%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:48:44 PM UTC 2026
% Result : Theorem 2.63s 1.27s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 59 ( 5 unt; 0 def)
% Number of atoms : 408 ( 121 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 527 ( 178 ~; 155 |; 175 &)
% ( 11 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 166 ( 107 !; 59 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X3,X4,X5] :
( ( ! [X6] :
( in(X6,X4)
<=> ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) ) )
& ! [X6] :
( in(X6,X5)
<=> ( in(X6,the_carrier(X1))
& ? [X9] :
( netstr_induced_subset(X9,X0,X1)
& ? [X10] :
( element(X10,the_carrier(X1))
& X3 = topstr_closure(X0,X9)
& X6 = X10
& X9 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X10)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X10))) ) ) ) ) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_xboole_0__e6_39_3__yellow19__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X3,X4,X5] :
( ( ! [X6] :
( in(X6,X4)
<=> ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) ) )
& ! [X6] :
( in(X6,X5)
<=> ( in(X6,the_carrier(X1))
& ? [X9] :
( netstr_induced_subset(X9,X0,X1)
& ? [X10] :
( element(X10,the_carrier(X1))
& X3 = topstr_closure(X0,X9)
& X6 = X10
& X9 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X10)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X10))) ) ) ) ) )
=> X4 = X5 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f70,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f71,plain,
~ ! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X3,X4,X5] :
( ( ! [X6] :
( in(X6,X4)
<=> ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) ) )
& ! [X9] :
( in(X9,X5)
<=> ( in(X9,the_carrier(X1))
& ? [X10] :
( netstr_induced_subset(X10,X0,X1)
& ? [X11] :
( element(X11,the_carrier(X1))
& topstr_closure(X0,X10) = X3
& X9 = X11
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10 ) ) ) ) )
=> X4 = X5 ) ),
inference(rectify,[],[f2]) ).
fof(f85,plain,
? [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ! [X6] :
( in(X6,X4)
<=> ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) ) )
& ! [X9] :
( in(X9,X5)
<=> ( in(X9,the_carrier(X1))
& ? [X10] :
( netstr_induced_subset(X10,X0,X1)
& ? [X11] :
( element(X11,the_carrier(X1))
& topstr_closure(X0,X10) = X3
& X9 = X11
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10 ) ) ) ) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f86,plain,
? [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ! [X6] :
( in(X6,X4)
<=> ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) ) )
& ! [X9] :
( in(X9,X5)
<=> ( in(X9,the_carrier(X1))
& ? [X10] :
( netstr_induced_subset(X10,X0,X1)
& ? [X11] :
( element(X11,the_carrier(X1))
& topstr_closure(X0,X10) = X3
& X9 = X11
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10 ) ) ) ) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) ),
inference(flattening,[],[f85]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f139,plain,
? [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ! [X6] :
( ( in(X6,X4)
| ~ in(X6,the_carrier(X1))
| ! [X7] :
( ~ netstr_induced_subset(X7,X0,X1)
| ! [X8] :
( ~ element(X8,the_carrier(X1))
| topstr_closure(X0,X7) != X3
| X6 != X8
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) != X7 ) ) )
& ( ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) )
| ~ in(X6,X4) ) )
& ! [X9] :
( ( in(X9,X5)
| ~ in(X9,the_carrier(X1))
| ! [X10] :
( ~ netstr_induced_subset(X10,X0,X1)
| ! [X11] :
( ~ element(X11,the_carrier(X1))
| topstr_closure(X0,X10) != X3
| X9 != X11
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) != X10 ) ) )
& ( ( in(X9,the_carrier(X1))
& ? [X10] :
( netstr_induced_subset(X10,X0,X1)
& ? [X11] :
( element(X11,the_carrier(X1))
& topstr_closure(X0,X10) = X3
& X9 = X11
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10 ) ) )
| ~ in(X9,X5) ) ) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f140,plain,
? [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ! [X6] :
( ( in(X6,X4)
| ~ in(X6,the_carrier(X1))
| ! [X7] :
( ~ netstr_induced_subset(X7,X0,X1)
| ! [X8] :
( ~ element(X8,the_carrier(X1))
| topstr_closure(X0,X7) != X3
| X6 != X8
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) != X7 ) ) )
& ( ( in(X6,the_carrier(X1))
& ? [X7] :
( netstr_induced_subset(X7,X0,X1)
& ? [X8] :
( element(X8,the_carrier(X1))
& X3 = topstr_closure(X0,X7)
& X6 = X8
& X7 = relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X8)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X8))) ) ) )
| ~ in(X6,X4) ) )
& ! [X9] :
( ( in(X9,X5)
| ~ in(X9,the_carrier(X1))
| ! [X10] :
( ~ netstr_induced_subset(X10,X0,X1)
