TSTP Solution File: SET807+4 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n007.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 May 1 03:49:03 EDT 2024
% Result : Theorem 0.64s 0.82s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 9 unt; 0 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 226 ( 78 ~; 62 |; 63 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 94 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f108,plain,
$false,
inference(avatar_sat_refutation,[],[f76,f101,f107]) ).
fof(f107,plain,
spl7_3,
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f106,plain,
( $false
| spl7_3 ),
inference(subsumption_resolution,[],[f105,f104]) ).
fof(f104,plain,
( member(sK2(sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1))),sK6(subset_predicate,power_set(sK1)))
| spl7_3 ),
inference(resolution,[],[f102,f49]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nHvUR1rhvE/Vampire---4.8_20086',subset) ).
fof(f102,plain,
( ~ subset(sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1)))
| spl7_3 ),
inference(resolution,[],[f75,f46]) ).
fof(f46,plain,
! [X0,X1] :
( apply(subset_predicate,X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( apply(subset_predicate,X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ apply(subset_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( apply(subset_predicate,X0,X1)
<=> subset(X0,X1) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X2,X4] :
( apply(subset_predicate,X2,X4)
<=> subset(X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.nHvUR1rhvE/Vampire---4.8_20086',rel_subset) ).
fof(f75,plain,
( ~ apply(subset_predicate,sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1)))
| spl7_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f73,plain,
( spl7_3
<=> apply(subset_predicate,sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f105,plain,
( ~ member(sK2(sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1))),sK6(subset_predicate,power_set(sK1)))
| spl7_3 ),
inference(resolution,[],[f102,f50]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f101,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f100,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[],[f99,f96]) ).
fof(f96,plain,
( member(sK2(sK3(subset_predicate,power_set(sK1)),sK5(subset_predicate,power_set(sK1))),sK3(subset_predicate,power_set(sK1)))
| ~ spl7_2 ),
inference(resolution,[],[f89,f70]) ).
fof(f70,plain,
( sP0(subset_predicate,power_set(sK1))
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl7_2
<=> sP0(subset_predicate,power_set(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f89,plain,
! [X0] :
( ~ sP0(subset_predicate,X0)
| member(sK2(sK3(subset_predicate,X0),sK5(subset_predicate,X0)),sK3(subset_predicate,X0)) ),
inference(resolution,[],[f83,f49]) ).
fof(f83,plain,
! [X0] :
( ~ subset(sK3(subset_predicate,X0),sK5(subset_predicate,X0))
| ~ sP0(subset_predicate,X0) ),
inference(resolution,[],[f46,f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ apply(X0,sK3(X0,X1),sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ apply(X0,sK3(X0,X1),sK5(X0,X1))
& apply(X0,sK4(X0,X1),sK5(X0,X1))
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& member(sK5(X0,X1),X1)
& member(sK4(X0,X1),X1)
& member(sK3(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f39,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ~ apply(X0,sK3(X0,X1),sK5(X0,X1))
& apply(X0,sK4(X0,X1),sK5(X0,X1))
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& member(sK5(X0,X1),X1)
& member(sK4(X0,X1),X1)
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f99,plain,
( ~ member(sK2(sK3(subset_predicate,power_set(sK1)),sK5(subset_predicate,power_set(sK1))),sK3(subset_predicate,power_set(sK1)))
| ~ spl7_2 ),
inference(resolution,[],[f98,f95]) ).
fof(f95,plain,
( ! [X0] :
( member(X0,sK4(subset_predicate,power_set(sK1)))
| ~ member(X0,sK3(subset_predicate,power_set(sK1))) )
| ~ spl7_2 ),
inference(resolution,[],[f87,f70]) ).
fof(f87,plain,
! [X0,X1] :
( ~ sP0(subset_predicate,X0)
| ~ member(X1,sK3(subset_predicate,X0))
| member(X1,sK4(subset_predicate,X0)) ),
inference(resolution,[],[f78,f48]) ).
fof(f48,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f78,plain,
! [X0] :
( subset(sK3(subset_predicate,X0),sK4(subset_predicate,X0))
| ~ sP0(subset_predicate,X0) ),
inference(resolution,[],[f45,f56]) ).
fof(f56,plain,
! [X0,X1] :
( apply(X0,sK3(X0,X1),sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apply(subset_predicate,X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f98,plain,
( ~ member(sK2(sK3(subset_predicate,power_set(sK1)),sK5(subset_predicate,power_set(sK1))),sK4(subset_predicate,power_set(sK1)))
| ~ spl7_2 ),
inference(resolution,[],[f97,f94]) ).
fof(f94,plain,
( ! [X0] :
( member(X0,sK5(subset_predicate,power_set(sK1)))
| ~ member(X0,sK4(subset_predicate,power_set(sK1))) )
| ~ spl7_2 ),
inference(resolution,[],[f85,f70]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sP0(subset_predicate,X0)
| ~ member(X1,sK4(subset_predicate,X0))
| member(X1,sK5(subset_predicate,X0)) ),
inference(resolution,[],[f77,f48]) ).
