TSTP Solution File: SEU323+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:05:48 EDT 2023
% Result : Theorem 2.67s 1.16s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 170 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 201 ( 88 ~; 76 |; 25 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn; 40 !; 8 ?)
% 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,[],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f45]) ).
fof(f55,plain,
( ? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0) )
=> ( ? [X1] :
( ~ open_subset(interior(sK4,X1),sK4)
& element(X1,powerset(the_carrier(sK4))) )
& top_str(sK4)
& topological_space(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X1] :
( ~ open_subset(interior(sK4,X1),sK4)
& element(X1,powerset(the_carrier(sK4))) )
=> ( ~ open_subset(interior(sK4,sK5),sK4)
& element(sK5,powerset(the_carrier(sK4))) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ~ open_subset(interior(sK4,sK5),sK4)
& element(sK5,powerset(the_carrier(sK4)))
& top_str(sK4)
& topological_space(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f46,f56,f55]) ).
fof(f58,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f63,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f64,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f65,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f73,plain,
! [X0,X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f74,plain,
topological_space(sK4),
inference(cnf_transformation,[],[f57]) ).
fof(f75,plain,
top_str(sK4),
inference(cnf_transformation,[],[f57]) ).
fof(f76,plain,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f57]) ).
fof(f77,plain,
~ open_subset(interior(sK4,sK5),sK4),
inference(cnf_transformation,[],[f57]) ).
cnf(c_49,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| open_subset(subset_complement(the_carrier(X1),X0),X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_54,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_55,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(topstr_closure(X1,X0),powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_56,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| closed_subset(topstr_closure(X1,X0),X1) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_64,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_65,negated_conjecture,
~ open_subset(interior(sK4,sK5),sK4),
inference(cnf_transformation,[],[f77]) ).
cnf(c_66,negated_conjecture,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f76]) ).
cnf(c_67,negated_conjecture,
top_str(sK4),
inference(cnf_transformation,[],[f75]) ).
cnf(c_68,negated_conjecture,
topological_space(sK4),
inference(cnf_transformation,[],[f74]) ).
cnf(c_323,plain,
( X0 != sK4
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_56,c_68]) ).
cnf(c_324,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| ~ top_str(sK4)
| closed_subset(topstr_closure(sK4,X0),sK4) ),
inference(unflattening,[status(thm)],[c_323]) ).
cnf(c_326,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| closed_subset(topstr_closure(sK4,X0),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_324,c_67,c_324]) ).
cnf(c_335,plain,
( X0 != sK4
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| ~ top_str(X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_49,c_68]) ).
cnf(c_336,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| ~ closed_subset(X0,sK4)
| ~ top_str(sK4)
| open_subset(subset_complement(the_carrier(sK4),X0),sK4) ),
inference(unflattening,[status(thm)],[c_335]) ).
cnf(c_338,plain,
( ~ closed_subset(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK4)))
| open_subset(subset_complement(the_carrier(sK4),X0),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_336,c_67,c_336]) ).
cnf(c_339,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| ~ closed_subset(X0,sK4)
| open_subset(subset_complement(the_carrier(sK4),X0),sK4) ),
inference(renaming,[status(thm)],[c_338]) ).
cnf(c_439,plain,
( topstr_closure(sK4,X0) != X1
| sK4 != sK4
| ~ element(X0,powerset(the_carrier(sK4)))
| ~ element(X1,powerset(the_carrier(sK4)))
| open_subset(subset_complement(the_carrier(sK4),X1),sK4) ),
inference(resolution_lifted,[status(thm)],[c_326,c_339]) ).
cnf(c_440,plain,
( ~ element(topstr_closure(sK4,X0),powerset(the_carrier(sK4)))
| ~ element(X0,powerset(the_carrier(sK4)))
| open_subset(subset_complement(the_carrier(sK4),topstr_closure(sK4,X0)),sK4) ),
inference(unflattening,[status(thm)],[c_439]) ).
cnf(c_485,plain,
( X0 != sK4
| ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_64,c_67]) ).
cnf(c_486,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),X0))) = interior(sK4,X0) ),
inference(unflattening,[status(thm)],[c_485]) ).
cnf(c_503,plain,
( X0 != sK4
| ~ element(X1,powerset(the_carrier(X0)))
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_55,c_67]) ).
cnf(c_504,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| element(topstr_closure(sK4,X0),powerset(the_carrier(sK4))) ),
inference(unflattening,[status(thm)],[c_503]) ).
cnf(c_524,plain,
( ~ element(X0,powerset(the_carrier(sK4)))
| open_subset(subset_complement(the_carrier(sK4),topstr_closure(sK4,X0)),sK4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_440,c_504]) ).
cnf(c_901,plain,
subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5))) = interior(sK4,sK5),
inference(superposition,[status(thm)],[c_66,c_486]) ).
cnf(c_957,plain,
( ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| open_subset(interior(sK4,sK5),sK4) ),
inference(superposition,[status(thm)],[c_901,c_524]) ).
cnf(c_958,plain,
~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4))),
inference(forward_subsumption_resolution,[status(thm)],[c_957,c_65]) ).
cnf(c_959,plain,
~ element(sK5,powerset(the_carrier(sK4))),
inference(superposition,[status(thm)],[c_54,c_958]) ).
cnf(c_960,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_959,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 01:32:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.67/1.16 % SZS status Started for theBenchmark.p
% 2.67/1.16 % SZS status Theorem for theBenchmark.p
% 2.67/1.16
% 2.67/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.67/1.16
% 2.67/1.16 ------ iProver source info
% 2.67/1.16
% 2.67/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.67/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.67/1.16 git: non_committed_changes: false
% 2.67/1.16 git: last_make_outside_of_git: false
% 2.67/1.16
% 2.67/1.16 ------ Parsing...
% 2.67/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.67/1.16
% 2.67/1.16 ------ 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
% 2.67/1.16
% 2.67/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.67/1.16
% 2.67/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/1.16 ------ Proving...
% 2.67/1.16 ------ Problem Properties
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16 clauses 18
% 2.67/1.16 conjectures 2
% 2.67/1.16 EPR 0
% 2.67/1.16 Horn 18
% 2.67/1.16 unary 8
% 2.67/1.16 binary 9
% 2.67/1.16 lits 29
% 2.67/1.16 lits eq 3
% 2.67/1.16 fd_pure 0
% 2.67/1.16 fd_pseudo 0
% 2.67/1.16 fd_cond 0
% 2.67/1.16 fd_pseudo_cond 0
% 2.67/1.16 AC symbols 0
% 2.67/1.16
% 2.67/1.16 ------ Schedule dynamic 5 is on
% 2.67/1.16
% 2.67/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16 ------
% 2.67/1.16 Current options:
% 2.67/1.16 ------
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16 ------ Proving...
% 2.67/1.16
% 2.67/1.16
% 2.67/1.16 % SZS status Theorem for theBenchmark.p
% 2.67/1.16
% 2.67/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/1.16
% 2.67/1.16
%------------------------------------------------------------------------------