TSTP Solution File: SEU324+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n018.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 : Wed Aug 31 18:28:46 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 10 unt; 0 def)
% Number of atoms : 251 ( 53 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 270 ( 87 ~; 77 |; 72 &)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 56 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f260,plain,
$false,
inference(avatar_sat_refutation,[],[f116,f121,f126,f127,f153,f253]) ).
fof(f253,plain,
( spl9_1
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f252,plain,
( $false
| spl9_1
| ~ spl9_4 ),
inference(subsumption_resolution,[],[f251,f111]) ).
fof(f111,plain,
( sK4 != interior(sK2,sK4)
| spl9_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f109,plain,
( spl9_1
<=> sK4 = interior(sK2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f251,plain,
( sK4 = interior(sK2,sK4)
| ~ spl9_4 ),
inference(forward_demodulation,[],[f250,f162]) ).
fof(f162,plain,
sK4 = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK4)),
inference(unit_resulting_resolution,[],[f87,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X1,X0] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X1,X0] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f87,plain,
element(sK4,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( topological_space(sK1)
& top_str(sK2)
& element(sK4,powerset(the_carrier(sK2)))
& ( ( sK4 != interior(sK2,sK4)
& open_subset(sK4,sK2) )
| ( interior(sK1,sK3) = sK3
& ~ open_subset(sK3,sK1) ) )
& element(sK3,powerset(the_carrier(sK1)))
& top_str(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f31,f62,f61,f60,f59]) ).
fof(f59,plain,
( ? [X0] :
( topological_space(X0)
& ? [X1] :
( top_str(X1)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ( ( interior(X1,X3) != X3
& open_subset(X3,X1) )
| ( interior(X0,X2) = X2
& ~ open_subset(X2,X0) ) ) )
& element(X2,powerset(the_carrier(X0))) ) )
& top_str(X0) )
=> ( topological_space(sK1)
& ? [X1] :
( top_str(X1)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ( ( interior(X1,X3) != X3
& open_subset(X3,X1) )
| ( interior(sK1,X2) = X2
& ~ open_subset(X2,sK1) ) ) )
& element(X2,powerset(the_carrier(sK1))) ) )
& top_str(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ? [X1] :
( top_str(X1)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ( ( interior(X1,X3) != X3
& open_subset(X3,X1) )
| ( interior(sK1,X2) = X2
& ~ open_subset(X2,sK1) ) ) )
& element(X2,powerset(the_carrier(sK1))) ) )
=> ( top_str(sK2)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(sK2)))
& ( ( interior(sK2,X3) != X3
& open_subset(X3,sK2) )
| ( interior(sK1,X2) = X2
& ~ open_subset(X2,sK1) ) ) )
& element(X2,powerset(the_carrier(sK1))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
( ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(sK2)))
& ( ( interior(sK2,X3) != X3
& open_subset(X3,sK2) )
| ( interior(sK1,X2) = X2
& ~ open_subset(X2,sK1) ) ) )
& element(X2,powerset(the_carrier(sK1))) )
=> ( ? [X3] :
( element(X3,powerset(the_carrier(sK2)))
& ( ( interior(sK2,X3) != X3
& open_subset(X3,sK2) )
| ( interior(sK1,sK3) = sK3
& ~ open_subset(sK3,sK1) ) ) )
& element(sK3,powerset(the_carrier(sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X3] :
( element(X3,powerset(the_carrier(sK2)))
& ( ( interior(sK2,X3) != X3
& open_subset(X3,sK2) )
| ( interior(sK1,sK3) = sK3
& ~ open_subset(sK3,sK1) ) ) )
=> ( element(sK4,powerset(the_carrier(sK2)))
& ( ( sK4 != interior(sK2,sK4)
& open_subset(sK4,sK2) )
| ( interior(sK1,sK3) = sK3
& ~ open_subset(sK3,sK1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( topological_space(X0)
& ? [X1] :
( top_str(X1)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ( ( interior(X1,X3) != X3
& open_subset(X3,X1) )
| ( interior(X0,X2) = X2
& ~ open_subset(X2,X0) ) ) )
& element(X2,powerset(the_carrier(X0))) ) )
& top_str(X0) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( top_str(X1)
& ? [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ( ( interior(X1,X3) != X3
& open_subset(X3,X1) )
| ( interior(X0,X2) = X2
& ~ open_subset(X2,X0) ) ) )
& element(X2,powerset(the_carrier(X0))) ) )
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [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)))
=> ( ( open_subset(X3,X1)
=> interior(X1,X3) = X3 )
& ( interior(X0,X2) = X2
=> open_subset(X2,X0) ) ) ) ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [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)))
=> ( ( 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(f250,plain,
( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK4)) = interior(sK2,sK4)
| ~ spl9_4 ),
inference(backward_demodulation,[],[f159,f246]) ).
