%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU318+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 : n002.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 12:48:19 PM UTC 2026
% Result : Theorem 6.85s 1.96s
% Output : Refutation 8.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 164 ( 21 unt; 7 def)
% Number of atoms : 649 ( 46 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 844 ( 359 ~; 372 |; 74 &)
% ( 14 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 206 ( 1 sgn 191 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f18,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f22,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f38,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f42,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( in(X2,X1)
=> closed_subset(X2,X0) ) )
=> closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_pre_topc) ).
fof(f43,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( closed_subset(X3,X0)
& subset(X1,X3) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f44,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( closed_subset(X3,X0)
& subset(X1,X3) ) ) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(f45,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f47,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 )
& ( ( topological_space(X0)
& topstr_closure(X0,X1) = X1 )
=> closed_subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f48,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 )
& ( ( topological_space(X0)
& topstr_closure(X0,X1) = X1 )
=> closed_subset(X1,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f38]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f83,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f22]) ).
fof(f84,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f83]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ? [X2] :
( ~ closed_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ? [X2] :
( ~ closed_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( in(X3,X2)
<=> ( closed_subset(X3,X0)
& subset(X1,X3) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( in(X3,X2)
<=> ( closed_subset(X3,X0)
& subset(X1,X3) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( ( ( topstr_closure(X0,X1) != X1
& closed_subset(X1,X0) )
| ( ~ closed_subset(X1,X0)
& topological_space(X0)
& topstr_closure(X0,X1) = X1 ) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f103,plain,
? [X0] :
( ? [X1] :
( ( ( topstr_closure(X0,X1) != X1
& closed_subset(X1,X0) )
| ( ~ closed_subset(X1,X0)
& topological_space(X0)
& topstr_closure(X0,X1) = X1 ) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f102]) ).
fof(f108,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f109,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f111,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f111]) ).
fof(f119,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ( ~ closed_subset(sK7(X0,X1),X0)
& in(sK7(X0,X1),X1)
& element(sK7(X0,X1),powerset(the_carrier(X0))) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f94]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ( ~ in(X2,sK8(X0,X1,X2))
& closed_subset(sK8(X0,X1,X2),X0)
& subset(X1,sK8(X0,X1,X2))
& element(sK8(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f122]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,X2)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3) )
& ( ( closed_subset(X3,X0)
& subset(X1,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,X2)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3) )
& ( ( closed_subset(X3,X0)
& subset(X1,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( element(sK9(X0,X1),powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,sK9(X0,X1))
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3) )
& ( ( closed_subset(X3,X0)
& subset(X1,X3) )
| ~ in(X3,sK9(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK9(X0,X1)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f125]) ).
fof(f127,plain,
( ( ( sK11 != topstr_closure(sK10,sK11)
& closed_subset(sK11,sK10) )
| ( ~ closed_subset(sK11,sK10)
& topological_space(sK10)
& sK11 = topstr_closure(sK10,sK11) ) )
& element(sK11,powerset(the_carrier(sK10)))
& top_str(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f103]) ).
fof(f155,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f156,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f157,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f159,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f183,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f186,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f188,plain,
! [X0,X1] :
( element(sK7(X0,X1),powerset(the_carrier(X0)))
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f189,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK7(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f190,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK7(X0,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f191,plain,
! [X2,X0,X1,X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| in(X2,X4)
| ~ in(X2,topstr_closure(X0,X1))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f196,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK9(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f198,plain,
! [X3,X0,X1] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK9(X0,X1))
| closed_subset(X3,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
! [X0,X1] :
( element(sK9(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f201,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f203,plain,
top_str(sK10),
inference(cnf_transformation,[],[f127]) ).
fof(f204,plain,
element(sK11,powerset(the_carrier(sK10))),
inference(cnf_transformation,[],[f127]) ).
fof(f205,plain,
( closed_subset(sK11,sK10)
| sK11 = topstr_closure(sK10,sK11) ),
inference(cnf_transformation,[],[f127]) ).
fof(f209,plain,
( sK11 != topstr_closure(sK10,sK11)
| topological_space(sK10) ),
inference(cnf_transformation,[],[f127]) ).
fof(f210,plain,
( sK11 != topstr_closure(sK10,sK11)
| ~ closed_subset(sK11,sK10) ),
inference(cnf_transformation,[],[f127]) ).
