%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU341+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 02:56:58 PM UTC 2026
% Result : Theorem 21.85s 4.75s
% Output : CNFRefutation 21.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 212 ( 12 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 267 ( 108 ~; 101 |; 36 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 86 !; 6 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f51,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(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(f139,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f517,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f528,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( interior(X0,X2) = X2
=> open_subset(X2,X0) )
& ( open_subset(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(f531,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f532,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f531]) ).
fof(f688,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f689,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(flattening,[],[f688]) ).
fof(f771,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f139]) ).
fof(f772,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f771]) ).
fof(f1184,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f517]) ).
fof(f1185,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f1184]) ).
fof(f1204,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ( ( interior(X0,X2) != X2
| open_subset(X2,X0) )
& ( ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ) ) ) ) ) ),
inference(ennf_transformation,[],[f528]) ).
fof(f1205,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ( ( interior(X0,X2) != X2
| open_subset(X2,X0) )
& ( ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ) ) ) ) ) ),
inference(flattening,[],[f1204]) ).
fof(f1210,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,X1)
& open_subset(X1,X0)
& ~ point_neighbourhood(X1,X0,X2) ) ) ),
inference(ennf_transformation,[],[f532]) ).
fof(f1211,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,X1)
& open_subset(X1,X0)
& ~ point_neighbourhood(X1,X0,X2) ) ) ),
inference(flattening,[],[f1210]) ).
fof(f1379,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( ~ point_neighbourhood(X2,X0,X1)
| in(X1,interior(X0,X2)) )
& ( ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f689]) ).
fof(f1939,plain,
( top_str(sK478)
& topological_space(sK478)
& ~ empty_carrier(sK478)
& element(sK479,powerset(the_carrier(sK478)))
& element(sK480,the_carrier(sK478))
& in(sK480,sK479)
& open_subset(sK479,sK478)
& ~ point_neighbourhood(sK479,sK478,sK480) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK478,sK479,sK480]),skolemize(X0,sK478),skolemize(X1,sK479),skolemize(X2,sK480)],[f1211]) ).
fof(f2085,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1) ),
inference(cnf_transformation,[],[f1379]) ).
fof(f2400,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f772]) ).
fof(f3450,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f3480,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,[],[f1205]) ).
fof(f3484,plain,
top_str(sK478),
inference(cnf_transformation,[],[f1939]) ).
fof(f3485,plain,
topological_space(sK478),
inference(cnf_transformation,[],[f1939]) ).
fof(f3486,plain,
~ empty_carrier(sK478),
inference(cnf_transformation,[],[f1939]) ).
fof(f3487,plain,
element(sK479,powerset(the_carrier(sK478))),
inference(cnf_transformation,[],[f1939]) ).
fof(f3489,plain,
in(sK480,sK479),
inference(cnf_transformation,[],[f1939]) ).
fof(f3490,plain,
open_subset(sK479,sK478),
inference(cnf_transformation,[],[f1939]) ).
fof(f3491,plain,
~ point_neighbourhood(sK479,sK478,sK480),
inference(cnf_transformation,[],[f1939]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X0)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,interior(X1,X2)) ),
inference(cnf_transformation,[],[f2085]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] :
( element(interior(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2400]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3450]) ).
tcf(c_1565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( interior(X3,X2) = X2 )
| ~ topological_space(X1)
| ~ top_str(X3)
| ~ top_str(X1)
| ~ open_subset(X2,X3)
| ~ element(X2,powerset(the_carrier(X3)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f3480]) ).
tcf(c_1570,negated_conjecture,
~ point_neighbourhood(sK479,sK478,sK480),
inference(cnf_transformation,[],[f3491]) ).
tcf(c_1571,negated_conjecture,
open_subset(sK479,sK478),
inference(cnf_transformation,[],[f3490]) ).
tcf(c_1572,negated_conjecture,
in(sK480,sK479),
inference(cnf_transformation,[],[f3489]) ).
tcf(c_1574,negated_conjecture,
element(sK479,powerset(the_carrier(sK478))),
inference(cnf_transformation,[],[f3487]) ).
tcf(c_1575,negated_conjecture,
~ empty_carrier(sK478),
inference(cnf_transformation,[],[f3486]) ).
tcf(c_1576,negated_conjecture,
topological_space(sK478),
inference(cnf_transformation,[],[f3485]) ).
tcf(c_1577,negated_conjecture,
top_str(sK478),
inference(cnf_transformation,[],[f3484]) ).
