TSTP Solution File: SEU341+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU341+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_sat --cores 0 -t %d %s
% Computer : n009.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 18:33:18 EDT 2022
% Result : Theorem 0.18s 0.57s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 224 ( 13 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 274 ( 98 ~; 82 |; 68 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 75 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f370,plain,
$false,
inference(subsumption_resolution,[],[f367,f180]) ).
fof(f180,plain,
in(sK6,sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( ~ point_neighbourhood(sK5,sK4,sK6)
& element(sK6,the_carrier(sK4))
& open_subset(sK5,sK4)
& in(sK6,sK5)
& element(sK5,powerset(the_carrier(sK4)))
& top_str(sK4)
& topological_space(sK4)
& ~ empty_carrier(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f101,f123,f122,f121]) ).
fof(f121,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& element(X2,the_carrier(X0))
& open_subset(X1,X0)
& in(X2,X1) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK4,X2)
& element(X2,the_carrier(sK4))
& open_subset(X1,sK4)
& in(X2,X1) )
& element(X1,powerset(the_carrier(sK4))) )
& top_str(sK4)
& topological_space(sK4)
& ~ empty_carrier(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK4,X2)
& element(X2,the_carrier(sK4))
& open_subset(X1,sK4)
& in(X2,X1) )
& element(X1,powerset(the_carrier(sK4))) )
=> ( ? [X2] :
( ~ point_neighbourhood(sK5,sK4,X2)
& element(X2,the_carrier(sK4))
& open_subset(sK5,sK4)
& in(X2,sK5) )
& element(sK5,powerset(the_carrier(sK4))) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
( ? [X2] :
( ~ point_neighbourhood(sK5,sK4,X2)
& element(X2,the_carrier(sK4))
& open_subset(sK5,sK4)
& in(X2,sK5) )
=> ( ~ point_neighbourhood(sK5,sK4,sK6)
& element(sK6,the_carrier(sK4))
& open_subset(sK5,sK4)
& in(sK6,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& element(X2,the_carrier(X0))
& open_subset(X1,X0)
& in(X2,X1) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,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))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(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(f41,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(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(f367,plain,
~ in(sK6,sK5),
inference(resolution,[],[f366,f183]) ).
fof(f183,plain,
~ point_neighbourhood(sK5,sK4,sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f366,plain,
! [X0] :
( point_neighbourhood(sK5,sK4,X0)
| ~ in(X0,sK5) ),
inference(subsumption_resolution,[],[f358,f244]) ).
fof(f244,plain,
! [X7] :
( element(X7,the_carrier(sK4))
| ~ in(X7,sK5) ),
inference(resolution,[],[f148,f179]) ).
fof(f179,plain,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f124]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(X2))
| ~ in(X1,X0)
| element(X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ in(X1,X0)
| ~ element(X0,powerset(X2))
| element(X1,X2) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X2,X0,X1] :
( element(X1,X2)
| ~ element(X0,powerset(X2))
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ( element(X0,powerset(X2))
& in(X1,X0) )
=> element(X1,X2) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X1,X0,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f358,plain,
! [X0] :
( point_neighbourhood(sK5,sK4,X0)
| ~ element(X0,the_carrier(sK4))
| ~ in(X0,sK5) ),
inference(superposition,[],[f297,f357]) ).
fof(f357,plain,
interior(sK4,sK5) = sK5,
inference(resolution,[],[f349,f195]) ).
fof(f195,plain,
! [X0] : element(sK8(X0),powerset(X0)),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f34,f128]) ).
fof(f128,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f349,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK4)))
| interior(sK4,sK5) = sK5 ),
inference(subsumption_resolution,[],[f347,f177]) ).
fof(f177,plain,
topological_space(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f347,plain,
! [X0] :
( interior(sK4,sK5) = sK5
| ~ element(X0,powerset(the_carrier(sK4)))
| ~ topological_space(sK4) ),
inference(resolution,[],[f345,f178]) ).
fof(f178,plain,
top_str(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f345,plain,
! [X14,X13] :
( ~ top_str(X13)
| ~ element(X14,powerset(the_carrier(X13)))
| interior(sK4,sK5) = sK5
| ~ topological_space(X13) ),
inference(subsumption_resolution,[],[f342,f181]) ).
fof(f181,plain,
open_subset(sK5,sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f342,plain,
! [X14,X13] :
( ~ open_subset(sK5,sK4)
| ~ topological_space(X13)
| ~ top_str(X13)
| interior(sK4,sK5) = sK5
| ~ element(X14,powerset(the_carrier(X13))) ),
inference(resolution,[],[f272,f179]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(the_carrier(sK4)))
| ~ open_subset(X1,sK4)
| interior(sK4,X1) = X1
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0) ),
inference(resolution,[],[f184,f178]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( ~ top_str(X1)
| ~ topological_space(X0)
| ~ open_subset(X3,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X3,powerset(the_carrier(X1)))
| interior(X1,X3) = X3 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ~ top_str(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 ) ) ) ) )
| ~ topological_space(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [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 ) ) ) ) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f40]) ).