fof(f217,definition,
sF12 = topstr_closure(sK10,sK11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f218,plain,
topstr_closure(sK10,sK11) = sF12,
inference(reorient_equations,[],[f217]) ).
fof(f219,plain,
( sK11 != sF12
| ~ closed_subset(sK11,sK10) ),
inference(definition_folding,[],[f210,f218]) ).
fof(f220,plain,
( sK11 != sF12
| topological_space(sK10) ),
inference(definition_folding,[],[f209,f218]) ).
fof(f222,plain,
( closed_subset(sK11,sK10)
| sK11 = sF12 ),
inference(definition_folding,[],[f205,f218]) ).
fof(f223,definition,
sF13 = the_carrier(sK10),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f224,plain,
the_carrier(sK10) = sF13,
inference(reorient_equations,[],[f223]) ).
fof(f225,definition,
sF14 = powerset(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f226,plain,
powerset(sF13) = sF14,
inference(reorient_equations,[],[f225]) ).
fof(f227,plain,
element(sK11,sF14),
inference(definition_folding,[],[f204,f226,f224]) ).
fof(f229,definition,
( spl15_1
<=> sK11 = sF12 ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f230,plain,
( sK11 != sF12
| spl15_1 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f231,plain,
( sK11 = sF12
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f233,definition,
( spl15_2
<=> closed_subset(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f234,plain,
( ~ closed_subset(sK11,sK10)
| spl15_2 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f235,plain,
( closed_subset(sK11,sK10)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f222,f233,f229]) ).
fof(f238,definition,
( spl15_3
<=> topological_space(sK10) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f240,plain,
( topological_space(sK10)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,plain,
( spl15_3
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f220,f229,f238]) ).
fof(f243,plain,
( ~ spl15_2
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f219,f229,f233]) ).
fof(f244,plain,
! [X0] :
( ~ element(X0,powerset(sF13))
| subset(X0,topstr_closure(sK10,X0))
| ~ top_str(sK10) ),
inference(superposition,[],[f201,f224]) ).
fof(f245,plain,
! [X0] :
( ~ element(X0,powerset(sF13))
| subset(X0,topstr_closure(sK10,X0)) ),
inference(forward_subsumption_resolution,[],[f244,f203]) ).
fof(f246,plain,
! [X0] :
( subset(X0,topstr_closure(sK10,X0))
| ~ element(X0,sF14) ),
inference(forward_demodulation,[],[f245,f226]) ).
fof(f247,plain,
( subset(sK11,sF12)
| ~ element(sK11,sF14) ),
inference(superposition,[],[f246,f218]) ).
fof(f248,plain,
subset(sK11,sF12),
inference(forward_subsumption_resolution,[],[f247,f227]) ).
fof(f249,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF13))
| ~ in(X0,sK9(sK10,X1))
| closed_subset(X0,sK10)
| ~ element(X1,powerset(sF13))
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f198,f224]) ).
fof(f250,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF13))
| ~ in(X0,sK9(sK10,X1))
| closed_subset(X0,sK10)
| ~ element(X1,powerset(sF13))
| ~ topological_space(sK10) ),
inference(forward_subsumption_resolution,[],[f249,f203]) ).
fof(f251,plain,
! [X0,X1] :
( ~ element(X0,sF14)
| ~ in(X0,sK9(sK10,X1))
| closed_subset(X0,sK10)
| ~ element(X1,powerset(sF13))
| ~ topological_space(sK10) ),
inference(forward_demodulation,[],[f250,f226]) ).
fof(f252,plain,
! [X0,X1] :
( ~ element(X1,sF14)
| ~ element(X0,sF14)
| ~ in(X0,sK9(sK10,X1))
| closed_subset(X0,sK10)
| ~ topological_space(sK10) ),
inference(forward_demodulation,[],[f251,f226]) ).
fof(f254,definition,
( spl15_4
<=> ! [X0,X1] :
( ~ element(X1,sF14)
| closed_subset(X0,sK10)
| ~ element(X0,sF14)
| ~ in(X0,sK9(sK10,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0,X1] :
( ~ in(X0,sK9(sK10,X1))
| closed_subset(X0,sK10)
| ~ element(X0,sF14)
| ~ element(X1,sF14) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f252,f254,f238]) ).