| ! [X11] :
( ~ element(X11,the_carrier(X1))
| topstr_closure(X0,X10) != X3
| X9 != X11
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) != X10 ) ) )
& ( ( in(X9,the_carrier(X1))
& ? [X10] :
( netstr_induced_subset(X10,X0,X1)
& ? [X11] :
( element(X11,the_carrier(X1))
& topstr_closure(X0,X10) = X3
& X9 = X11
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X11)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X11))) = X10 ) ) )
| ~ in(X9,X5) ) ) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
? [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ! [X5] :
( ( in(X5,X3)
| ~ in(X5,the_carrier(X1))
| ! [X6] :
( ~ netstr_induced_subset(X6,X0,X1)
| ! [X7] :
( ~ element(X7,the_carrier(X1))
| topstr_closure(X0,X6) != X2
| X5 != X7
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X7)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X7))) != X6 ) ) )
& ( ( in(X5,the_carrier(X1))
& ? [X8] :
( netstr_induced_subset(X8,X0,X1)
& ? [X9] :
( element(X9,the_carrier(X1))
& topstr_closure(X0,X8) = X2
& X5 = X9
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X9)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X9))) = X8 ) ) )
| ~ in(X5,X3) ) )
& ! [X10] :
( ( in(X10,X4)
| ~ in(X10,the_carrier(X1))
| ! [X11] :
( ~ netstr_induced_subset(X11,X0,X1)
| ! [X12] :
( ~ element(X12,the_carrier(X1))
| topstr_closure(X0,X11) != X2
| X10 != X12
| relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X12)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X12))) != X11 ) ) )
& ( ( in(X10,the_carrier(X1))
& ? [X13] :
( netstr_induced_subset(X13,X0,X1)
& ? [X14] :
( element(X14,the_carrier(X1))
& topstr_closure(X0,X13) = X2
& X10 = X14
& relation_rng_as_subset(the_carrier(subnetstr_of_element(X0,X1,X14)),the_carrier(X0),the_mapping(X0,subnetstr_of_element(X0,X1,X14))) = X13 ) ) )
| ~ in(X10,X4) ) ) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
( sK3 != sK4
& ! [X5] :
( ( in(X5,sK3)
| ~ in(X5,the_carrier(sK1))
| ! [X6] :
( ~ netstr_induced_subset(X6,sK0,sK1)
| ! [X7] :
( ~ element(X7,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X6)
| X5 != X7
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6 ) ) )
& ( ( in(X5,the_carrier(sK1))
& netstr_induced_subset(sK5(X5),sK0,sK1)
& element(sK6(X5),the_carrier(sK1))
& sK2 = topstr_closure(sK0,sK5(X5))
& sK6(X5) = X5
& sK5(X5) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X5))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X5)))) )
| ~ in(X5,sK3) ) )
& ! [X10] :
( ( in(X10,sK4)
| ~ in(X10,the_carrier(sK1))
| ! [X11] :
( ~ netstr_induced_subset(X11,sK0,sK1)
| ! [X12] :
( ~ element(X12,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X11)
| X10 != X12
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11 ) ) )
& ( ( in(X10,the_carrier(sK1))
& netstr_induced_subset(sK7(X10),sK0,sK1)
& element(sK8(X10),the_carrier(sK1))
& sK2 = topstr_closure(sK0,sK7(X10))
& sK8(X10) = X10
& sK7(X10) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X10))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X10)))) )
| ~ in(X10,sK4) ) )
& ~ empty_carrier(sK0)
& topological_space(sK0)
& top_str(sK0)
& ~ empty_carrier(sK1)
& transitive_relstr(sK1)
& directed_relstr(sK1)
& net_str(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X8,sK5(X5)),skolemize(X9,sK6(X5)),skolemize(X13,sK7(X10)),skolemize(X14,sK8(X10))],[f141]) ).
fof(f145,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f146,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) )
& ( in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f145]) ).
fof(f168,plain,
! [X10] :
( sK7(X10) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK8(X10))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK8(X10))))
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f169,plain,
! [X10] :
( sK8(X10) = X10
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f170,plain,
! [X10] :
( sK2 = topstr_closure(sK0,sK7(X10))
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f171,plain,
! [X10] :
( element(sK8(X10),the_carrier(sK1))
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f172,plain,
! [X10] :
( netstr_induced_subset(sK7(X10),sK0,sK1)
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f173,plain,
! [X10] :
( in(X10,the_carrier(sK1))
| ~ in(X10,sK4) ),
inference(cnf_transformation,[],[f142]) ).
fof(f174,plain,
! [X10,X11,X12] :
( in(X10,sK4)
| ~ in(X10,the_carrier(sK1))
| ~ netstr_induced_subset(X11,sK0,sK1)
| ~ element(X12,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X11)
| X10 != X12
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11 ),
inference(cnf_transformation,[],[f142]) ).
