :
( relstr_set_smaller(sK1,sK2,sK3(X2))
| ~ relstr_set_smaller(sK1,sK2,X2)
| ~ element(X2,the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X2] :
( ~ related(sK1,X2,sK3(X2))
| ~ relstr_set_smaller(sK1,sK2,X2)
| ~ element(X2,the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X2,X0,X1] :
( element(sK6(X0,X1,X2),the_carrier(X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( related(X2,sK6(X0,X1,X2),X4)
| sP0(X0,X1,X2)
| ~ relstr_set_smaller(X2,X1,X4)
| ~ element(X4,the_carrier(X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X2,X1,sK6(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != X0
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1,X5] :
( related(X0,sK9(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X1] :
( relstr_set_smaller(X0,X1,sK9(X0,X1))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X0,X1] :
( element(sK9(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X2,X0,X1] :
( element(sK8(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP0(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,sK8(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP0(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK8(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ex_sup_of_relstr_set(X0,X1)
| ~ sP0(X2,X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f56,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,[],[f18]) ).
fof(f65,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,X0,sK3(sK9(sK1,X0)))
| ~ element(sK3(sK9(sK1,X0)),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,X0)
| ~ rel_str(sK1)
| ~ relstr_set_smaller(sK1,sK2,sK9(sK1,X0))
| ~ element(sK9(sK1,X0),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(resolution,[],[f49,f39]) ).
fof(f66,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,X0,sK3(sK9(sK1,X0)))
| ~ element(sK3(sK9(sK1,X0)),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,X0)
| ~ relstr_set_smaller(sK1,sK2,sK9(sK1,X0))
| ~ element(sK9(sK1,X0),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f65,f32]) ).
fof(f67,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,X0,sK3(sK9(sK1,X0)))
| ~ ex_sup_of_relstr_set(sK1,X0)
| ~ relstr_set_smaller(sK1,sK2,sK9(sK1,X0))
| ~ element(sK9(sK1,X0),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f66,f37]) ).
fof(f68,plain,
( ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ relstr_set_smaller(sK1,sK2,sK9(sK1,sK2))
| ~ element(sK9(sK1,sK2),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ relstr_set_smaller(sK1,sK2,sK9(sK1,sK2))
| ~ element(sK9(sK1,sK2),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2) ),
inference(resolution,[],[f67,f38]) ).
fof(f69,plain,
( ~ relstr_set_smaller(sK1,sK2,sK9(sK1,sK2))
| ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ element(sK9(sK1,sK2),the_carrier(sK1)) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f70,plain,
( ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ element(sK9(sK1,sK2),the_carrier(sK1))
| ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ rel_str(sK1) ),
inference(resolution,[],[f69,f50]) ).
fof(f71,plain,
( ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ element(sK9(sK1,sK2),the_carrier(sK1))
| ~ rel_str(sK1) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f72,plain,
( ~ ex_sup_of_relstr_set(sK1,sK2)
| ~ rel_str(sK1) ),
inference(forward_subsumption_resolution,[],[f71,f51]) ).
fof(f73,plain,
~ ex_sup_of_relstr_set(sK1,sK2),
inference(forward_subsumption_resolution,[],[f72,f32]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( ~ related(X0,X1,sK6(X2,X3,X0))
| sK6(X2,X3,X0) = X1
| ~ element(sK6(X2,X3,X0),the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| sP0(X2,X3,X0)
| ~ relstr_set_smaller(X0,X3,X1)
| ~ element(X1,the_carrier(X0)) ),
inference(resolution,[],[f56,f45]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ related(X0,X1,sK6(X2,X3,X0))
| sK6(X2,X3,X0) = X1
| ~ element(sK6(X2,X3,X0),the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| sP0(X2,X3,X0)
| ~ relstr_set_smaller(X0,X3,X1) ),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ related(X0,X1,sK6(X2,X3,X0))
| sK6(X2,X3,X0) = X1
| ~ element(X1,the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| sP0(X2,X3,X0)
| ~ relstr_set_smaller(X0,X3,X1) ),
inference(forward_subsumption_resolution,[],[f87,f44]) ).
fof(f110,plain,
! [X0] :
( ~ element(sK4,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,X0,sK4)
| ex_sup_of_relstr_set(sK1,X0)
| ~ sP0(sK4,X0,sK1)
| ~ rel_str(sK1)
| ~ relstr_set_smaller(sK1,sK2,sK8(sK1,X0,sK4))
| ~ element(sK8(sK1,X0,sK4),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(resolution,[],[f54,f34]) ).