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)))
=> ( ( 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(f297,plain,
! [X8] :
( ~ in(X8,interior(sK4,sK5))
| ~ element(X8,the_carrier(sK4))
| point_neighbourhood(sK5,sK4,X8) ),
inference(resolution,[],[f270,f179]) ).
fof(f270,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(sK4)))
| ~ in(X1,interior(sK4,X0))
| point_neighbourhood(X0,sK4,X1)
| ~ element(X1,the_carrier(sK4)) ),
inference(subsumption_resolution,[],[f269,f177]) ).
fof(f269,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK4))
| ~ element(X0,powerset(the_carrier(sK4)))
| ~ topological_space(sK4)
| point_neighbourhood(X0,sK4,X1)
| ~ in(X1,interior(sK4,X0)) ),
inference(subsumption_resolution,[],[f267,f176]) ).
fof(f176,plain,
~ empty_carrier(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f267,plain,
! [X0,X1] :
( empty_carrier(sK4)
| ~ element(X1,the_carrier(sK4))
| ~ in(X1,interior(sK4,X0))
| ~ topological_space(sK4)
| point_neighbourhood(X0,sK4,X1)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(resolution,[],[f144,f178]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ in(X1,interior(X0,X2))
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,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)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,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)) )
| ~ topological_space(X0)
| ~ top_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU341+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 15:12:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.50 % (32398)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.18/0.53 % (32399)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.54 % (32396)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.54 % (32395)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.54 % (32414)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.54 TRYING [1]
% 0.18/0.54 % (32415)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.55 TRYING [2]
% 0.18/0.55 % (32397)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.55 % (32400)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.55 % (32407)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.55 TRYING [3]
% 0.18/0.55 % (32401)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.55 % (32401)Instruction limit reached!
% 0.18/0.55 % (32401)------------------------------
% 0.18/0.55 % (32401)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.55 % (32401)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55 % (32401)Termination reason: Unknown
% 0.18/0.55 % (32401)Termination phase: Preprocessing 2
% 0.18/0.55
% 0.18/0.55 % (32401)Memory used [KB]: 895
% 0.18/0.55 % (32401)Time elapsed: 0.002 s
% 0.18/0.55 % (32401)Instructions burned: 2 (million)
% 0.18/0.55 % (32401)------------------------------
% 0.18/0.55 % (32401)------------------------------
% 0.18/0.55 % (32412)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.56 % (32400)Instruction limit reached!
% 0.18/0.56 % (32400)------------------------------
% 0.18/0.56 % (32400)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56 % (32400)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56 % (32400)Termination reason: Unknown
% 0.18/0.56 % (32400)Termination phase: Saturation
% 0.18/0.56
% 0.18/0.56 % (32400)Memory used [KB]: 5628
% 0.18/0.56 % (32400)Time elapsed: 0.166 s
% 0.18/0.56 % (32400)Instructions burned: 7 (million)
% 0.18/0.56 % (32400)------------------------------
% 0.18/0.56 % (32400)------------------------------
% 0.18/0.56 % (32408)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.18/0.56 % (32394)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.57 TRYING [4]
% 0.18/0.57 % (32395)First to succeed.
% 0.18/0.57 % (32416)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.18/0.57 % (32395)Refutation found. Thanks to Tanya!
% 0.18/0.57 % SZS status Theorem for theBenchmark
% 0.18/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.57 % (32395)------------------------------
% 0.18/0.57 % (32395)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.57 % (32395)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.57 % (32395)Termination reason: Refutation
% 0.18/0.57
% 0.18/0.57 % (32395)Memory used [KB]: 1151
% 0.18/0.57 % (32395)Time elapsed: 0.169 s
% 0.18/0.57 % (32395)Instructions burned: 11 (million)
% 0.18/0.57 % (32395)------------------------------
% 0.18/0.57 % (32395)------------------------------
% 0.18/0.57 % (32392)Success in time 0.225 s
%------------------------------------------------------------------------------