%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU323+1 : 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 : n006.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 02:56:51 PM UTC 2026
% Result : Theorem 3.10s 11.31s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 18 unt; 3 def)
% Number of atoms : 200 ( 18 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 196 ( 89 ~; 80 |; 17 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 73 !; 4 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& closed_subset(X1,X0)
& top_str(X0)
& topological_space(X0) )
=> open_subset(subset_complement(the_carrier(X0),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(f6,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f7,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f9,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> closed_subset(topstr_closure(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f20,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f21,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(flattening,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ~ open_subset(interior(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f46,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ~ open_subset(interior(X0,X1),X0) ) ),
inference(flattening,[],[f45]) ).
fof(f51,plain,
( top_str(sK4)
& topological_space(sK4)
& element(sK5,powerset(the_carrier(sK4)))
& ~ open_subset(interior(sK4,sK5),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f67,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
top_str(sK4),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
topological_space(sK4),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
~ open_subset(interior(sK4,sK5),sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( closed_subset(topstr_closure(X1,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) )
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_65,negated_conjecture,
~ open_subset(interior(sK4,sK5),sK4),
inference(cnf_transformation,[],[f71]) ).
tcf(c_66,negated_conjecture,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f70]) ).
tcf(c_67,negated_conjecture,
topological_space(sK4),
inference(cnf_transformation,[],[f69]) ).
tcf(c_68,negated_conjecture,
top_str(sK4),
inference(cnf_transformation,[],[f68]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_67]) ).
tcf(c_324,plain,
! [X0: $i] :
( closed_subset(topstr_closure(sK4,X0),sK4)
| ~ top_str(sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_323]) ).
tcf(c_326,plain,
! [X0: $i] :
( closed_subset(topstr_closure(sK4,X0),sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_324,c_68,c_324]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_67]) ).
tcf(c_336,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK4),X0),sK4)
| ~ top_str(sK4)
| ~ closed_subset(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_335]) ).
tcf(c_338,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK4),X0),sK4)
| ~ element(X0,powerset(the_carrier(sK4)))
| ~ closed_subset(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_336,c_68,c_336]) ).
tcf(c_339,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK4),X0),sK4)
| ~ closed_subset(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(renaming,[status(thm)],[c_338]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(sK4),X1),sK4)
| ~ element(X1,powerset(the_carrier(sK4)))
| ~ element(X0,powerset(the_carrier(sK4)))
| ( sK4 != sK4 )
| ( topstr_closure(sK4,X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_326,c_339]) ).
tcf(c_440,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK4),topstr_closure(sK4,X0)),sK4)
| ~ element(X0,powerset(the_carrier(sK4)))
| ~ element(topstr_closure(sK4,X0),powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_439]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_68]) ).
tcf(c_486,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),X0))) = interior(sK4,X0) )
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_485]) ).
tcf(c_503,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_68]) ).
tcf(c_504,plain,
! [X0: $i] :
( element(topstr_closure(sK4,X0),powerset(the_carrier(sK4)))
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_503]) ).
tcf(c_524,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK4),topstr_closure(sK4,X0)),sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_440,c_504]) ).
tcf(c_636,definition,
iPr_def_10 = the_carrier(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_637,definition,
iPr_def_11 = powerset(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_641,definition,
iPr_def_15 = interior(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_642,plain,
! [X0: $i] :
( open_subset(subset_complement(iPr_def_10,topstr_closure(sK4,X0)),sK4)
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_524,c_636,c_637]) ).
tcf(c_645,plain,
! [X0: $i] :
( ( subset_complement(iPr_def_10,topstr_closure(sK4,subset_complement(iPr_def_10,X0))) = interior(sK4,X0) )
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_486]) ).
tcf(c_651,negated_conjecture,
element(sK5,iPr_def_11),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_652,negated_conjecture,
~ open_subset(iPr_def_15,sK4),
inference(demodulation,[status(thm)],[c_65,c_641]) ).
tcf(c_951,plain,
subset_complement(iPr_def_10,topstr_closure(sK4,subset_complement(iPr_def_10,sK5))) = interior(sK4,sK5),
inference(superposition,[status(thm)],[c_651,c_645]) ).
tcf(c_952,plain,
subset_complement(iPr_def_10,topstr_closure(sK4,subset_complement(iPr_def_10,sK5))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_951,c_641]) ).
tcf(c_967,plain,
( open_subset(iPr_def_15,sK4)
| ~ element(subset_complement(iPr_def_10,sK5),iPr_def_11) ),
inference(superposition,[status(thm)],[c_952,c_642]) ).
tcf(c_968,plain,
~ element(subset_complement(iPr_def_10,sK5),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_967,c_652]) ).
tcf(c_1014,plain,
! [X0: $i] :
( element(subset_complement(iPr_def_10,X0),iPr_def_11)
| ~ element(X0,powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_637,c_54]) ).
tcf(c_1017,plain,
! [X0: $i] :
( element(subset_complement(iPr_def_10,X0),iPr_def_11)
| ~ element(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1014,c_637]) ).
tcf(c_1076,plain,
~ element(sK5,iPr_def_11),
inference(superposition,[status(thm)],[c_1017,c_968]) ).
tcf(c_1077,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1076,c_651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.37 % Computer : n006.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Thu Sep 24 13:41:41 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.44 % Proving...
% 3.10/11.31 % SZS status Started for theBenchmark.p
% 3.10/11.31 % SZS status Theorem for theBenchmark.p
% 3.10/11.31
% 3.10/11.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.10/11.31
% 3.10/11.31 % ------ iProver source info
% 3.10/11.31
% 3.10/11.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.10/11.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.10/11.31 % git: non_committed_changes: false
% 3.10/11.31
% 3.10/11.31 % ------ Parsing...
% 3.10/11.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.10/11.31
% 3.10/11.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.10/11.31
% 3.10/11.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.10/11.31
% 3.10/11.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.10/11.31 % ------ Proving...
% 3.10/11.31 % ------ Problem Properties
% 3.10/11.31
% 3.10/11.31 %
% 3.10/11.31 % clauses 24
% 3.10/11.31 % conjectures 2
% 3.10/11.31 % EPR 6
% 3.10/11.31 % Horn 24
% 3.10/11.31 % unary 14
% 3.10/11.31 % binary 9
% 3.10/11.31 % lits 35
% 3.10/11.31 % lits eq 9
% 3.10/11.31 % fd_pure 0
% 3.10/11.31 % fd_pseudo 0
% 3.10/11.31 % fd_cond 0
% 3.10/11.31 % fd_pseudo_cond 0
% 3.10/11.31 % AC symbols 0
% 3.10/11.31
% 3.10/11.31 % ------ Schedule dynamic 5 is on
% 3.10/11.31
% 3.10/11.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.10/11.31
% 3.10/11.31
% 3.10/11.31 % ------
% 3.10/11.31 % Current options:
% 3.10/11.31 % ------
% 3.10/11.31
% 3.10/11.31
% 3.10/11.31 %
% 3.10/11.31
% 3.10/11.31 % ------ Proving...
% 3.10/11.31 %
% 3.10/11.31
% 3.10/11.31 % SZS status Theorem for theBenchmark.p
% 3.10/11.31
% 3.10/11.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.10/11.31
% 3.10/11.31
%------------------------------------------------------------------------------