%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:48:17 PM UTC 2026
% Result : Theorem 2.92s 2.01s
% Output : Refutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 76 ( 8 unt; 3 def)
% Number of atoms : 356 ( 47 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 429 ( 149 ~; 179 |; 82 &)
% ( 9 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 136 ( 0 sgn 93 !; 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/sandbox2/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/sandbox2/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(f58,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(f59,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,[],[f58]) ).
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,[],[f59,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(f86,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(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( sK5(X0,X1) != sK6(X0,X1)
& sK4(X0,X1) = sK5(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK5(X0,X1)),X0)
& sK4(X0,X1) = sK6(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK6(X0,X1)),X0) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1))],[f87]) ).
fof(f89,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(f90,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,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK7(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& ( ( in(sK8(X0,X1,X3),powerset(the_carrier(X0)))
& sK8(X0,X1,X3) = X3
& in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
| ~ in(X3,sK7(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,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X5,sK8(X0,X1,X3))],[f90]) ).
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(f103,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK4(X0,X1) = sK6(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f105,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK4(X0,X1) = sK5(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f106,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f107,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK7(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f108,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK7(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| sK8(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f91]) ).
fof(f109,plain,
! [X3,X0,X1] :
( in(sK8(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK7(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f110,plain,
! [X3,X0,X1,X4] :
( in(X3,sK7(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,[],[f91]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK7(X0,X1))
| sP0(X1,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f110]) ).
fof(f328,plain,
! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(resolution,[],[f107,f96]) ).
fof(f332,plain,
! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| sP0(sK2,sK1)
| ~ top_str(sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(forward_subsumption_resolution,[],[f328,f98]) ).
fof(f333,plain,
! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| sP0(sK2,sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ),
inference(forward_subsumption_resolution,[],[f332,f97]) ).
fof(f335,definition,
( spl13_11
<=> sP0(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f336,plain,
( ~ sP0(sK2,sK1)
| spl13_11 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( sP0(sK2,sK1)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f339,definition,
( spl13_12
<=> ! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| in(set_difference(cast_as_carrier_subset(sK1),X0),sK2) ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f340,plain,
( ! [X0] :
( in(set_difference(cast_as_carrier_subset(sK1),X0),sK2)
| ~ in(X0,sK7(sK1,sK2)) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f341,plain,
( spl13_11
| spl13_12 ),
inference(avatar_split_clause,[],[f333,f339,f335]) ).
fof(f343,plain,
( sK4(sK2,sK1) = sK6(sK2,sK1)
| ~ spl13_11 ),
inference(resolution,[],[f337,f103]) ).
fof(f344,plain,
! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| sK8(sK1,sK2,X0) = X0 ),
inference(resolution,[],[f108,f96]) ).
fof(f352,plain,
( sK4(sK2,sK1) != sK5(sK2,sK1)
| ~ sP0(sK2,sK1)
| ~ spl13_11 ),
inference(superposition,[],[f106,f343]) ).
fof(f353,plain,
( ~ sP0(sK2,sK1)
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f352,f105]) ).
fof(f354,plain,
( $false
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f353,f337]) ).
fof(f355,plain,
~ spl13_11,
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f356,plain,
( ! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| ~ topological_space(sK1)
| ~ top_str(sK1)
| sK8(sK1,sK2,X0) = X0 )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f344,f336]) ).
fof(f357,plain,
( ! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| ~ top_str(sK1)
| sK8(sK1,sK2,X0) = X0 )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f356,f98]) ).
fof(f358,plain,
( ! [X0] :
( ~ in(X0,sK7(sK1,sK2))
| sK8(sK1,sK2,X0) = X0 )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f357,f97]) ).
fof(f359,plain,
! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK7(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(f362,plain,
( ! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK7(sK1,sK2))
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f359,f336]) ).
fof(f363,plain,
( ! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK7(sK1,sK2))
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f362,f98]) ).
fof(f364,plain,
( ! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK7(sK1,sK2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK3(X0),X0) )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f363,f97]) ).
