TSTP Solution File: SEU341+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 17:06:16 EDT 2023
% Result : Theorem 2.08s 1.20s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 236 ( 23 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 306 ( 121 ~; 100 |; 62 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 82 ( 8 sgn; 37 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,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(f40,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(f41,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(f42,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,[],[f41]) ).
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)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(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)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f77]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( open_subset(X2,X0)
| interior(X0,X2) != X2 )
& ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( open_subset(X2,X0)
| interior(X0,X2) != X2 )
& ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f94]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2)) )
& ( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f113,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK6,X2)
& in(X2,X1)
& open_subset(X1,sK6)
& element(X2,the_carrier(sK6)) )
& element(X1,powerset(the_carrier(sK6))) )
& top_str(sK6)
& topological_space(sK6)
& ~ empty_carrier(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK6,X2)
& in(X2,X1)
& open_subset(X1,sK6)
& element(X2,the_carrier(sK6)) )
& element(X1,powerset(the_carrier(sK6))) )
=> ( ? [X2] :
( ~ point_neighbourhood(sK7,sK6,X2)
& in(X2,sK7)
& open_subset(sK7,sK6)
& element(X2,the_carrier(sK6)) )
& element(sK7,powerset(the_carrier(sK6))) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X2] :
( ~ point_neighbourhood(sK7,sK6,X2)
& in(X2,sK7)
& open_subset(sK7,sK6)
& element(X2,the_carrier(sK6)) )
=> ( ~ point_neighbourhood(sK7,sK6,sK8)
& in(sK8,sK7)
& open_subset(sK7,sK6)
& element(sK8,the_carrier(sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( ~ point_neighbourhood(sK7,sK6,sK8)
& in(sK8,sK7)
& open_subset(sK7,sK6)
& element(sK8,the_carrier(sK6))
& element(sK7,powerset(the_carrier(sK6)))
& top_str(sK6)
& topological_space(sK6)
& ~ empty_carrier(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f95,f115,f114,f113]) ).
fof(f143,plain,
! [X2,X0,X1] :
( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( interior(X1,X3) = X3
| ~ open_subset(X3,X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f173,plain,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f116]) ).
fof(f174,plain,
topological_space(sK6),
inference(cnf_transformation,[],[f116]) ).
fof(f175,plain,
top_str(sK6),
inference(cnf_transformation,[],[f116]) ).
fof(f176,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f116]) ).
fof(f177,plain,
element(sK8,the_carrier(sK6)),
inference(cnf_transformation,[],[f116]) ).
fof(f178,plain,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f116]) ).
fof(f179,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f116]) ).
fof(f180,plain,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f116]) ).
cnf(c_74,plain,
( ~ in(X0,interior(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(X2,X1,X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_104,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ open_subset(X2,X3)
| ~ top_str(X1)
| ~ top_str(X3)
| ~ topological_space(X1)
| interior(X3,X2) = X2 ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_105,negated_conjecture,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f180]) ).
cnf(c_106,negated_conjecture,
in(sK8,sK7),
inference(cnf_transformation,[],[f179]) ).
cnf(c_107,negated_conjecture,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f178]) ).
cnf(c_108,negated_conjecture,
element(sK8,the_carrier(sK6)),
inference(cnf_transformation,[],[f177]) ).
cnf(c_109,negated_conjecture,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f176]) ).
cnf(c_110,negated_conjecture,
top_str(sK6),
inference(cnf_transformation,[],[f175]) ).
cnf(c_111,negated_conjecture,
topological_space(sK6),
inference(cnf_transformation,[],[f174]) ).
cnf(c_112,negated_conjecture,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f173]) ).
cnf(c_734,plain,
( X0 != sK7
| X1 != sK6
| ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ top_str(X1)
| ~ top_str(X3)
| ~ topological_space(X3)
| interior(X1,X0) = X0 ),
inference(resolution_lifted,[status(thm)],[c_104,c_107]) ).
cnf(c_735,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ top_str(sK6)
| interior(sK6,sK7) = sK7 ),
inference(unflattening,[status(thm)],[c_734]) ).
cnf(c_737,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1)))
| interior(sK6,sK7) = sK7 ),
inference(global_subsumption_just,[status(thm)],[c_735,c_110,c_109,c_735]) ).