fof(f265,plain,
( element(sF12,powerset(the_carrier(sK10)))
| ~ top_str(sK10)
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(superposition,[],[f159,f218]) ).
fof(f272,plain,
( element(sF12,powerset(the_carrier(sK10)))
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(forward_subsumption_resolution,[],[f265,f203]) ).
fof(f274,plain,
( element(sF12,powerset(sF13))
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(forward_demodulation,[],[f272,f224]) ).
fof(f276,plain,
( element(sF12,sF14)
| ~ element(sK11,powerset(the_carrier(sK10))) ),
inference(forward_demodulation,[],[f274,f226]) ).
fof(f277,plain,
( ~ element(sK11,powerset(sF13))
| element(sF12,sF14) ),
inference(forward_demodulation,[],[f276,f224]) ).
fof(f278,plain,
( ~ element(sK11,sF14)
| element(sF12,sF14) ),
inference(forward_demodulation,[],[f277,f226]) ).
fof(f279,plain,
element(sF12,sF14),
inference(forward_subsumption_resolution,[],[f278,f227]) ).
fof(f280,plain,
! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| in(sK7(sK10,X0),X0)
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f189,f224]) ).
fof(f282,plain,
! [X0] :
( ~ element(X0,sF14)
| subset(X0,sF13) ),
inference(superposition,[],[f186,f226]) ).
fof(f284,plain,
( ~ subset(sF12,sK11)
| sK11 = sF12 ),
inference(resolution,[],[f155,f248]) ).
fof(f285,plain,
( ~ subset(sF12,sK11)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f284,f230]) ).
fof(f289,plain,
subset(sF12,sF13),
inference(resolution,[],[f282,f279]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(sF13))
| ~ closed_subset(X0,sK10)
| ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,topstr_closure(sK10,X1))
| ~ in(X2,sF13)
| ~ element(X1,powerset(sF13))
| ~ top_str(sK10) ),
inference(superposition,[],[f191,f224]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(sF13))
| ~ closed_subset(X0,sK10)
| ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,topstr_closure(sK10,X1))
| ~ in(X2,sF13)
| ~ element(X1,powerset(sF13)) ),
inference(forward_subsumption_resolution,[],[f311,f203]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ element(X0,sF14)
| ~ closed_subset(X0,sK10)
| ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,topstr_closure(sK10,X1))
| ~ in(X2,sF13)
| ~ element(X1,powerset(sF13)) ),
inference(forward_demodulation,[],[f313,f226]) ).
fof(f315,plain,
! [X2,X0,X1] :
( ~ in(X2,topstr_closure(sK10,X1))
| ~ element(X0,sF14)
| ~ closed_subset(X0,sK10)
| ~ subset(X1,X0)
| in(X2,X0)
| ~ element(X1,sF14)
| ~ in(X2,sF13) ),
inference(forward_demodulation,[],[f314,f226]) ).
fof(f316,plain,
! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| ~ closed_subset(sK7(sK10,X0),sK10)
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f190,f224]) ).
fof(f318,plain,
! [X0] :
( ~ element(X0,powerset(sF13))
| topstr_closure(sK10,X0) = meet_of_subsets(sF13,sK9(sK10,X0))
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f196,f224]) ).
fof(f321,plain,
! [X0,X1] :
( ~ in(X0,sF12)
| ~ element(X1,sF14)
| ~ closed_subset(X1,sK10)
| ~ subset(sK11,X1)
| in(X0,X1)
| ~ element(sK11,sF14)
| ~ in(X0,sF13) ),
inference(superposition,[],[f315,f218]) ).
fof(f322,plain,
! [X0,X1] :
( ~ closed_subset(X1,sK10)
| ~ element(X1,sF14)
| ~ in(X0,sF12)
| ~ subset(sK11,X1)
| in(X0,X1)
| ~ in(X0,sF13) ),
inference(forward_subsumption_resolution,[],[f321,f227]) ).
fof(f323,plain,
( ! [X0] :
( ~ element(sK11,sF14)
| ~ in(X0,sF12)
| ~ subset(sK11,sK11)
| in(X0,sK11)
| ~ in(X0,sF13) )
| ~ spl15_2 ),
inference(resolution,[],[f322,f235]) ).