fof(f175,plain,
! [X5] :
( sK5(X5) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,sK6(X5))),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,sK6(X5))))
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f176,plain,
! [X5] :
( sK6(X5) = X5
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f177,plain,
! [X5] :
( sK2 = topstr_closure(sK0,sK5(X5))
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f178,plain,
! [X5] :
( element(sK6(X5),the_carrier(sK1))
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f179,plain,
! [X5] :
( netstr_induced_subset(sK5(X5),sK0,sK1)
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f180,plain,
! [X5] :
( in(X5,the_carrier(sK1))
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f181,plain,
! [X6,X7,X5] :
( in(X5,sK3)
| ~ in(X5,the_carrier(sK1))
| ~ netstr_induced_subset(X6,sK0,sK1)
| ~ element(X7,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X6)
| X5 != X7
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6 ),
inference(cnf_transformation,[],[f142]) ).
fof(f182,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f142]) ).
fof(f197,plain,
! [X0,X1] :
( in(sK11(X0,X1),X1)
| X0 = X1
| in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f198,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| X0 = X1
| ~ in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f253,plain,
! [X6,X7] :
( in(X7,sK3)
| ~ in(X7,the_carrier(sK1))
| ~ netstr_induced_subset(X6,sK0,sK1)
| ~ element(X7,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X6)
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))) != X6 ),
inference(equality_resolution,[],[f181]) ).
fof(f254,plain,
! [X7] :
( sK2 != topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))))
| ~ in(X7,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X7)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X7))),sK0,sK1)
| ~ element(X7,the_carrier(sK1))
| in(X7,sK3) ),
inference(equality_resolution,[],[f253]) ).
fof(f255,plain,
! [X11,X12] :
( in(X12,sK4)
| ~ in(X12,the_carrier(sK1))
| ~ netstr_induced_subset(X11,sK0,sK1)
| ~ element(X12,the_carrier(sK1))
| sK2 != topstr_closure(sK0,X11)
| relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))) != X11 ),
inference(equality_resolution,[],[f174]) ).
fof(f256,plain,
! [X12] :
( sK2 != topstr_closure(sK0,relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))))
| ~ in(X12,the_carrier(sK1))
| ~ netstr_induced_subset(relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X12)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X12))),sK0,sK1)
| ~ element(X12,the_carrier(sK1))
| in(X12,sK4) ),
inference(equality_resolution,[],[f255]) ).
fof(f257,plain,
! [X0] :
( element(X0,the_carrier(sK1))
| ~ in(X0,sK4)
| ~ in(X0,sK4) ),
inference(superposition,[],[f171,f169]) ).
fof(f258,plain,
! [X0] :
( element(X0,the_carrier(sK1))
| ~ in(X0,sK4) ),
inference(duplicate_literal_removal,[],[f257]) ).
fof(f259,plain,
! [X0] :
( element(X0,the_carrier(sK1))
| ~ in(X0,sK3)
| ~ in(X0,sK3) ),
inference(superposition,[],[f178,f176]) ).
fof(f260,plain,
! [X0] :
( element(X0,the_carrier(sK1))
| ~ in(X0,sK3) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f261,plain,
! [X0] :
( sK7(X0) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))
| ~ in(X0,sK4)
| ~ in(X0,sK4) ),
inference(superposition,[],[f168,f169]) ).
fof(f262,plain,
! [X0] :
( sK7(X0) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))
| ~ in(X0,sK4) ),
inference(duplicate_literal_removal,[],[f261]) ).
fof(f269,plain,
! [X0] :
( sK5(X0) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))
| ~ in(X0,sK3)
| ~ in(X0,sK3) ),
inference(superposition,[],[f175,f176]) ).
fof(f272,plain,
! [X0] :
( sK5(X0) = relation_rng_as_subset(the_carrier(subnetstr_of_element(sK0,sK1,X0)),the_carrier(sK0),the_mapping(sK0,subnetstr_of_element(sK0,sK1,X0)))
| ~ in(X0,sK3) ),
inference(duplicate_literal_removal,[],[f269]) ).
fof(f319,plain,
! [X0] :
( sK2 != topstr_closure(sK0,sK7(X0))
| ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(sK7(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK3)
| ~ in(X0,sK4) ),
inference(superposition,[],[f254,f262]) ).
fof(f322,plain,
! [X0] :
( ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(sK7(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK3)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f319,f170]) ).
fof(f325,plain,
! [X0] :
( ~ netstr_induced_subset(sK7(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK3)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f322,f173]) ).
fof(f328,plain,
! [X0] :
( ~ element(X0,the_carrier(sK1))
| in(X0,sK3)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f325,f172]) ).
fof(f330,plain,
! [X0] :
( in(X0,sK3)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f328,f258]) ).
