%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU341+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 12:52:56 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 18 unt; 2 def)
% Number of atoms : 196 ( 12 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 241 ( 103 ~; 86 |; 27 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f35,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f40,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( open_subset(X3,X1)
=> interior(X1,X3) = X3 )
& ( interior(X0,X2) = X2
=> open_subset(X2,X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(f41,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f35]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f77]) ).
fof(f89,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f90,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) )
& ( open_subset(X2,X0)
| interior(X0,X2) != X2 ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) )
& ( open_subset(X2,X0)
| interior(X0,X2) != X2 ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& open_subset(X1,X0)
& in(X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& open_subset(X1,X0)
& in(X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f94]) ).
fof(f125,plain,
! [X2,X0,X1] :
( point_neighbourhood(X2,X0,X1)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,interior(X0,X2))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f149,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f152,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f157,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f95]) ).
fof(f160,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f95]) ).
fof(f161,plain,
top_str(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
topological_space(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f169,definition,
( spl9_1
<=> ! [X1,X3] :
( ~ top_str(X1)
| interior(X1,X3) = X3
| ~ open_subset(X3,X1)
| ~ element(X3,powerset(the_carrier(X1))) ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f170,plain,
( ! [X3,X1] :
( ~ open_subset(X3,X1)
| interior(X1,X3) = X3
| ~ top_str(X1)
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,definition,
( spl9_2
<=> ! [X2,X0] :
( ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f173,plain,
( ! [X2,X0] :
( ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X0) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f154,f172,f169]) ).
fof(f189,plain,
! [X0] : element(X0,powerset(X0)),
inference(resolution,[],[f152,f149]) ).
fof(f218,plain,
( ! [X0] :
( ~ element(X0,powerset(the_carrier(sK6)))
| ~ top_str(sK6) )
| ~ spl9_2 ),
inference(resolution,[],[f173,f162]) ).
fof(f219,plain,
( ! [X0] : ~ element(X0,powerset(the_carrier(sK6)))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f218,f161]) ).
fof(f220,plain,
! [X0] :
( ~ element(sK7,powerset(X0))
| element(sK8,X0) ),
inference(resolution,[],[f153,f157]) ).
fof(f222,plain,
( $false
| ~ spl9_2 ),
inference(resolution,[],[f219,f189]) ).
fof(f231,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f236,plain,
( sK7 = interior(sK6,sK7)
| ~ top_str(sK6)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ spl9_1 ),
inference(resolution,[],[f170,f158]) ).
fof(f237,plain,
( sK7 = interior(sK6,sK7)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f236,f161]) ).
fof(f238,plain,
( sK7 = interior(sK6,sK7)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f237,f160]) ).
fof(f244,plain,
( ~ topological_space(sK6)
| empty_carrier(sK6)
| ~ element(sK8,the_carrier(sK6))
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ in(sK8,interior(sK6,sK7))
| ~ top_str(sK6) ),
inference(resolution,[],[f125,f159]) ).
fof(f249,plain,
( ~ topological_space(sK6)
| empty_carrier(sK6)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ in(sK8,interior(sK6,sK7))
| ~ top_str(sK6) ),
inference(forward_subsumption_resolution,[],[f244,f220]) ).
fof(f250,plain,
( empty_carrier(sK6)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ in(sK8,interior(sK6,sK7))
| ~ top_str(sK6) ),
inference(forward_subsumption_resolution,[],[f249,f162]) ).
fof(f251,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| ~ in(sK8,interior(sK6,sK7))
| ~ top_str(sK6) ),
inference(forward_subsumption_resolution,[],[f250,f163]) ).
fof(f252,plain,
( ~ in(sK8,interior(sK6,sK7))
| ~ top_str(sK6) ),
inference(forward_subsumption_resolution,[],[f251,f160]) ).
fof(f253,plain,
~ in(sK8,interior(sK6,sK7)),
inference(forward_subsumption_resolution,[],[f252,f161]) ).
fof(f254,plain,
( ~ in(sK8,sK7)
| ~ spl9_1 ),
inference(forward_demodulation,[],[f253,f238]) ).
fof(f255,plain,
( $false
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f254,f157]) ).
fof(f256,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f255]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s7,plain,
~ spl9_2,
inference(sat_conversion,[],[f231]) ).
cnf(s8,plain,
~ spl9_1,
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
fof(f257,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 04:48:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 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
% 0.12/0.43 % (808832)Will run a generic schedule for satisfiability detection.
% 0.12/0.43 % (808841)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2079153634:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.43 % (808838)% WARNING: option uhcvi not known.
% 0.12/0.43 % (808841) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-808832-808841"...
% 0.12/0.43 % (808841)...printing done.
% 0.12/0.43 % (808841)Refutation found. Thanks to Tanya!
% 0.12/0.43 % SZS status Theorem for theBenchmark
% 0.12/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.43 % (808841)------------------------------
% 0.12/0.43 % (808841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.43 % (808841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.43 % (808841)CaDiCaL version: 2.1.3
% 0.12/0.43 % (808841)Termination reason: Refutation
% 0.12/0.43 % (808841)Time elapsed: 0.003 s
% 0.12/0.43 % (808841)Peak memory usage: 12 MB
% 0.12/0.43 % (808841)Instructions burned: 6 (million)
% 0.12/0.43 % (808832)Success in time 0.032 s
% 0.12/0.43 % Vampire exiting
%------------------------------------------------------------------------------