fof(f324,plain,
( ! [X0] :
( ~ in(X0,sF12)
| ~ subset(sK11,sK11)
| in(X0,sK11)
| ~ in(X0,sF13) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f323,f227]) ).
fof(f325,plain,
( ! [X0] :
( ~ in(X0,sF13)
| in(X0,sK11)
| ~ in(X0,sF12) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f324,f183]) ).
fof(f337,plain,
! [X0] :
( ~ in(X0,sF12)
| in(X0,sF13) ),
inference(resolution,[],[f156,f289]) ).
fof(f339,plain,
! [X0] :
( in(sK0(sF12,X0),sF13)
| subset(sF12,X0) ),
inference(resolution,[],[f337,f157]) ).
fof(f372,plain,
! [X0] :
( element(sK7(sK10,X0),powerset(sF13))
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ element(X0,powerset(powerset(sF13)))
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f188,f224]) ).
fof(f386,plain,
! [X0] :
( element(sK9(sK10,X0),powerset(powerset(sF13)))
| ~ element(X0,powerset(sF13))
| ~ topological_space(sK10)
| ~ top_str(sK10) ),
inference(superposition,[],[f200,f224]) ).
fof(f446,plain,
( ! [X0] :
( subset(sF12,X0)
| in(sK0(sF12,X0),sK11)
| ~ in(sK0(sF12,X0),sF12) )
| ~ spl15_2 ),
inference(resolution,[],[f339,f325]) ).
fof(f457,plain,
( ! [X0] :
( in(sK0(sF12,X0),sK11)
| subset(sF12,X0) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f446,f157]) ).
fof(f458,plain,
( subset(sF12,sK11)
| subset(sF12,sK11)
| ~ spl15_2 ),
inference(resolution,[],[f457,f158]) ).
fof(f463,plain,
( subset(sF12,sK11)
| ~ spl15_2 ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f469,plain,
( $false
| spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f463,f285]) ).
fof(f470,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f473,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| in(sK7(sK10,X0),X0)
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ top_str(sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f280,f240]) ).
fof(f474,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| ~ closed_subset(sK7(sK10,X0),sK10)
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ top_str(sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f316,f240]) ).
fof(f475,plain,
( ! [X0] :
( ~ element(X0,powerset(sF13))
| topstr_closure(sK10,X0) = meet_of_subsets(sF13,sK9(sK10,X0))
| ~ top_str(sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f318,f240]) ).
fof(f476,plain,
( ! [X0] :
( element(sK7(sK10,X0),powerset(sF13))
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ element(X0,powerset(powerset(sF13)))
| ~ top_str(sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f372,f240]) ).
fof(f477,plain,
( ! [X0] :
( element(sK9(sK10,X0),powerset(powerset(sF13)))
| ~ element(X0,powerset(sF13))
| ~ top_str(sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f386,f240]) ).
fof(f480,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| in(sK7(sK10,X0),X0)
| closed_subset(meet_of_subsets(sF13,X0),sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f473,f203]) ).
fof(f481,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sF13)))
| ~ closed_subset(sK7(sK10,X0),sK10)
| closed_subset(meet_of_subsets(sF13,X0),sK10) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f474,f203]) ).
fof(f482,plain,
( ! [X0] :
( ~ element(X0,powerset(sF13))
| topstr_closure(sK10,X0) = meet_of_subsets(sF13,sK9(sK10,X0)) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f475,f203]) ).
fof(f483,plain,
( ! [X0] :
( element(sK7(sK10,X0),powerset(sF13))
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ element(X0,powerset(powerset(sF13))) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f476,f203]) ).
fof(f484,plain,
( ! [X0] :
( element(sK9(sK10,X0),powerset(powerset(sF13)))
| ~ element(X0,powerset(sF13)) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f477,f203]) ).
fof(f487,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,X0),sK10)
| in(sK7(sK10,X0),X0)
| ~ element(X0,powerset(sF14)) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f480,f226]) ).
fof(f488,plain,
( ! [X0] :
( ~ closed_subset(sK7(sK10,X0),sK10)
| ~ element(X0,powerset(sF14))
| closed_subset(meet_of_subsets(sF13,X0),sK10) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f481,f226]) ).