tcf(c_3491,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,the_carrier(X1))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,interior(X1,X2)) ),
inference(superposition,[status(thm)],[c_487,c_1536]) ).
tcf(c_3658,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X0)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ in(X0,interior(X1,X2))
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_173,c_173,c_3491]) ).
tcf(c_3659,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X0)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,interior(X1,X2)) ),
inference(renaming,[status(thm)],[c_3658]) ).
tcf(c_3676,plain,
! [X0: $i] :
( empty_carrier(sK478)
| point_neighbourhood(sK479,sK478,X0)
| ~ topological_space(sK478)
| ~ top_str(sK478)
| ~ in(X0,interior(sK478,sK479)) ),
inference(superposition,[status(thm)],[c_1574,c_3659]) ).
tcf(c_3722,plain,
! [X0: $i,X1: $i] :
( ( interior(X1,X0) = X0 )
| ~ topological_space(sK478)
| ~ top_str(sK478)
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(superposition,[status(thm)],[c_1574,c_1565]) ).
tcf(c_4631,plain,
! [X0: $i] :
( ~ in(X0,interior(sK478,sK479))
| point_neighbourhood(sK479,sK478,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3676,c_1577,c_1576,c_1575,c_3676]) ).
tcf(c_4632,plain,
! [X0: $i] :
( point_neighbourhood(sK479,sK478,X0)
| ~ in(X0,interior(sK478,sK479)) ),
inference(renaming,[status(thm)],[c_4631]) ).
tcf(c_4698,plain,
! [X0: $i,X1: $i] :
( ( interior(X1,X0) = X0 )
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_3722,c_1577,c_1576,c_3722]) ).
tcf(c_4712,plain,
( ( interior(sK478,sK479) = sK479 )
| ~ top_str(sK478)
| ~ open_subset(sK479,sK478) ),
inference(superposition,[status(thm)],[c_1574,c_4698]) ).
tcf(c_9040,plain,
interior(sK478,sK479) = sK479,
inference(global_subsumption_just,[status(thm)],[c_4712,c_1577,c_1571,c_4712]) ).
tcf(c_9061,plain,
! [X0: $i] :
( point_neighbourhood(sK479,sK478,X0)
| ~ in(X0,sK479) ),
inference(superposition,[status(thm)],[c_9040,c_4632]) ).
tcf(c_39541,plain,
~ in(sK480,sK479),
inference(superposition,[status(thm)],[c_9061,c_1570]) ).
tcf(c_39579,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1572,c_39541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU341+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:41:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 21.85/4.75 % SZS status Started for theBenchmark.p
% 21.85/4.75 % SZS status Theorem for theBenchmark.p
% 21.85/4.75
% 21.85/4.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.85/4.75
% 21.85/4.75 % ------ iProver source info
% 21.85/4.75
% 21.85/4.75 % git: date: 2026-07-19 20:42:38 +0200
% 21.85/4.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.85/4.75 % git: non_committed_changes: false
% 21.85/4.75
% 21.85/4.75 % ------ Parsing...
% 21.85/4.75 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 21.85/4.75 % ------ Proving...
% 21.85/4.75 % ------ Problem Properties
% 21.85/4.75
% 21.85/4.75 %
% 21.85/4.75 % clauses 1596
% 21.85/4.75 % conjectures 8
% 21.85/4.75 % EPR 237
% 21.85/4.75 % Horn 1197
% 21.85/4.75 % unary 190
% 21.85/4.75 % binary 475
% 21.85/4.75 % lits 4994
% 21.85/4.75 % lits eq 613
% 21.85/4.75 % fd_pure 0
% 21.85/4.75 % fd_pseudo 0
% 21.85/4.75 % fd_cond 53
% 21.85/4.75 % fd_pseudo_cond 121
% 21.85/4.75 % AC symbols 0
% 21.85/4.75
% 21.85/4.75 % ------ Input Options Time Limit: Unbounded
% 21.85/4.75
% 21.85/4.75
% 21.85/4.75 % ------
% 21.85/4.75 % Current options:
% 21.85/4.75 % ------
% 21.85/4.75
% 21.85/4.75
% 21.85/4.75 %
% 21.85/4.75
% 21.85/4.75 % ------ Proving...
% 21.85/4.75 %
% 21.85/4.75
% 21.85/4.75 % ------ Proving...
% 21.85/4.75 %
% 21.85/4.75
% 21.85/4.75 % SZS status Theorem for theBenchmark.p
% 21.85/4.75
% 21.85/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.85/4.75
% 21.85/4.75
%------------------------------------------------------------------------------