fof(f365,plain,
( ! [X0] :
( ~ in(sK3(X0),powerset(the_carrier(sK1)))
| in(sK3(X0),sK7(sK1,sK2))
| in(sK3(X0),X0) )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f364,f96]) ).
fof(f366,plain,
( ! [X0] :
( in(sK3(X0),sK7(sK1,sK2))
| in(sK3(X0),X0) )
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f365,f100]) ).
fof(f369,plain,
( in(sK3(sK7(sK1,sK2)),sK7(sK1,sK2))
| spl13_11 ),
inference(factoring,[],[f366]) ).
fof(f371,plain,
( ! [X0] :
( ~ in(sK3(X0),sK7(sK1,sK2))
| ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(sK3(X0),X0) )
| ~ spl13_12 ),
inference(resolution,[],[f340,f101]) ).
fof(f376,plain,
( sK3(sK7(sK1,sK2)) = sK8(sK1,sK2,sK3(sK7(sK1,sK2)))
| spl13_11 ),
inference(resolution,[],[f358,f369]) ).
fof(f383,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ in(sK3(sK7(sK1,sK2)),sK7(sK1,sK2))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11 ),
inference(superposition,[],[f109,f376]) ).
fof(f384,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| sP0(sK2,sK1)
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f383,f100]) ).
fof(f385,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ topological_space(sK1)
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f384,f336]) ).
fof(f386,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ top_str(sK1)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f385,f98]) ).
fof(f387,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f386,f97]) ).
fof(f388,plain,
( in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f387,f96]) ).
fof(f393,plain,
( ~ in(sK3(sK7(sK1,sK2)),powerset(the_carrier(sK1)))
| ~ in(sK3(sK7(sK1,sK2)),sK7(sK1,sK2))
| spl13_11
| ~ spl13_12 ),
inference(resolution,[],[f371,f369]) ).
fof(f394,plain,
( ~ in(sK3(sK7(sK1,sK2)),sK7(sK1,sK2))
| spl13_11
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f393,f388]) ).
fof(f395,plain,
( $false
| spl13_11
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f394,f369]) ).
fof(f396,plain,
( spl13_11
| ~ spl13_12 ),
inference(avatar_contradiction_clause,[],[f395]) ).
cnf(s6,plain,
( spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f341]) ).
cnf(s7,plain,
~ spl13_11,
inference(sat_conversion,[],[f355]) ).
cnf(s8,plain,
( spl13_11
| ~ spl13_12 ),
inference(sat_conversion,[],[f396]) ).
cnf(s9,plain,
~ spl13_12,
inference(rat,[],[s8,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s9,s7]) ).
fof(f397,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 04:38:22 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.92/2.01 % (4152644)Detected formulas, will run a generic FOF schedule.
% 2.92/2.01 % (4152675)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=1451028721:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.92/2.01 % (4152673)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=1857680596:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.92/2.01 % (4152678)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3734833055:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.92/2.01 % (4152678)Refutation not found, incomplete strategy
% 2.92/2.01 % (4152678)------------------------------
% 2.92/2.01 % (4152678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152678)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152678)Termination reason: Refutation not found, incomplete strategy
% 2.92/2.01 % (4152678)Time elapsed: 0.008 s
% 2.92/2.01 % (4152678)Peak memory usage: 89 MB
% 2.92/2.01 % (4152678)Instructions burned: 7 (million)
% 2.92/2.01 % (4152674)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=4293921153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.92/2.01 % (4152677)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=147473038:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.92/2.01 % (4152676)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2106183456:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.92/2.01 % (4152676)Refutation not found, incomplete strategy
% 2.92/2.01 % (4152676)------------------------------
% 2.92/2.01 % (4152676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152676)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152676)Termination reason: Refutation not found, incomplete strategy
% 2.92/2.01 % (4152676)Time elapsed: 0.003 s
% 2.92/2.01 % (4152676)Peak memory usage: 88 MB
% 2.92/2.01 % (4152676)Instructions burned: 1 (million)
% 2.92/2.01 % (4152677)Refutation not found, incomplete strategy
% 2.92/2.01 % (4152677)------------------------------
% 2.92/2.01 % (4152677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152677)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152677)Termination reason: Refutation not found, incomplete strategy
% 2.92/2.01 % (4152677)Time elapsed: 0.003 s
% 2.92/2.01 % (4152677)Peak memory usage: 88 MB
% 2.92/2.01 % (4152677)Instructions burned: 1 (million)
% 2.92/2.01 % (4152679)dis-21_1_sil=8000:lcm=predicate:random_seed=1035255675: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)
% 2.92/2.01 % (4152679)Instruction limit reached!