fof(f77,plain,
! [X0] :
( subset(sK4(subset_predicate,X0),sK5(subset_predicate,X0))
| ~ sP0(subset_predicate,X0) ),
inference(resolution,[],[f45,f57]) ).
fof(f57,plain,
! [X0,X1] :
( apply(X0,sK4(X0,X1),sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f97,plain,
( ~ member(sK2(sK3(subset_predicate,power_set(sK1)),sK5(subset_predicate,power_set(sK1))),sK5(subset_predicate,power_set(sK1)))
| ~ spl7_2 ),
inference(resolution,[],[f90,f70]) ).
fof(f90,plain,
! [X0] :
( ~ sP0(subset_predicate,X0)
| ~ member(sK2(sK3(subset_predicate,X0),sK5(subset_predicate,X0)),sK5(subset_predicate,X0)) ),
inference(resolution,[],[f83,f50]) ).
fof(f76,plain,
( ~ spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f62,f68,f73]) ).
fof(f62,plain,
( sP0(subset_predicate,power_set(sK1))
| ~ apply(subset_predicate,sK6(subset_predicate,power_set(sK1)),sK6(subset_predicate,power_set(sK1))) ),
inference(resolution,[],[f47,f60]) ).
fof(f60,plain,
! [X0,X1] :
( pre_order(X0,X1)
| sP0(X0,X1)
| ~ apply(X0,sK6(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( pre_order(X0,X1)
| sP0(X0,X1)
| ( ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f42,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) )
=> ( ~ apply(X0,sK6(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0,X1] :
( pre_order(X0,X1)
| sP0(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( pre_order(X0,X1)
| sP0(X0,X1)
| ? [X5] :
( ~ apply(X0,X5,X5)
& member(X5,X1) ) ),
inference(definition_folding,[],[f28,f29]) ).
fof(f28,plain,
! [X0,X1] :
( pre_order(X0,X1)
| ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ? [X5] :
( ~ apply(X0,X5,X5)
& member(X5,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( pre_order(X0,X1)
| ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ? [X5] :
( ~ apply(X0,X5,X5)
& member(X5,X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) )
=> pre_order(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X6,X3] :
( pre_order(X6,X3)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X3)
& member(X4,X3)
& member(X2,X3) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2] :
( member(X2,X3)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nHvUR1rhvE/Vampire---4.8_20086',pre_order) ).
fof(f47,plain,
~ pre_order(subset_predicate,power_set(sK1)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
~ pre_order(subset_predicate,power_set(sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f32]) ).
fof(f32,plain,
( ? [X0] : ~ pre_order(subset_predicate,power_set(X0))
=> ~ pre_order(subset_predicate,power_set(sK1)) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0] : ~ pre_order(subset_predicate,power_set(X0)),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] : pre_order(subset_predicate,power_set(X0)),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X3] : pre_order(subset_predicate,power_set(X3)),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X3] : pre_order(subset_predicate,power_set(X3)),
file('/export/starexec/sandbox2/tmp/tmp.nHvUR1rhvE/Vampire---4.8_20086',thIV18a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 17:13:03 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.33 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.nHvUR1rhvE/Vampire---4.8_20086
% 0.64/0.82 % (20201)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.64/0.82 % (20199)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.64/0.82 % (20198)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.64/0.82 % (20196)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.64/0.82 % (20194)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.64/0.82 % (20197)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.64/0.82 % (20195)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.64/0.82 % (20200)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.64/0.82 % (20199)Refutation not found, incomplete strategy% (20199)------------------------------
% 0.64/0.82 % (20199)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.64/0.82 % (20199)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.82
% 0.64/0.82 % (20199)Memory used [KB]: 1042
% 0.64/0.82 % (20199)Time elapsed: 0.002 s
% 0.64/0.82 % (20199)Instructions burned: 2 (million)
% 0.64/0.82 % (20199)------------------------------
% 0.64/0.82 % (20199)------------------------------
% 0.64/0.82 % (20201)First to succeed.
% 0.64/0.82 % (20194)Also succeeded, but the first one will report.
% 0.64/0.82 % (20201)Refutation found. Thanks to Tanya!
% 0.64/0.82 % SZS status Theorem for Vampire---4
% 0.64/0.82 % SZS output start Proof for Vampire---4
% See solution above
% 0.64/0.82 % (20201)------------------------------
% 0.64/0.82 % (20201)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.64/0.82 % (20201)Termination reason: Refutation
% 0.64/0.82
% 0.64/0.82 % (20201)Memory used [KB]: 1067
% 0.64/0.82 % (20201)Time elapsed: 0.004 s
% 0.64/0.82 % (20201)Instructions burned: 5 (million)
% 0.64/0.82 % (20201)------------------------------
% 0.64/0.82 % (20201)------------------------------
% 0.64/0.82 % (20193)Success in time 0.481 s
% 0.64/0.82 % Vampire---4.8 exiting
%------------------------------------------------------------------------------