%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:52:49 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 94 ( 12 unt; 7 def)
% Number of atoms : 398 ( 53 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 475 ( 171 ~; 199 |; 82 &)
% ( 13 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 96 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f37,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,powerset(the_carrier(X0)))
& X4 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(f38,plain,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
=> X3 = X4 )
=> ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(X7,powerset(the_carrier(X0)))
& X6 = X7
& in(set_difference(cast_as_carrier_subset(X0),X6),X1) ) ) ) ),
inference(rectify,[],[f37]) ).
fof(f56,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f57,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f56]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(X7,powerset(the_carrier(X0)))
& X6 = X7
& in(set_difference(cast_as_carrier_subset(X0),X6),X1) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(X7,powerset(the_carrier(X0)))
& X6 = X7
& in(set_difference(cast_as_carrier_subset(X0),X6),X1) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f79]) ).
fof(f81,definition,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
| ~ sP0(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(X7,powerset(the_carrier(X0)))
& X6 = X7
& in(set_difference(cast_as_carrier_subset(X0),X6),X1) ) )
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f80,f81]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| in(X3,X2) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(nnf_transformation,[],[f57]) ).
fof(f84,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,powerset(the_carrier(X0)))
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| in(X3,X2) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
( ! [X2] :
( ( ~ in(sK3(X2),powerset(the_carrier(sK1)))
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),X2) )
& ( ( in(sK3(X2),powerset(the_carrier(sK1)))
& in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2) )
| in(sK3(X2),X2) ) )
& topological_space(sK1)
& top_str(sK1)
& element(sK2,powerset(powerset(the_carrier(sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X3,sK3(X2))],[f84]) ).
fof(f90,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X4),X1) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X0) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( sK9(X0,X1) != sK10(X0,X1)
& sK8(X0,X1) = sK9(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
& sK8(X0,X1) = sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1))],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X5] :
! [X6] :
( ( in(X6,X5)
| ! [X7] :
( ~ in(X7,powerset(the_carrier(X0)))
| X6 != X7
| ~ in(set_difference(cast_as_carrier_subset(X0),X6),X1) ) )
& ( ? [X7] :
( in(X7,powerset(the_carrier(X0)))
& X6 = X7
& in(set_difference(cast_as_carrier_subset(X0),X6),X1) )
| ~ in(X6,X5) ) )
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(nnf_transformation,[],[f82]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& ( ? [X5] :
( in(X5,powerset(the_carrier(X0)))
& X3 = X5
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,X2) ) )
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& ( ( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
& sK12(X0,X1,X3) = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,sK11(X0,X1)) ) )
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X2,sK11(X0,X1)),skolemize(X5,sK12(X0,X1,X3))],[f94]) ).
fof(f96,plain,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f85]) ).
fof(f97,plain,
top_str(sK1),
inference(cnf_transformation,[],[f85]) ).
fof(f98,plain,
topological_space(sK1),
inference(cnf_transformation,[],[f85]) ).
fof(f99,plain,
! [X2] :
( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f100,plain,
! [X2] :
( in(sK3(X2),powerset(the_carrier(sK1)))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f101,plain,
! [X2] :
( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1)))
| ~ in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK8(X0,X1) = sK10(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK8(X0,X1) = sK9(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f160,plain,
! [X0,X1] :
( sK9(X0,X1) != sK10(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f161,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| sK12(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f164,plain,
! [X3,X0,X1,X4] :
( in(X3,sK11(X0,X1))
| ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK11(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f164]) ).
fof(f320,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(resolution,[],[f161,f96]) ).
fof(f324,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ top_str(sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(forward_subsumption_resolution,[],[f320,f98]) ).
fof(f325,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(forward_subsumption_resolution,[],[f324,f97]) ).