fof(f489,plain,
( ! [X0] :
( ~ element(X0,sF14)
| topstr_closure(sK10,X0) = meet_of_subsets(sF13,sK9(sK10,X0)) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f482,f226]) ).
fof(f490,plain,
( ! [X0] :
( element(sK7(sK10,X0),sF14)
| closed_subset(meet_of_subsets(sF13,X0),sK10)
| ~ element(X0,powerset(powerset(sF13))) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f483,f226]) ).
fof(f491,plain,
( ! [X0] :
( element(sK9(sK10,X0),powerset(sF14))
| ~ element(X0,powerset(sF13)) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f484,f226]) ).
fof(f494,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,X0),sK10)
| element(sK7(sK10,X0),sF14)
| ~ element(X0,powerset(sF14)) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f490,f226]) ).
fof(f495,plain,
( ! [X0] :
( element(sK9(sK10,X0),powerset(sF14))
| ~ element(X0,sF14) )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f491,f226]) ).
fof(f505,plain,
( topstr_closure(sK10,sK11) = meet_of_subsets(sF13,sK9(sK10,sK11))
| ~ spl15_3 ),
inference(resolution,[],[f489,f227]) ).
fof(f508,plain,
( sF12 = meet_of_subsets(sF13,sK9(sK10,sK11))
| ~ spl15_3 ),
inference(forward_demodulation,[],[f505,f218]) ).
fof(f510,plain,
( sK11 = meet_of_subsets(sF13,sK9(sK10,sK11))
| ~ spl15_1
| ~ spl15_3 ),
inference(forward_demodulation,[],[f508,f231]) ).
fof(f528,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,sK9(sK10,X0)),sK10)
| ~ element(sK9(sK10,X0),powerset(sF14))
| closed_subset(sK7(sK10,sK9(sK10,X0)),sK10)
| ~ element(sK7(sK10,sK9(sK10,X0)),sF14)
| ~ element(X0,sF14) )
| ~ spl15_3
| ~ spl15_4 ),
inference(resolution,[],[f487,f255]) ).
fof(f529,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,sK9(sK10,X0)),sK10)
| ~ element(sK9(sK10,X0),powerset(sF14))
| ~ element(sK7(sK10,sK9(sK10,X0)),sF14)
| ~ element(X0,sF14) )
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f528,f488]) ).
fof(f533,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,sK9(sK10,X0)),sK10)
| ~ element(sK9(sK10,X0),powerset(sF14))
| ~ element(X0,sF14) )
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f529,f494]) ).
fof(f537,plain,
( ! [X0] :
( closed_subset(meet_of_subsets(sF13,sK9(sK10,X0)),sK10)
| ~ element(X0,sF14) )
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f533,f495]) ).
fof(f564,plain,
( closed_subset(sK11,sK10)
| ~ element(sK11,sF14)
| ~ spl15_1
| ~ spl15_3
| ~ spl15_4 ),
inference(superposition,[],[f537,f510]) ).
fof(f565,plain,
( ~ element(sK11,sF14)
| ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f564,f234]) ).
fof(f567,plain,
( $false
| ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f565,f227]) ).
fof(f568,plain,
( ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(avatar_contradiction_clause,[],[f567]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f236]) ).
cnf(s3,plain,
( ~ spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f242]) ).
cnf(s4,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s5,plain,
( ~ spl15_3
| spl15_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s14,plain,
( spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f470]) ).
cnf(s16,plain,
( ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s17,plain,
spl15_1,
inference(rat,[],[s1,s14]) ).
cnf(s18,plain,
~ spl15_2,
inference(rat,[],[s4,s17]) ).
cnf(s19,plain,
spl15_3,
inference(rat,[],[s3,s17]) ).
cnf(s20,plain,
~ spl15_4,
inference(rat,[],[s16,s17,s19,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s5,s20,s19]) ).
fof(f570,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU318+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:43:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.40 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
% 6.85/1.96 % (4150878)Detected formulas, will run a generic FOF schedule.