fof(f246,plain,
( topstr_closure(sK2,subset_complement(the_carrier(sK2),sK4)) = subset_complement(the_carrier(sK2),sK4)
| ~ spl9_4 ),
inference(unit_resulting_resolution,[],[f88,f160,f163,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| topstr_closure(X0,X1) = X1
| ~ top_str(X0)
| ~ closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( closed_subset(X1,X0)
| topstr_closure(X0,X1) != X1
| ~ topological_space(X0) )
& ( ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) ) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ topological_space(X0)
| topstr_closure(X0,X1) != X1 )
& ( ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( ( topological_space(X0)
& topstr_closure(X0,X1) = X1 )
=> closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f163,plain,
element(subset_complement(the_carrier(sK2),sK4),powerset(the_carrier(sK2))),
inference(unit_resulting_resolution,[],[f87,f95]) ).
fof(f95,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f160,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK4),sK2)
| ~ spl9_4 ),
inference(unit_resulting_resolution,[],[f88,f125,f87,f106]) ).
fof(f106,plain,
! [X0,X1] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
<=> open_subset(X1,X0) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
<=> open_subset(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f125,plain,
( open_subset(sK4,sK2)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f123,plain,
( spl9_4
<=> open_subset(sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f88,plain,
top_str(sK2),
inference(cnf_transformation,[],[f63]) ).
fof(f159,plain,
subset_complement(the_carrier(sK2),topstr_closure(sK2,subset_complement(the_carrier(sK2),sK4))) = interior(sK2,sK4),
inference(unit_resulting_resolution,[],[f88,f87,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,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,[],[f1]) ).
fof(f1,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(f153,plain,
( spl9_2
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f152,plain,
( $false
| spl9_2
| ~ spl9_3 ),
inference(subsumption_resolution,[],[f151,f115]) ).
fof(f115,plain,
( ~ open_subset(sK3,sK1)
| spl9_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f113,plain,
( spl9_2
<=> open_subset(sK3,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f151,plain,
( open_subset(sK3,sK1)
| ~ spl9_3 ),
inference(forward_demodulation,[],[f144,f120]) ).
fof(f120,plain,
( interior(sK1,sK3) = sK3
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f118,plain,
( spl9_3
<=> interior(sK1,sK3) = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f144,plain,
open_subset(interior(sK1,sK3),sK1),
inference(unit_resulting_resolution,[],[f81,f89,f82,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X1,X0] :
( ~ element(X0,powerset(the_carrier(X1)))
| open_subset(interior(X1,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( open_subset(interior(X1,X0),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( topological_space(X1)
& top_str(X1)
& element(X0,powerset(the_carrier(X1))) )
=> open_subset(interior(X1,X0),X1) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X1,X0] :
( ( topological_space(X0)
& element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f82,plain,
element(sK3,powerset(the_carrier(sK1))),
inference(cnf_transformation,[],[f63]) ).
fof(f89,plain,
topological_space(sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f81,plain,
top_str(sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f127,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f84,f123,f118]) ).
fof(f84,plain,
( open_subset(sK4,sK2)
| interior(sK1,sK3) = sK3 ),
inference(cnf_transformation,[],[f63]) ).
fof(f126,plain,
( spl9_4
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f83,f113,f123]) ).
fof(f83,plain,
( ~ open_subset(sK3,sK1)
| open_subset(sK4,sK2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f121,plain,
( ~ spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f86,f118,f109]) ).
fof(f86,plain,
( interior(sK1,sK3) = sK3
| sK4 != interior(sK2,sK4) ),
inference(cnf_transformation,[],[f63]) ).
fof(f116,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f85,f113,f109]) ).
fof(f85,plain,
( ~ open_subset(sK3,sK1)
| sK4 != interior(sK2,sK4) ),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n018.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 : Tue Aug 30 15:14:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (12636)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.49 % (12636)First to succeed.
% 0.20/0.50 % (12644)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50 % (12652)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.51 % (12644)Instruction limit reached!
% 0.20/0.51 % (12644)------------------------------
% 0.20/0.51 % (12644)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (12642)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51 % (12636)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (12636)------------------------------
% 0.20/0.51 % (12636)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (12636)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (12636)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (12636)Memory used [KB]: 6140
% 0.20/0.51 % (12636)Time elapsed: 0.101 s
% 0.20/0.51 % (12636)Instructions burned: 9 (million)
% 0.20/0.51 % (12636)------------------------------
% 0.20/0.51 % (12636)------------------------------
% 0.20/0.51 % (12626)Success in time 0.167 s
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