TSTP Solution File: SET076+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET076+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : n020.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 18:18:57 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 167 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 171 ( 63 ~; 52 |; 42 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 100 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f302,plain,
$false,
inference(avatar_sat_refutation,[],[f248,f275,f300]) ).
fof(f300,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f299,plain,
( $false
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f217,f286]) ).
fof(f286,plain,
( ! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK1,sK1))),cross_product(X4,sK2))
| ~ spl4_1 ),
inference(forward_demodulation,[],[f169,f243]) ).
fof(f243,plain,
( sK0(sK2,unordered_pair(sK1,sK3)) = sK1
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f241,plain,
( spl4_1
<=> sK0(sK2,unordered_pair(sK1,sK3)) = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f169,plain,
! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))))),cross_product(X4,sK2)),
inference(resolution,[],[f122,f93]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(X1,X3))
| member(X0,X3) ),
inference(definition_unfolding,[],[f86,f91]) ).
fof(f91,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))) = ordered_pair(X1,X0),
inference(definition_unfolding,[],[f71,f72,f72]) ).
fof(f72,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f71,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( member(X0,X3)
| ~ member(ordered_pair(X2,X0),cross_product(X1,X3)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ( ( member(X2,X1)
& member(X0,X3) )
| ~ member(ordered_pair(X2,X0),cross_product(X1,X3)) )
& ( member(ordered_pair(X2,X0),cross_product(X1,X3))
| ~ member(X2,X1)
| ~ member(X0,X3) ) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X2,X0,X1,X3] :
( ( ( member(X1,X0)
& member(X2,X3) )
| ~ member(ordered_pair(X1,X2),cross_product(X0,X3)) )
& ( member(ordered_pair(X1,X2),cross_product(X0,X3))
| ~ member(X1,X0)
| ~ member(X2,X3) ) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X2,X0,X1,X3] :
( ( ( member(X1,X0)
& member(X2,X3) )
| ~ member(ordered_pair(X1,X2),cross_product(X0,X3)) )
& ( member(ordered_pair(X1,X2),cross_product(X0,X3))
| ~ member(X1,X0)
| ~ member(X2,X3) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1,X3] :
( ( member(X1,X0)
& member(X2,X3) )
<=> member(ordered_pair(X1,X2),cross_product(X0,X3)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0,X2,X3,X1] :
( ( member(X2,X0)
& member(X3,X1) )
<=> member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f122,plain,
~ member(sK0(sK2,unordered_pair(sK1,sK3)),sK2),
inference(unit_resulting_resolution,[],[f82,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| subclass(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subclass(X1,X0) )
& ( subclass(X1,X0)
| ( member(sK0(X0,X1),X1)
& ~ member(sK0(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f60,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) )
=> ( member(sK0(X0,X1),X1)
& ~ member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subclass(X1,X0) )
& ( subclass(X1,X0)
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subclass(X0,X1) )
& ( subclass(X0,X1)
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
<=> subclass(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f82,plain,
~ subclass(unordered_pair(sK1,sK3),sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
( member(sK3,sK2)
& member(sK1,sK2)
& ~ subclass(unordered_pair(sK1,sK3),sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f63,f64]) ).
fof(f64,plain,
( ? [X0,X1,X2] :
( member(X2,X1)
& member(X0,X1)
& ~ subclass(unordered_pair(X0,X2),X1) )
=> ( member(sK3,sK2)
& member(sK1,sK2)
& ~ subclass(unordered_pair(sK1,sK3),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0,X1,X2] :
( member(X2,X1)
& member(X0,X1)
& ~ subclass(unordered_pair(X0,X2),X1) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
? [X2,X0,X1] :
( member(X1,X0)
& member(X2,X0)
& ~ subclass(unordered_pair(X2,X1),X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
? [X0,X2,X1] :
( ~ subclass(unordered_pair(X2,X1),X0)
& member(X1,X0)
& member(X2,X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
~ ! [X0,X2,X1] :
( ( member(X1,X0)
& member(X2,X0) )
=> subclass(unordered_pair(X2,X1),X0) ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X4,X1,X0] :
( ( member(X0,X4)
& member(X1,X4) )
=> subclass(unordered_pair(X0,X1),X4) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X4,X1,X0] :
( ( member(X0,X4)
& member(X1,X4) )
=> subclass(unordered_pair(X0,X1),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(f217,plain,
member(unordered_pair(unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))),unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK1,sK1))),cross_product(unordered_pair(sK1,sK3),sK2)),
inference(unit_resulting_resolution,[],[f83,f121,f94]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(X1,X3))
| ~ member(X2,X1) ),
inference(definition_unfolding,[],[f85,f91]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X0),cross_product(X1,X3))
| ~ member(X2,X1)
| ~ member(X0,X3) ),
inference(cnf_transformation,[],[f68]) ).