% 6.85/1.96 % (4150888)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1452978870:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.85/1.96 % (4150885)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=1637431685:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.85/1.96 % (4150884)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=2754920950:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.85/1.96 % (4150887)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=979889802:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.85/1.96 % (4150883)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=1809526734:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.85/1.96 % (4150889)dis-21_1_sil=8000:lcm=predicate:random_seed=1604364966: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)
% 6.85/1.96 % (4150886)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3139896277:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.85/1.96 % (4150886)Refutation not found, incomplete strategy
% 6.85/1.96 % (4150886)------------------------------
% 6.85/1.96 % (4150886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150886)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150886)Termination reason: Refutation not found, incomplete strategy
% 6.85/1.96 % (4150886)Time elapsed: 0.006 s
% 6.85/1.96 % (4150886)Peak memory usage: 88 MB
% 6.85/1.96 % (4150886)Instructions burned: 7 (million)
% 6.85/1.96 % (4150888)Instruction limit reached!
% 6.85/1.96 % (4150888)------------------------------
% 6.85/1.96 % (4150888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150888)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150888)Termination reason: Instruction limit
% 6.85/1.96 % (4150888)Termination phase: Saturation
% 6.85/1.96 % (4150888)Time elapsed: 0.055 s
% 6.85/1.96 % (4150888)Peak memory usage: 89 MB
% 6.85/1.96 % (4150888)Instructions burned: 142 (million)
% 6.85/1.96 % (4150887)Instruction limit reached!
% 6.85/1.96 % (4150887)------------------------------
% 6.85/1.96 % (4150887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150887)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150887)Termination reason: Instruction limit
% 6.85/1.96 % (4150887)Termination phase: Saturation
% 6.85/1.96 % (4150887)Time elapsed: 0.078 s
% 6.85/1.96 % (4150887)Peak memory usage: 88 MB
% 6.85/1.96 % (4150887)Instructions burned: 119 (million)
% 6.85/1.96 % (4150889)Instruction limit reached!
% 6.85/1.96 % (4150889)------------------------------
% 6.85/1.96 % (4150889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150889)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150889)Termination reason: Instruction limit
% 6.85/1.96 % (4150889)Termination phase: Saturation
% 6.85/1.96 % (4150889)Time elapsed: 0.082 s
% 6.85/1.96 % (4150889)Peak memory usage: 90 MB
% 6.85/1.96 % (4150889)Instructions burned: 130 (million)
% 6.85/1.96 % (4150897)lrs+10_1_sil=8000:sp=occurrence:random_seed=3978682169:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.85/1.96 % (4150899)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3295874391:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.85/1.96 % (4150898)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2825909264:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.85/1.96 % (4150886)------------------------------
% 6.85/1.96 % (4150886)------------------------------
% 6.85/1.96 % (4150897)Instruction limit reached!
% 6.85/1.96 % (4150897)------------------------------
% 6.85/1.96 % (4150897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150897)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150897)Termination reason: Instruction limit
% 6.85/1.96 % (4150897)Termination phase: Saturation
% 6.85/1.96 % (4150897)Time elapsed: 0.096 s
% 6.85/1.96 % (4150897)Peak memory usage: 92 MB
% 6.85/1.96 % (4150897)Instructions burned: 285 (million)
% 6.85/1.96 % (4150898)Instruction limit reached!
% 6.85/1.96 % (4150898)------------------------------
% 6.85/1.96 % (4150898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150898)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150898)Termination reason: Instruction limit
% 6.85/1.96 % (4150898)Termination phase: Saturation
% 6.85/1.96 % (4150898)Time elapsed: 0.082 s
% 6.85/1.96 % (4150898)Peak memory usage: 89 MB
% 6.85/1.96 % (4150898)Instructions burned: 157 (million)
% 6.85/1.96 % (4150904)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1226828835:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.85/1.96 % (4150904)Refutation not found, incomplete strategy
% 6.85/1.96 % (4150904)------------------------------
% 6.85/1.96 % (4150904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150904)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150904)Termination reason: Refutation not found, incomplete strategy
% 6.85/1.96 % (4150904)Time elapsed: 0.004 s
% 6.85/1.96 % (4150904)Peak memory usage: 88 MB
% 6.85/1.96 % (4150904)Instructions burned: 9 (million)
% 6.85/1.96 % (4150903)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1118616370:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.85/1.96 % (4150899)Instruction limit reached!