fof(f327,definition,
( spl13_11
<=> sP0(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f328,plain,
( ~ sP0(sK2,sK1)
| spl13_11 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f329,plain,
( sP0(sK2,sK1)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f331,definition,
( spl13_12
<=> ! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f332,plain,
( ! [X0] :
( in(set_difference(cast_as_carrier_subset(sK1),X0),sK2)
| ~ in(X0,sK11(sK1,sK2)) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( spl13_11
| spl13_12 ),
inference(avatar_split_clause,[],[f325,f331,f327]) ).
fof(f335,plain,
( sK8(sK2,sK1) = sK10(sK2,sK1)
| ~ spl13_11 ),
inference(resolution,[],[f329,f157]) ).
fof(f336,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| sK12(sK1,sK2,X0) = X0 ),
inference(resolution,[],[f162,f96]) ).
fof(f344,plain,
( sK8(sK2,sK1) != sK9(sK2,sK1)
| ~ sP0(sK2,sK1)
| ~ spl13_11 ),
inference(superposition,[],[f160,f335]) ).
fof(f345,plain,
( ~ sP0(sK2,sK1)
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f344,f159]) ).
fof(f347,plain,
( $false
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f345,f329]) ).
fof(f348,plain,
~ spl13_11,
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f349,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ top_str(sK1)
| sK12(sK1,sK2,X0) = X0 ),
inference(forward_subsumption_resolution,[],[f336,f98]) ).
fof(f350,plain,
! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sP0(sK2,sK1)
| sK12(sK1,sK2,X0) = X0 ),
inference(forward_subsumption_resolution,[],[f349,f97]) ).
fof(f352,definition,
( spl13_13
<=> ! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sK12(sK1,sK2,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f353,plain,
( ! [X0] :
( ~ in(X0,sK11(sK1,sK2))
| sK12(sK1,sK2,X0) = X0 )
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f354,plain,
( spl13_11
| spl13_13 ),
inference(avatar_split_clause,[],[f350,f352,f327]) ).
fof(f355,plain,
! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) ),
inference(resolution,[],[f165,f99]) ).
fof(f358,plain,
! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f355,f98]) ).
fof(f359,plain,
! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f358,f97]) ).
fof(f360,plain,
! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK11(sK1,sK2))
| sP0(sK2,sK1)
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f359,f96]) ).
fof(f361,plain,
! [X0] :
( in(sK3(X0),sK11(sK1,sK2))
| sP0(sK2,sK1)
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f360,f100]) ).
fof(f363,definition,
( spl13_14
<=> ! [X0] :
( in(sK3(X0),sK11(sK1,sK2))
| in(sK3(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f364,plain,
( ! [X0] :
( in(sK3(X0),sK11(sK1,sK2))
| in(sK3(X0),X0) )
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( spl13_11
| spl13_14 ),
inference(avatar_split_clause,[],[f361,f363,f327]) ).
fof(f368,plain,
( in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ spl13_14 ),
inference(factoring,[],[f364]) ).
fof(f370,plain,
( ! [X0] :
( ~ in(sK3(X0),sK11(sK1,sK2))
| ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(sK3(X0),X0) )
| ~ spl13_12 ),
inference(resolution,[],[f332,f101]) ).
fof(f373,plain,
( ! [X0] :
( in(sK3(X0),X0)
| sK3(X0) = sK12(sK1,sK2,sK3(X0)) )
| ~ spl13_13
| ~ spl13_14 ),
inference(resolution,[],[f353,f364]) ).
fof(f379,definition,
( spl13_15
<=> in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1))) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f383,definition,
( spl13_16
<=> sK3(sK11(sK1,sK2)) = sK12(sK1,sK2,sK3(sK11(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f385,plain,
( sK3(sK11(sK1,sK2)) = sK12(sK1,sK2,sK3(sK11(sK1,sK2)))
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f393,plain,
( sK3(sK11(sK1,sK2)) = sK12(sK1,sK2,sK3(sK11(sK1,sK2)))
| sK3(sK11(sK1,sK2)) = sK12(sK1,sK2,sK3(sK11(sK1,sK2)))
| ~ spl13_13
| ~ spl13_14 ),
inference(resolution,[],[f373,f353]) ).