fof(f121,plain,
member(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK1,sK3)),
inference(unit_resulting_resolution,[],[f82,f79]) ).
fof(f79,plain,
! [X0,X1] :
( subclass(X1,X0)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
member(sK1,sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f275,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f274,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f261,f253]) ).
fof(f253,plain,
( ! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK3,sK3))),cross_product(X4,sK2))
| ~ spl4_2 ),
inference(backward_demodulation,[],[f169,f247]) ).
fof(f247,plain,
( sK3 = sK0(sK2,unordered_pair(sK1,sK3))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f245,plain,
( spl4_2
<=> sK3 = sK0(sK2,unordered_pair(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f261,plain,
( member(unordered_pair(unordered_pair(sK3,sK3),unordered_pair(sK3,unordered_pair(sK3,sK3))),cross_product(unordered_pair(sK1,sK3),sK2))
| ~ spl4_2 ),
inference(backward_demodulation,[],[f221,f247]) ).
fof(f221,plain,
member(unordered_pair(unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))),unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK3,sK3))),cross_product(unordered_pair(sK1,sK3),sK2)),
inference(unit_resulting_resolution,[],[f84,f121,f94]) ).
fof(f84,plain,
member(sK3,sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f248,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f236,f245,f241]) ).
fof(f236,plain,
( sK3 = sK0(sK2,unordered_pair(sK1,sK3))
| sK0(sK2,unordered_pair(sK1,sK3)) = sK1 ),
inference(resolution,[],[f121,f73]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X2,X1))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X2,X1))
| ~ member(X0,universal_class)
| ( X0 != X2
& X0 != X1 ) )
& ( ( member(X0,universal_class)
& ( X0 = X2
| X0 = X1 ) )
| ~ member(X0,unordered_pair(X2,X1)) ) ),
inference(rectify,[],[f56]) ).
fof(f56,plain,
! [X0,X2,X1] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X2,X1] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X2,X1] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ( ( X0 = X2
| X1 = X2 )
& member(X2,universal_class) )
<=> member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET076+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 13:11:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47 % (31810)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)
% 0.19/0.48 % (31818)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.48 % (31801)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.48 % (31810)Instruction limit reached!
% 0.19/0.48 % (31810)------------------------------
% 0.19/0.48 % (31810)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (31810)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (31810)Termination reason: Unknown
% 0.19/0.48 % (31810)Termination phase: Saturation
% 0.19/0.48
% 0.19/0.48 % (31810)Memory used [KB]: 6140
% 0.19/0.48 % (31810)Time elapsed: 0.009 s
% 0.19/0.48 % (31810)Instructions burned: 8 (million)
% 0.19/0.48 % (31810)------------------------------
% 0.19/0.48 % (31810)------------------------------
% 0.19/0.50 % (31817)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50 % (31814)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.50 % (31796)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (31796)Instruction limit reached!
% 0.19/0.50 % (31796)------------------------------
% 0.19/0.50 % (31796)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (31796)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (31796)Termination reason: Unknown
% 0.19/0.50 % (31796)Termination phase: Function definition elimination
% 0.19/0.50
% 0.19/0.50 % (31796)Memory used [KB]: 1535
% 0.19/0.50 % (31796)Time elapsed: 0.005 s
% 0.19/0.50 % (31796)Instructions burned: 4 (million)
% 0.19/0.50 % (31796)------------------------------
% 0.19/0.50 % (31796)------------------------------
% 0.19/0.50 % (31798)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51 % (31806)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)
% 0.19/0.51 % (31801)First to succeed.
% 0.19/0.51 % (31799)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.51 % (31801)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (31801)------------------------------
% 0.19/0.51 % (31801)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (31801)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (31801)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (31801)Memory used [KB]: 6140
% 0.19/0.51 % (31801)Time elapsed: 0.080 s
% 0.19/0.51 % (31801)Instructions burned: 10 (million)
% 0.19/0.51 % (31801)------------------------------
% 0.19/0.51 % (31801)------------------------------
% 0.19/0.51 % (31792)Success in time 0.163 s
%------------------------------------------------------------------------------