% 2.92/2.01 % (4152679)------------------------------
% 2.92/2.01 % (4152679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152679)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152679)Termination reason: Instruction limit
% 2.92/2.01 % (4152679)Termination phase: Saturation
% 2.92/2.01 % (4152679)Time elapsed: 0.113 s
% 2.92/2.01 % (4152679)Peak memory usage: 89 MB
% 2.92/2.01 % (4152679)Instructions burned: 130 (million)
% 2.92/2.01 % (4152691)lrs+10_1_sil=8000:sp=occurrence:random_seed=3490766497:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 2.92/2.01 % (4152691)First to succeed.
% 2.92/2.01 % (4152691)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4152644"
% 2.92/2.01 % (4152678)------------------------------
% 2.92/2.01 % (4152678)------------------------------
% 2.92/2.01 % (4152676)------------------------------
% 2.92/2.01 % (4152676)------------------------------
% 2.92/2.01 % (4152677)------------------------------
% 2.92/2.01 % (4152677)------------------------------
% 2.92/2.01 % (4152695)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1032969204:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/157Mi)
% 2.92/2.01 % (4152695)Refutation not found, incomplete strategy
% 2.92/2.01 % (4152695)------------------------------
% 2.92/2.01 % (4152695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152695)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152695)Termination reason: Refutation not found, incomplete strategy
% 2.92/2.01 % (4152695)Time elapsed: 0.004 s
% 2.92/2.01 % (4152695)Peak memory usage: 89 MB
% 2.92/2.01 % (4152695)Instructions burned: 3 (million)
% 2.92/2.01 % (4152697)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=3360694181:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 2.92/2.01 % (4152696)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1100165459:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 2.92/2.01 % (4152696)Also succeeded, but the first one will report.
% 2.92/2.01 % (4152675)Also succeeded, but the first one will report.
% 2.92/2.01 % (4152697)Instruction limit reached!
% 2.92/2.01 % (4152697)------------------------------
% 2.92/2.01 % (4152697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/2.01 % (4152697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/2.01 % (4152697)CaDiCaL version: 2.1.3
% 2.92/2.01 % (4152697)Termination reason: Instruction limit
% 2.92/2.01 % (4152697)Termination phase: Saturation
% 2.92/2.01 % (4152697)Time elapsed: 0.099 s
% 2.92/2.01 % (4152697)Peak memory usage: 89 MB
% 2.92/2.01 % (4152697)Instructions burned: 249 (million)
% 2.92/2.01 % (4152691)Refutation found. Thanks to Tanya!
% 2.92/2.01 % SZS status Theorem for theBenchmark
% 2.92/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 7.60/2.22 % (4152691)------------------------------
% 7.60/2.22 % (4152691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/2.22 % (4152691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/2.22 % (4152691)CaDiCaL version: 2.1.3
% 7.60/2.22 % (4152691)Termination reason: Refutation
% 7.60/2.22 % (4152691)Time elapsed: 0.016 s
% 7.60/2.22 % (4152691)Peak memory usage: 89 MB
% 7.60/2.22 % (4152691)Instructions burned: 12 (million)
% 7.60/2.22 % (4152691)------------------------------
% 7.60/2.22 % (4152691)------------------------------
% 7.60/2.22 % (4152644)Success in time 0.963 s
% 7.60/2.22 % Vampire exiting
%------------------------------------------------------------------------------