TSTP Solution File: SET812+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% 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 : n013.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 18:22:20 EDT 2022
% Result : Theorem 0.19s 0.58s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 4 unt; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 237 ( 83 ~; 81 |; 48 &)
% ( 15 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 86 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f311,plain,
$false,
inference(avatar_sat_refutation,[],[f197,f204,f252,f294,f310]) ).
fof(f310,plain,
( spl15_2
| spl15_9 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f305,plain,
( $false
| spl15_2
| spl15_9 ),
inference(resolution,[],[f251,f205]) ).
fof(f205,plain,
( member(sK13(sK2,intersection(sK2,power_set(sK2))),sK2)
| spl15_2 ),
inference(resolution,[],[f196,f175]) ).
fof(f175,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( member(sK13(X0,X1),X0)
& ~ member(sK13(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) )
=> ( member(sK13(X0,X1),X0)
& ~ member(sK13(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) ) ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( member(X2,X1)
& ~ member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X1)
=> member(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f196,plain,
( ~ subset(sK2,intersection(sK2,power_set(sK2)))
| spl15_2 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl15_2
<=> subset(sK2,intersection(sK2,power_set(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f251,plain,
( ~ member(sK13(sK2,intersection(sK2,power_set(sK2))),sK2)
| spl15_9 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f250,plain,
( spl15_9
<=> member(sK13(sK2,intersection(sK2,power_set(sK2))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f294,plain,
( spl15_2
| spl15_8 ),
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f285,plain,
( $false
| spl15_2
| spl15_8 ),
inference(unit_resulting_resolution,[],[f205,f248,f138,f229]) ).
fof(f229,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,on)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f143,f130]) ).
fof(f130,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
! [X1,X0] :
( ( member(X1,power_set(X0))
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ~ member(X1,power_set(X0)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( member(X1,power_set(X0))
<=> subset(X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X2] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f143,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& set(X0)
& strict_well_order(member_predicate,X0) )
| ~ member(X0,on) )
& ( member(X0,on)
| ( ~ subset(sK3(X0),X0)
& member(sK3(X0),X0) )
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f78,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X2] :
( ~ subset(X2,X0)
& member(X2,X0) )
=> ( ~ subset(sK3(X0),X0)
& member(sK3(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0] :
( ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& set(X0)
& strict_well_order(member_predicate,X0) )
| ~ member(X0,on) )
& ( member(X0,on)
| ? [X2] :
( ~ subset(X2,X0)
& member(X2,X0) )
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& set(X0)
& strict_well_order(member_predicate,X0) )
| ~ member(X0,on) )
& ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0) ) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& set(X0)
& strict_well_order(member_predicate,X0) )
| ~ member(X0,on) )
& ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& set(X0)
& strict_well_order(member_predicate,X0) )
<=> member(X0,on) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
<=> member(X0,on) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( member(X2,X0)
=> subset(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_number) ).
fof(f138,plain,
member(sK2,on),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( member(sK2,on)
& ~ equal_set(sK2,intersection(sK2,power_set(sK2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f74]) ).
fof(f74,plain,
( ? [X0] :
( member(X0,on)
& ~ equal_set(X0,intersection(X0,power_set(X0))) )
=> ( member(sK2,on)
& ~ equal_set(sK2,intersection(sK2,power_set(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] :
( member(X0,on)
& ~ equal_set(X0,intersection(X0,power_set(X0))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV10) ).
fof(f248,plain,
( ~ member(sK13(sK2,intersection(sK2,power_set(sK2))),power_set(sK2))
| spl15_8 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f247,plain,
( spl15_8
<=> member(sK13(sK2,intersection(sK2,power_set(sK2))),power_set(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f252,plain,
( ~ spl15_8
| ~ spl15_9
| spl15_2 ),
inference(avatar_split_clause,[],[f245,f195,f250,f247]) ).
fof(f245,plain,
( ~ member(sK13(sK2,intersection(sK2,power_set(sK2))),sK2)
| ~ member(sK13(sK2,intersection(sK2,power_set(sK2))),power_set(sK2))
| spl15_2 ),
inference(resolution,[],[f117,f206]) ).
fof(f206,plain,
( ~ member(sK13(sK2,intersection(sK2,power_set(sK2))),intersection(sK2,power_set(sK2)))
| spl15_2 ),
inference(resolution,[],[f196,f174]) ).
fof(f174,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f117,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) )
& ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X2,X1,X0] :
( ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) )
& ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X2,X1,X0] :
( ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) )
& ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X2,X1,X0] :
( ( member(X2,X1)
& member(X2,X0) )
<=> member(X2,intersection(X1,X0)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ( member(X2,X0)
& member(X2,X1) )
<=> member(X2,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f204,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f201]) ).
fof(f201,plain,
( $false
| spl15_1 ),
inference(unit_resulting_resolution,[],[f199,f198,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f198,plain,
( member(sK13(intersection(sK2,power_set(sK2)),sK2),intersection(sK2,power_set(sK2)))
| spl15_1 ),
inference(resolution,[],[f193,f175]) ).
fof(f193,plain,
( ~ subset(intersection(sK2,power_set(sK2)),sK2)
| spl15_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f192,plain,
( spl15_1
<=> subset(intersection(sK2,power_set(sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f199,plain,
( ~ member(sK13(intersection(sK2,power_set(sK2)),sK2),sK2)
| spl15_1 ),
inference(resolution,[],[f193,f174]) ).
fof(f197,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f190,f195,f192]) ).
fof(f190,plain,
( ~ subset(sK2,intersection(sK2,power_set(sK2)))
| ~ subset(intersection(sK2,power_set(sK2)),sK2) ),
inference(resolution,[],[f121,f137]) ).
fof(f137,plain,
~ equal_set(sK2,intersection(sK2,power_set(sK2))),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X1,X0] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> equal_set(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % 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 : n013.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 14:18:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.54 % (27670)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55 % (27695)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.56 % (27678)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.56 % (27695)First to succeed.
% 0.19/0.57 % (27694)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.57 % (27678)Instruction limit reached!
% 0.19/0.57 % (27678)------------------------------
% 0.19/0.57 % (27678)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57 % (27681)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.58 % (27695)Refutation found. Thanks to Tanya!
% 0.19/0.58 % SZS status Theorem for theBenchmark
% 0.19/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.58 % (27695)------------------------------
% 0.19/0.58 % (27695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58 % (27695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.58 % (27695)Termination reason: Refutation
% 0.19/0.58
% 0.19/0.58 % (27695)Memory used [KB]: 6140
% 0.19/0.58 % (27695)Time elapsed: 0.145 s
% 0.19/0.58 % (27695)Instructions burned: 8 (million)
% 0.19/0.58 % (27695)------------------------------
% 0.19/0.58 % (27695)------------------------------
% 0.19/0.58 % (27660)Success in time 0.228 s
%------------------------------------------------------------------------------