fof(f116,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,X0,sK4)
| ex_sup_of_relstr_set(sK1,X0)
| ~ sP0(sK4,X0,sK1)
| ~ rel_str(sK1)
| ~ relstr_set_smaller(sK1,sK2,sK8(sK1,X0,sK4))
| ~ element(sK8(sK1,X0,sK4),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f110,f36]) ).
fof(f117,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,X0,sK4)
| ex_sup_of_relstr_set(sK1,X0)
| ~ sP0(sK4,X0,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK8(sK1,X0,sK4))
| ~ element(sK8(sK1,X0,sK4),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f116,f32]) ).
fof(f118,plain,
! [X0] :
( ~ relstr_set_smaller(sK1,sK2,sK8(sK1,X0,sK4))
| ex_sup_of_relstr_set(sK1,X0)
| ~ sP0(sK4,X0,sK1)
| ~ relstr_set_smaller(sK1,X0,sK4)
| ~ element(sK8(sK1,X0,sK4),the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f117,f73]) ).
fof(f119,plain,
( ex_sup_of_relstr_set(sK1,sK2)
| ~ sP0(sK4,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ element(sK8(sK1,sK2,sK4),the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ex_sup_of_relstr_set(sK1,sK2)
| ~ sP0(sK4,sK2,sK1)
| ~ rel_str(sK1) ),
inference(resolution,[],[f118,f53]) ).
fof(f120,plain,
( ex_sup_of_relstr_set(sK1,sK2)
| ~ sP0(sK4,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ element(sK8(sK1,sK2,sK4),the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ rel_str(sK1) ),
inference(duplicate_literal_removal,[],[f119]) ).
fof(f121,plain,
( ~ sP0(sK4,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ element(sK8(sK1,sK2,sK4),the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ rel_str(sK1) ),
inference(forward_subsumption_resolution,[],[f120,f73]) ).
fof(f122,plain,
( ~ element(sK8(sK1,sK2,sK4),the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ sP0(sK4,sK2,sK1)
| ~ element(sK4,the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f121,f32]) ).
fof(f123,plain,
( ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ sP0(sK4,sK2,sK1)
| ~ element(sK4,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK2,sK4)
| ex_sup_of_relstr_set(sK1,sK2)
| ~ sP0(sK4,sK2,sK1)
| ~ rel_str(sK1) ),
inference(resolution,[],[f122,f52]) ).
fof(f124,plain,
( ~ relstr_set_smaller(sK1,sK2,sK4)
| ~ sP0(sK4,sK2,sK1)
| ~ element(sK4,the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2)
| ~ rel_str(sK1) ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f125,plain,
( ~ sP0(sK4,sK2,sK1)
| ~ element(sK4,the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2)
| ~ rel_str(sK1) ),
inference(forward_subsumption_resolution,[],[f124,f35]) ).
fof(f126,plain,
( ~ sP0(sK4,sK2,sK1)
| ex_sup_of_relstr_set(sK1,sK2)
| ~ rel_str(sK1) ),
inference(forward_subsumption_resolution,[],[f125,f36]) ).
fof(f127,plain,
( ~ sP0(sK4,sK2,sK1)
| ~ rel_str(sK1) ),
inference(forward_subsumption_resolution,[],[f126,f73]) ).
fof(f128,plain,
~ sP0(sK4,sK2,sK1),
inference(forward_subsumption_resolution,[],[f127,f32]) ).
fof(f142,plain,
! [X0,X1] :
( sK4 = sK6(X0,X1,sK1)
| ~ element(sK4,the_carrier(sK1))
| ~ antisymmetric_relstr(sK1)
| ~ rel_str(sK1)
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| ~ element(sK6(X0,X1,sK1),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(resolution,[],[f90,f34]) ).
fof(f148,plain,
! [X0,X1] :
( sK4 = sK6(X0,X1,sK1)
| ~ antisymmetric_relstr(sK1)
| ~ rel_str(sK1)
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| ~ element(sK6(X0,X1,sK1),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f142,f36]) ).
fof(f151,plain,
! [X0,X1] :
( sK4 = sK6(X0,X1,sK1)
| ~ rel_str(sK1)
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| ~ element(sK6(X0,X1,sK1),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f148,f33]) ).