fof(f394,plain,
( sK3(sK11(sK1,sK2)) = sK12(sK1,sK2,sK3(sK11(sK1,sK2)))
| ~ spl13_13
| ~ spl13_14 ),
inference(duplicate_literal_removal,[],[f393]) ).
fof(f395,plain,
( spl13_16
| ~ spl13_13
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f394,f363,f352,f383]) ).
fof(f397,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ spl13_16 ),
inference(superposition,[],[f163,f385]) ).
fof(f398,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f397,f100]) ).
fof(f404,plain,
( ~ in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ spl13_12
| ~ spl13_14 ),
inference(resolution,[],[f370,f368]) ).
fof(f408,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f398,f328]) ).
fof(f409,plain,
( ~ in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ spl13_12
| ~ spl13_14 ),
inference(forward_subsumption_resolution,[],[f404,f368]) ).
fof(f410,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f408,f98]) ).
fof(f411,plain,
( ~ spl13_15
| ~ spl13_12
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f409,f363,f331,f379]) ).
fof(f412,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f410,f97]) ).
fof(f413,plain,
( in(sK3(sK11(sK1,sK2)),powerset(the_carrier(sK1)))
| spl13_11
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f412,f96]) ).
fof(f414,plain,
( spl13_15
| spl13_11
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f413,f383,f327,f379]) ).
cnf(s6,plain,
( spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f333]) ).
cnf(s7,plain,
~ spl13_11,
inference(sat_conversion,[],[f348]) ).
cnf(s8,plain,
( spl13_11
| spl13_13 ),
inference(sat_conversion,[],[f354]) ).
cnf(s9,plain,
( spl13_11
| spl13_14 ),
inference(sat_conversion,[],[f365]) ).
cnf(s11,plain,
( ~ spl13_13
| ~ spl13_14
| spl13_16 ),
inference(sat_conversion,[],[f395]) ).
cnf(s13,plain,
( ~ spl13_12
| ~ spl13_14
| ~ spl13_15 ),
inference(sat_conversion,[],[f411]) ).
cnf(s14,plain,
( spl13_11
| spl13_15
| ~ spl13_16 ),
inference(sat_conversion,[],[f414]) ).
cnf(s15,plain,
spl13_14,
inference(rat,[],[s9,s7]) ).
cnf(s16,plain,
spl13_13,
inference(rat,[],[s8,s7]) ).
cnf(s17,plain,
spl13_16,
inference(rat,[],[s11,s15,s16]) ).
cnf(s18,plain,
spl13_15,
inference(rat,[],[s14,s7,s17]) ).
cnf(s19,plain,
~ spl13_12,
inference(rat,[],[s13,s15,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s6,s19,s7]) ).
fof(f415,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n011.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 04:38:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 % (3019319)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (3019328)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3644913975:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (3019325)% WARNING: option uhcvi not known.
% 0.18/0.49 % (3019326)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1627947510:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (3019324)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2674154304_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (3019325)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4031112866:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (3019327)dis+10_1_sil=32000:sp=arity:random_seed=4216039781:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (3019329)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=491962239:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (3019330)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1892800779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % TRYING [2]
% 0.18/0.49 % TRYING [3]
% 0.18/0.49 % (3019327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3019319-3019327"...
% 0.18/0.49 % (3019329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3019319-3019329"...
% 0.18/0.49 % (3019327)...printing done.
% 0.18/0.49 % (3019327)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (3019327)------------------------------
% 0.18/0.49 % (3019327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (3019327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (3019327)CaDiCaL version: 2.1.3
% 0.18/0.49 % (3019327)Termination reason: Refutation
% 0.18/0.49 % (3019327)Time elapsed: 0.010 s
% 0.18/0.49 % (3019327)Peak memory usage: 12 MB
% 0.18/0.49 % (3019327)Instructions burned: 13 (million)
% 0.18/0.49 % (3019319)Success in time 0.054 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------