%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU315+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 : n013.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 12:52:50 PM UTC 2026
% Result : Theorem 1.04s 0.60s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 96 ( 16 unt; 2 def)
% Number of atoms : 425 ( 27 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 535 ( 206 ~; 207 |; 100 &)
% ( 11 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 162 ( 0 sgn 125 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f31,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f58,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f59,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f58]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f59]) ).
fof(f82,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(sK0)))
| sK2(X2) != X4
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,sK2(X2)) )
| ~ in(sK2(X2),X2) )
& ( ( element(sK3(X2),powerset(the_carrier(sK0)))
& sK2(X2) = sK3(X2)
& closed_subset(sK3(X2),sK0)
& subset(sK1,sK2(X2)) )
| in(sK2(X2),X2) )
& element(sK2(X2),powerset(the_carrier(sK0))) ) )
& topological_space(sK0)
& top_str(sK0)
& element(sK1,powerset(the_carrier(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X5,sK3(X2))],[f83]) ).
fof(f89,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f75]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK8(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& element(sK9(X0,X1,X3),powerset(the_carrier(X0)))
& sK9(X0,X1,X3) = X3
& closed_subset(sK9(X0,X1,X3),X0)
& subset(X1,X3) )
| ~ in(X3,sK8(X0,X1)) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8(X0,X1)),skolemize(X5,sK9(X0,X1,X3))],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f95,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f77]) ).
fof(f98,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f84]) ).
fof(f99,plain,
top_str(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f100,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f101,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| element(sK2(X2),powerset(the_carrier(sK0))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f102,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| subset(sK1,sK2(X2))
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f103,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| closed_subset(sK3(X2),sK0)
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f104,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| sK2(X2) = sK3(X2)
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
! [X2,X4] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ element(X4,powerset(the_carrier(sK0)))
| sK2(X2) != X4
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,sK2(X2))
| ~ in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f145,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f146,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| subset(X1,X3)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f147,plain,
! [X3,X0,X1] :
( closed_subset(sK9(X0,X1,X3),X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f148,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| sK9(X0,X1,X3) = X3
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f150,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| in(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f151,plain,
! [X3,X0,X1,X4] :
( in(X3,sK8(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f165,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ element(sK2(X2),powerset(the_carrier(sK0)))
| ~ closed_subset(sK2(X2),sK0)
| ~ subset(sK1,sK2(X2))
| ~ in(sK2(X2),X2) ),
inference(equality_resolution,[],[f106]) ).
fof(f166,plain,
! [X0,X1,X4] :
( ~ top_str(X0)
| ~ in(X4,powerset(the_carrier(X0)))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ topological_space(X0)
| in(X4,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(equality_resolution,[],[f151]) ).
fof(f167,plain,
! [X0,X1] :
( ~ in(X1,X0)
| element(X1,X0) ),
inference(forward_subsumption_resolution,[],[f155,f163]) ).
fof(f168,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| closed_subset(X3,X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(backward_subsumption_demodulation,[],[f147,f148]) ).
fof(f170,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| closed_subset(sK2(X2),sK0)
| in(sK2(X2),X2) ),
inference(backward_subsumption_demodulation,[],[f103,f104]) ).
fof(f172,plain,
! [X2] :
( ~ in(sK2(X2),X2)
| ~ closed_subset(sK2(X2),sK0)
| ~ subset(sK1,sK2(X2))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f165,f101]) ).
fof(f311,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f146,f99]) ).
fof(f312,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(sK0)))
| subset(X1,X0)
| ~ in(X0,sK8(sK0,X1)) ),
inference(forward_subsumption_resolution,[],[f311,f100]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| closed_subset(X0,sK0)
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f168,f99]) ).
fof(f316,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(sK0)))
| closed_subset(X0,sK0)
| ~ in(X0,sK8(sK0,X1)) ),
inference(forward_subsumption_resolution,[],[f315,f100]) ).
fof(f317,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f150,f99]) ).
fof(f318,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(sK0)))
| in(X0,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(forward_subsumption_resolution,[],[f317,f100]) ).
fof(f325,plain,
! [X0,X1] :
( ~ in(X0,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ closed_subset(X0,sK0)
| ~ subset(X1,X0)
| ~ topological_space(sK0)
| in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f166,f99]) ).
fof(f326,plain,
! [X0,X1] :
( ~ in(X0,powerset(the_carrier(sK0)))
| ~ closed_subset(X0,sK0)
| ~ subset(X1,X0)
| ~ topological_space(sK0)
| in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f325,f167]) ).
fof(f327,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ closed_subset(X0,sK0)
| ~ in(X0,powerset(the_carrier(sK0)))
| in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f326,f100]) ).