fof(f152,plain,
! [X0,X1] :
( sK4 = sK6(X0,X1,sK1)
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| ~ element(sK6(X0,X1,sK1),the_carrier(sK1))
| ex_sup_of_relstr_set(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f151,f32]) ).
fof(f153,plain,
! [X0,X1] :
( sK4 = sK6(X0,X1,sK1)
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| ~ element(sK6(X0,X1,sK1),the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f152,f73]) ).
fof(f154,plain,
! [X0,X1] :
( ~ relstr_set_smaller(sK1,sK2,sK6(X0,X1,sK1))
| sP0(X0,X1,sK1)
| ~ relstr_set_smaller(sK1,X1,sK4)
| sK4 = sK6(X0,X1,sK1) ),
inference(forward_subsumption_resolution,[],[f153,f44]) ).
fof(f155,plain,
! [X0] :
( sP0(X0,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| sK4 = sK6(X0,sK2,sK1)
| sP0(X0,sK2,sK1) ),
inference(resolution,[],[f154,f46]) ).
fof(f156,plain,
! [X0] :
( sK4 = sK6(X0,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| sP0(X0,sK2,sK1) ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f162,plain,
! [X0] :
( sK4 != X0
| sP0(X0,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4)
| sP0(X0,sK2,sK1) ),
inference(superposition,[],[f47,f156]) ).
fof(f163,plain,
! [X0] :
( sK4 != X0
| sP0(X0,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4) ),
inference(duplicate_literal_removal,[],[f162]) ).
fof(f173,plain,
( sP0(sK4,sK2,sK1)
| ~ relstr_set_smaller(sK1,sK2,sK4) ),
inference(equality_resolution,[],[f163]) ).
fof(f174,plain,
~ relstr_set_smaller(sK1,sK2,sK4),
inference(forward_subsumption_resolution,[],[f173,f128]) ).
fof(f177,plain,
ex_sup_of_relstr_set(sK1,sK2),
inference(resolution,[],[f174,f35]) ).
fof(f178,plain,
$false,
inference(forward_subsumption_resolution,[],[f177,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU356+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n020.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 04:54:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.70/1.29 % (4031117)Detected formulas, will run a generic FOF schedule.
% 2.70/1.29 % (4031124)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=1916507970:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.29 % (4031126)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2487226650:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.29 % (4031123)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=896472383:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.29 % (4031127)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1358079577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.29 % (4031128)dis-21_1_sil=8000:lcm=predicate:random_seed=3723364664: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)
% 2.70/1.29 % (4031125)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2546449725:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.29 % (4031122)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=53162583:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.29 % (4031126)First to succeed.
% 2.70/1.29 % (4031125)Also succeeded, but the first one will report.
% 2.70/1.29 % (4031127)Also succeeded, but the first one will report.
% 2.70/1.29 % (4031126)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4031117"
% 2.70/1.29 % (4031128)Instruction limit reached!
% 2.70/1.29 % (4031128)------------------------------
% 2.70/1.29 % (4031128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.29 % (4031128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.29 % (4031128)CaDiCaL version: 2.1.3
% 2.70/1.29 % (4031128)Termination reason: Instruction limit
% 2.70/1.29 % (4031128)Termination phase: Saturation
% 2.70/1.29 % (4031128)Time elapsed: 0.052 s
% 2.70/1.29 % (4031128)Peak memory usage: 88 MB
% 2.70/1.29 % (4031128)Instructions burned: 129 (million)
% 2.70/1.29 % (4031136)lrs+10_1_sil=8000:sp=occurrence:random_seed=1588925552:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.70/1.29 % (4031136)Also succeeded, but the first one will report.
% 2.70/1.29 % (4031126)Refutation found. Thanks to Tanya!
% 2.70/1.29 % SZS status Theorem for theBenchmark
% 2.70/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.50 % (4031126)------------------------------
% 3.61/1.50 % (4031126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.50 % (4031126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.50 % (4031126)CaDiCaL version: 2.1.3
% 3.61/1.50 % (4031126)Termination reason: Refutation
% 3.61/1.50 % (4031126)Time elapsed: 0.007 s
% 3.61/1.50 % (4031126)Peak memory usage: 88 MB
% 3.61/1.50 % (4031126)Instructions burned: 9 (million)
% 3.61/1.50 % (4031126)------------------------------
% 3.61/1.50 % (4031126)------------------------------
% 3.61/1.50 % (4031117)Success in time 0.433 s
% 3.61/1.50 % Vampire exiting
%------------------------------------------------------------------------------