% 6.85/1.96 % (4150899)------------------------------
% 6.85/1.96 % (4150899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150899)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150899)Termination reason: Instruction limit
% 6.85/1.96 % (4150899)Termination phase: Saturation
% 6.85/1.96 % (4150899)Time elapsed: 0.230 s
% 6.85/1.96 % (4150899)Peak memory usage: 91 MB
% 6.85/1.96 % (4150899)Instructions burned: 325 (million)
% 6.85/1.96 % (4150905)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2762626702:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.85/1.96 % (4150904)------------------------------
% 6.85/1.96 % (4150904)------------------------------
% 6.85/1.96 % (4150903)Instruction limit reached!
% 6.85/1.96 % (4150903)------------------------------
% 6.85/1.96 % (4150903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150903)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150903)Termination reason: Instruction limit
% 6.85/1.96 % (4150903)Termination phase: Saturation
% 6.85/1.96 % (4150903)Time elapsed: 0.152 s
% 6.85/1.96 % (4150903)Peak memory usage: 90 MB
% 6.85/1.96 % (4150903)Instructions burned: 249 (million)
% 6.85/1.96 % (4150908)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1346034455:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.85/1.96 % (4150910)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2952130969:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.85/1.96 % (4150883)First to succeed.
% 6.85/1.96 % (4150883)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4150878"
% 6.85/1.96 % (4150884)Also succeeded, but the first one will report.
% 6.85/1.96 % (4150910)Instruction limit reached!
% 6.85/1.96 % (4150910)------------------------------
% 6.85/1.96 % (4150910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150910)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150910)Termination reason: Instruction limit
% 6.85/1.96 % (4150910)Termination phase: Saturation
% 6.85/1.96 % (4150910)Time elapsed: 0.036 s
% 6.85/1.96 % (4150910)Peak memory usage: 89 MB
% 6.85/1.96 % (4150910)Instructions burned: 127 (million)
% 6.85/1.96 % (4150908)Instruction limit reached!
% 6.85/1.96 % (4150908)------------------------------
% 6.85/1.96 % (4150908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150908)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150908)Termination reason: Instruction limit
% 6.85/1.96 % (4150908)Termination phase: Saturation
% 6.85/1.96 % (4150908)Time elapsed: 0.080 s
% 6.85/1.96 % (4150908)Peak memory usage: 89 MB
% 6.85/1.96 % (4150908)Instructions burned: 114 (million)
% 6.85/1.96 % (4150911)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1537524470:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.85/1.96 % (4150911)Instruction limit reached!
% 6.85/1.96 % (4150911)------------------------------
% 6.85/1.96 % (4150911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/1.96 % (4150911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/1.96 % (4150911)CaDiCaL version: 2.1.3
% 6.85/1.96 % (4150911)Termination reason: Instruction limit
% 6.85/1.96 % (4150911)Termination phase: Saturation
% 6.85/1.96 % (4150911)Time elapsed: 0.068 s
% 6.85/1.96 % (4150911)Peak memory usage: 89 MB
% 6.85/1.96 % (4150911)Instructions burned: 115 (million)
% 6.85/1.96 % (4150914)lrs+10_1_sil=8000:sp=occurrence:random_seed=2061701393:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.85/1.96 % (4150885)Also succeeded, but the first one will report.
% 6.85/1.96 % (4150915)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=54188918:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.85/1.96 % (4150914)Also succeeded, but the first one will report.
% 6.85/1.96 % (4150883)Refutation found. Thanks to Tanya!
% 6.85/1.96 % SZS status Theorem for theBenchmark
% 6.85/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.46/2.15 % (4150883)------------------------------
% 8.46/2.15 % (4150883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.46/2.15 % (4150883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.46/2.15 % (4150883)CaDiCaL version: 2.1.3
% 8.46/2.15 % (4150883)Termination reason: Refutation
% 8.46/2.15 % (4150883)Time elapsed: 0.677 s
% 8.46/2.15 % (4150883)Peak memory usage: 128 MB
% 8.46/2.15 % (4150883)Instructions burned: 998 (million)
% 8.46/2.15 % (4150883)------------------------------
% 8.46/2.15 % (4150883)------------------------------
% 8.46/2.15 % (4150878)Success in time 1.117 s
% 8.46/2.15 % Vampire exiting
%------------------------------------------------------------------------------