fof(f330,plain,
! [X0] :
( ~ in(X0,sK8(sK0,sK1))
| subset(sK1,X0) ),
inference(resolution,[],[f312,f98]) ).
fof(f608,plain,
! [X0] :
( ~ in(X0,sK8(sK0,sK1))
| closed_subset(X0,sK0) ),
inference(resolution,[],[f316,f98]) ).
fof(f620,plain,
! [X0] :
( ~ in(X0,sK8(sK0,sK1))
| in(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f318,f98]) ).
fof(f1378,plain,
! [X0] :
( in(sK11(sK8(sK0,sK1),X0),powerset(the_carrier(sK0)))
| element(sK8(sK0,sK1),powerset(X0)) ),
inference(resolution,[],[f620,f158]) ).
fof(f1780,plain,
( element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0)))) ),
inference(resolution,[],[f1378,f159]) ).
fof(f1783,plain,
element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0)))),
inference(duplicate_literal_removal,[],[f1780]) ).
fof(f1793,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(resolution,[],[f1783,f170]) ).
fof(f1794,plain,
( subset(sK1,sK2(sK8(sK0,sK1)))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(resolution,[],[f1783,f102]) ).
fof(f1795,plain,
element(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0))),
inference(resolution,[],[f1783,f101]) ).
fof(f1798,plain,
subset(sK1,sK2(sK8(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f1794,f330]) ).
fof(f1799,plain,
closed_subset(sK2(sK8(sK0,sK1)),sK0),
inference(forward_subsumption_resolution,[],[f1793,f608]) ).
fof(f1801,definition,
( spl14_63
<=> in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_63])],[avatar_definition]) ).
fof(f1802,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| spl14_63 ),
inference(avatar_component_clause,[],[f1801]) ).
fof(f1803,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ spl14_63 ),
inference(avatar_component_clause,[],[f1801]) ).
fof(f1816,plain,
( ~ closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f1798,f327]) ).
fof(f1823,definition,
( spl14_66
<=> in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0))) ),
introduced(definition,[new_symbols(definition,[spl14_66])],[avatar_definition]) ).
fof(f1824,plain,
( in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f1823]) ).
fof(f1825,plain,
( ~ in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| spl14_66 ),
inference(avatar_component_clause,[],[f1823]) ).
fof(f1839,plain,
( in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| empty(powerset(the_carrier(sK0))) ),
inference(resolution,[],[f1795,f154]) ).
fof(f1840,plain,
( empty(powerset(the_carrier(sK0)))
| spl14_66 ),
inference(forward_subsumption_resolution,[],[f1839,f1825]) ).
fof(f1841,plain,
( $false
| spl14_66 ),
inference(forward_subsumption_resolution,[],[f1840,f145]) ).
fof(f1842,plain,
spl14_66,
inference(avatar_contradiction_clause,[],[f1841]) ).
fof(f1850,plain,
( ~ closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_63 ),
inference(resolution,[],[f1803,f172]) ).
fof(f1858,plain,
( ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_63 ),
inference(forward_subsumption_resolution,[],[f1850,f1799]) ).
fof(f1859,plain,
( ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_63 ),
inference(forward_subsumption_resolution,[],[f1858,f1798]) ).
fof(f1860,plain,
( $false
| ~ spl14_63 ),
inference(forward_subsumption_resolution,[],[f1859,f1783]) ).
fof(f1861,plain,
~ spl14_63,
inference(avatar_contradiction_clause,[],[f1860]) ).
fof(f1862,plain,
( ~ in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f1816,f1799]) ).
fof(f1863,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ spl14_66 ),
inference(forward_subsumption_resolution,[],[f1862,f1824]) ).
fof(f1864,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| spl14_63
| ~ spl14_66 ),
inference(forward_subsumption_resolution,[],[f1863,f1802]) ).
fof(f1865,plain,
( $false
| spl14_63
| ~ spl14_66 ),
inference(forward_subsumption_resolution,[],[f1864,f98]) ).
fof(f1866,plain,
( spl14_63
| ~ spl14_66 ),
inference(avatar_contradiction_clause,[],[f1865]) ).
cnf(s65,plain,
spl14_66,
inference(sat_conversion,[],[f1842]) ).
cnf(s66,plain,
~ spl14_63,
inference(sat_conversion,[],[f1861]) ).
cnf(s67,plain,
( spl14_63
| ~ spl14_66 ),
inference(sat_conversion,[],[f1866]) ).
cnf(s68,plain,
~ spl14_66,
inference(rat,[],[s67,s66]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s65,s68]) ).
fof(f1867,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:39:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 1.04/0.60 % (804208)Will run a generic schedule for satisfiability detection.