cnf(c_738,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| interior(sK6,sK7) = sK7 ),
inference(renaming,[status(thm)],[c_737]) ).
cnf(c_798,plain,
( X0 != sK6
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| point_neighbourhood(X2,X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_74,c_112]) ).
cnf(c_799,plain,
( ~ in(X0,interior(sK6,X1))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| ~ top_str(sK6)
| ~ topological_space(sK6)
| point_neighbourhood(X1,sK6,X0) ),
inference(unflattening,[status(thm)],[c_798]) ).
cnf(c_801,plain,
( ~ in(X0,interior(sK6,X1))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| point_neighbourhood(X1,sK6,X0) ),
inference(global_subsumption_just,[status(thm)],[c_799,c_111,c_110,c_799]) ).
cnf(c_828,plain,
( X0 != sK6
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| interior(sK6,sK7) = sK7 ),
inference(resolution_lifted,[status(thm)],[c_738,c_111]) ).
cnf(c_829,plain,
( ~ element(X0,powerset(the_carrier(sK6)))
| ~ top_str(sK6)
| interior(sK6,sK7) = sK7 ),
inference(unflattening,[status(thm)],[c_828]) ).
cnf(c_831,plain,
( ~ element(X0,powerset(the_carrier(sK6)))
| interior(sK6,sK7) = sK7 ),
inference(global_subsumption_just,[status(thm)],[c_829,c_110,c_829]) ).
cnf(c_871,plain,
( X0 != sK7
| X1 != sK8
| sK6 != sK6
| ~ in(X1,interior(sK6,X0))
| ~ element(X0,powerset(the_carrier(sK6)))
| ~ element(X1,the_carrier(sK6)) ),
inference(resolution_lifted,[status(thm)],[c_105,c_801]) ).
cnf(c_872,plain,
( ~ in(sK8,interior(sK6,sK7))
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ element(sK8,the_carrier(sK6)) ),
inference(unflattening,[status(thm)],[c_871]) ).
cnf(c_873,plain,
~ in(sK8,interior(sK6,sK7)),
inference(global_subsumption_just,[status(thm)],[c_872,c_108,c_109,c_872]) ).
cnf(c_1378,plain,
interior(sK6,sK7) = sK7,
inference(superposition,[status(thm)],[c_109,c_831]) ).
cnf(c_1379,plain,
~ in(sK8,sK7),
inference(demodulation,[status(thm)],[c_873,c_1378]) ).
cnf(c_1380,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1379,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 15:32:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.08/1.20 % SZS status Started for theBenchmark.p
% 2.08/1.20 % SZS status Theorem for theBenchmark.p
% 2.08/1.20
% 2.08/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.08/1.20
% 2.08/1.20 ------ iProver source info
% 2.08/1.20
% 2.08/1.20 git: date: 2023-05-31 18:12:56 +0000
% 2.08/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.08/1.20 git: non_committed_changes: false
% 2.08/1.20 git: last_make_outside_of_git: false
% 2.08/1.20
% 2.08/1.20 ------ Parsing...
% 2.08/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.08/1.20
% 2.08/1.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe_e
% 2.08/1.20
% 2.08/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.08/1.20
% 2.08/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.20 ------ Proving...
% 2.08/1.20 ------ Problem Properties
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20 clauses 27
% 2.08/1.20 conjectures 3
% 2.08/1.20 EPR 9
% 2.08/1.20 Horn 25
% 2.08/1.20 unary 12
% 2.08/1.20 binary 11
% 2.08/1.20 lits 46
% 2.08/1.20 lits eq 4
% 2.08/1.20 fd_pure 0
% 2.08/1.20 fd_pseudo 0
% 2.08/1.20 fd_cond 1
% 2.08/1.20 fd_pseudo_cond 1
% 2.08/1.20 AC symbols 0
% 2.08/1.20
% 2.08/1.20 ------ Schedule dynamic 5 is on
% 2.08/1.20
% 2.08/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20 ------
% 2.08/1.20 Current options:
% 2.08/1.20 ------
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20 ------ Proving...
% 2.08/1.20
% 2.08/1.20
% 2.08/1.20 % SZS status Theorem for theBenchmark.p
% 2.08/1.20
% 2.08/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.20
% 2.08/1.20
%------------------------------------------------------------------------------