fof(f332,plain,
! [X0] :
( sK2 != topstr_closure(sK0,sK5(X0))
| ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(sK5(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK4)
| ~ in(X0,sK3) ),
inference(superposition,[],[f256,f272]) ).
fof(f336,plain,
! [X0] :
( ~ in(X0,the_carrier(sK1))
| ~ netstr_induced_subset(sK5(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK4)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f332,f177]) ).
fof(f339,plain,
! [X0] :
( ~ netstr_induced_subset(sK5(X0),sK0,sK1)
| ~ element(X0,the_carrier(sK1))
| in(X0,sK4)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f336,f180]) ).
fof(f342,plain,
! [X0] :
( ~ element(X0,the_carrier(sK1))
| in(X0,sK4)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f339,f179]) ).
fof(f344,plain,
! [X0] :
( in(X0,sK4)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f342,f260]) ).
fof(f465,plain,
! [X0] :
( ~ in(sK11(X0,sK3),sK4)
| ~ in(sK11(X0,sK3),X0)
| sK3 = X0 ),
inference(resolution,[],[f198,f330]) ).
fof(f470,plain,
( ~ in(sK11(sK4,sK3),sK4)
| sK3 = sK4 ),
inference(factoring,[],[f465]) ).
fof(f471,plain,
~ in(sK11(sK4,sK3),sK4),
inference(forward_subsumption_resolution,[],[f470,f182]) ).
fof(f477,plain,
~ in(sK11(sK4,sK3),sK3),
inference(resolution,[],[f471,f344]) ).
fof(f478,plain,
( sK3 = sK4
| in(sK11(sK4,sK3),sK4) ),
inference(resolution,[],[f477,f197]) ).
fof(f480,plain,
in(sK11(sK4,sK3),sK4),
inference(forward_subsumption_resolution,[],[f478,f182]) ).
fof(f481,plain,
$false,
inference(forward_subsumption_resolution,[],[f480,f471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.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 05:08:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/1.27 % (2672713)Detected formulas, will run a generic FOF schedule.
% 2.63/1.27 % (2672718)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=1206677780:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.27 % (2672722)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1998933357:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.27 % (2672721)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2213985685:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.27 % (2672719)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=2808594156:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.27 % (2672720)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=634499069:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.27 % (2672722)First to succeed.
% 2.63/1.27 % (2672722)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2672713"
% 2.63/1.27 % (2672721)Also succeeded, but the first one will report.
% 2.63/1.27 % (2672724)dis-21_1_sil=8000:lcm=predicate:random_seed=3082315938: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)
% 2.63/1.27 % (2672723)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1180684078:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.27 % (2672724)Instruction limit reached!
% 2.63/1.27 % (2672724)------------------------------
% 2.63/1.27 % (2672724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.27 % (2672724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.27 % (2672724)CaDiCaL version: 2.1.3
% 2.63/1.27 % (2672724)Termination reason: Instruction limit
% 2.63/1.27 % (2672724)Termination phase: Saturation
% 2.63/1.27 % (2672724)Time elapsed: 0.079 s
% 2.63/1.27 % (2672724)Peak memory usage: 91 MB
% 2.63/1.27 % (2672724)Instructions burned: 130 (million)
% 2.63/1.27 % (2672723)Instruction limit reached!
% 2.63/1.27 % (2672723)------------------------------
% 2.63/1.27 % (2672723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.27 % (2672723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.27 % (2672723)CaDiCaL version: 2.1.3
% 2.63/1.27 % (2672723)Termination reason: Instruction limit
% 2.63/1.27 % (2672723)Termination phase: Saturation
% 2.63/1.27 % (2672723)Time elapsed: 0.098 s
% 2.63/1.27 % (2672723)Peak memory usage: 90 MB
% 2.63/1.27 % (2672723)Instructions burned: 140 (million)
% 2.63/1.27 % (2672732)lrs+10_1_sil=8000:sp=occurrence:random_seed=1170266429:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.63/1.27 % (2672733)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4017056711:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.63/1.27 % (2672722)Refutation found. Thanks to Tanya!
% 2.63/1.27 % SZS status Theorem for theBenchmark
% 2.63/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.46 % (2672722)------------------------------
% 3.46/1.46 % (2672722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (2672722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (2672722)CaDiCaL version: 2.1.3
% 3.46/1.46 % (2672722)Termination reason: Refutation
% 3.46/1.46 % (2672722)Time elapsed: 0.013 s
% 3.46/1.46 % (2672722)Peak memory usage: 88 MB
% 3.46/1.46 % (2672722)Instructions burned: 18 (million)
% 3.46/1.46 % (2672722)------------------------------
% 3.46/1.46 % (2672722)------------------------------
% 3.46/1.46 % (2672713)Success in time 0.408 s
% 3.46/1.46 % Vampire exiting
%------------------------------------------------------------------------------