% 1.04/0.60 % (804219)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=179651091:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.04/0.60 % (804214)% WARNING: option uhcvi not known.
% 1.04/0.60 % (804213)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4219809105_2999 on theBenchmark for (2999ds/0Mi)
% 1.04/0.60 % (804215)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2347651599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.04/0.60 % (804214)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=237691670:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.04/0.60 % (804216)dis+10_1_sil=32000:sp=arity:random_seed=4142831705:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.04/0.60 % (804218)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2621129673:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.04/0.60 % (804217)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4264118840:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.04/0.60 % TRYING [1]
% 1.04/0.60 % TRYING [2]
% 1.04/0.60 % TRYING [3]
% 1.04/0.60 % TRYING [4]
% 1.04/0.60 % TRYING [5]
% 1.04/0.60 % (804219)Instruction limit reached!
% 1.04/0.60 % (804219)------------------------------
% 1.04/0.60 % (804219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.60 % (804219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.60 % (804219)CaDiCaL version: 2.1.3
% 1.04/0.60 % (804219)Termination reason: Instruction limit
% 1.04/0.60 % (804219)Termination phase: Saturation
% 1.04/0.60 % (804219)Time elapsed: 0.062 s
% 1.04/0.60 % (804219)Peak memory usage: 14 MB
% 1.04/0.60 % (804219)Instructions burned: 161 (million)
% 1.04/0.60 % (804216)Instruction limit reached!
% 1.04/0.60 % (804216)------------------------------
% 1.04/0.60 % (804216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.60 % (804216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.60 % (804216)CaDiCaL version: 2.1.3
% 1.04/0.60 % (804216)Termination reason: Instruction limit
% 1.04/0.60 % (804216)Termination phase: Saturation
% 1.04/0.60 % (804216)Time elapsed: 0.062 s
% 1.04/0.60 % (804216)Peak memory usage: 12 MB
% 1.04/0.60 % (804216)Instructions burned: 104 (million)
% 1.04/0.60 % (804227)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=880987329:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.04/0.60 % TRYING [1]
% 1.04/0.60 % TRYING [2]
% 1.04/0.60 % TRYING [3]
% 1.04/0.60 % TRYING [4]
% 1.04/0.60 % (804217)Instruction limit reached!
% 1.04/0.60 % (804217)------------------------------
% 1.04/0.60 % (804217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.60 % (804217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.60 % (804217)CaDiCaL version: 2.1.3
% 1.04/0.60 % (804217)Termination reason: Instruction limit
% 1.04/0.60 % (804217)Termination phase: Saturation
% 1.04/0.60 % (804217)Time elapsed: 0.076 s
% 1.04/0.60 % (804217)Peak memory usage: 12 MB
% 1.04/0.60 % (804217)Instructions burned: 117 (million)
% 1.04/0.60 % (804218)Instruction limit reached!
% 1.04/0.60 % (804218)------------------------------
% 1.04/0.60 % (804218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.60 % (804218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.60 % (804218)CaDiCaL version: 2.1.3
% 1.04/0.60 % (804218)Termination reason: Instruction limit
% 1.04/0.60 % (804218)Termination phase: Saturation
% 1.04/0.60 % (804218)Time elapsed: 0.080 s
% 1.04/0.60 % (804218)Peak memory usage: 13 MB
% 1.04/0.60 % (804218)Instructions burned: 133 (million)
% 1.04/0.60 % TRYING [5]
% 1.04/0.60 % (804228)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=87102008:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.04/0.60 % (804230)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3550158719:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.04/0.60 % (804231)ott-21_1_sil=16000:fs=off:random_seed=4197920305:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.04/0.60 % (804228) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-804208-804228"...
% 1.04/0.60 % (804228)...printing done.
% 1.04/0.60 % (804228)Refutation found. Thanks to Tanya!
% 1.04/0.60 % SZS status Theorem for theBenchmark
% 1.04/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.04/0.60 % (804228)------------------------------
% 1.04/0.60 % (804228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.60 % (804228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.60 % (804228)CaDiCaL version: 2.1.3
% 1.04/0.60 % (804228)Termination reason: Refutation
% 1.04/0.60 % (804228)Time elapsed: 0.066 s
% 1.04/0.60 % (804228)Peak memory usage: 13 MB
% 1.04/0.60 % (804228)Instructions burned: 101 (million)
% 1.04/0.60 % (804208)Success in time 0.185 s
% 1.04/0.60 % Vampire exiting
%------------------------------------------------------------------------------