TSTP Solution File: SET666+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.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 03:48:32 EDT 2024
% Result : Theorem 0.60s 0.77s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 202 ( 80 ~; 74 |; 7 &)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f152,plain,
$false,
inference(avatar_sat_refutation,[],[f111,f141,f151]) ).
fof(f151,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f150,plain,
( $false
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f146,f55]) ).
fof(f55,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p24) ).
fof(f146,plain,
( ~ ilf_type(cross_product(sK0,sK0),set_type)
| ~ spl9_2 ),
inference(resolution,[],[f110,f81]) ).
fof(f81,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p17) ).
fof(f110,plain,
( empty(power_set(cross_product(sK0,sK0)))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl9_2
<=> empty(power_set(cross_product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f141,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f140,plain,
( $false
| spl9_1 ),
inference(subsumption_resolution,[],[f136,f55]) ).
fof(f136,plain,
( ~ ilf_type(sK0,set_type)
| spl9_1 ),
inference(resolution,[],[f130,f57]) ).
fof(f57,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p3) ).
fof(f130,plain,
( ~ subset(identity_relation_of(sK0),cross_product(sK0,sK0))
| spl9_1 ),
inference(unit_resulting_resolution,[],[f55,f55,f113,f55,f114,f69]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p14) ).
fof(f114,plain,
( ~ member(sK7(identity_relation_of(sK0),cross_product(sK0,sK0)),cross_product(sK0,sK0))
| spl9_1 ),
inference(unit_resulting_resolution,[],[f55,f55,f106,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p16) ).
fof(f106,plain,
( ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| spl9_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl9_1
<=> member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f113,plain,
( member(sK7(identity_relation_of(sK0),cross_product(sK0,sK0)),identity_relation_of(sK0))
| spl9_1 ),
inference(unit_resulting_resolution,[],[f55,f55,f106,f85]) ).
fof(f85,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f111,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f102,f108,f104]) ).
fof(f102,plain,
( empty(power_set(cross_product(sK0,sK0)))
| ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0))) ),
inference(subsumption_resolution,[],[f101,f55]) ).
fof(f101,plain,
( empty(power_set(cross_product(sK0,sK0)))
| ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(subsumption_resolution,[],[f100,f55]) ).
fof(f100,plain,
( empty(power_set(cross_product(sK0,sK0)))
| ~ ilf_type(power_set(cross_product(sK0,sK0)),set_type)
| ~ member(identity_relation_of(sK0),power_set(cross_product(sK0,sK0)))
| ~ ilf_type(identity_relation_of(sK0),set_type) ),
inference(resolution,[],[f95,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p18) ).
fof(f95,plain,
~ ilf_type(identity_relation_of(sK0),member_type(power_set(cross_product(sK0,sK0)))),
inference(unit_resulting_resolution,[],[f55,f55,f92,f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p12) ).
fof(f92,plain,
~ ilf_type(identity_relation_of(sK0),subset_type(cross_product(sK0,sK0))),
inference(unit_resulting_resolution,[],[f55,f55,f90,f67]) ).
fof(f67,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ilf_type(X3,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p1) ).
fof(f90,plain,
~ ilf_type(identity_relation_of(sK0),relation_type(sK0,sK0)),
inference(unit_resulting_resolution,[],[f55,f55,f54,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ilf_type(X1,identity_relation_of_type(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',p6) ).
fof(f54,plain,
~ ilf_type(identity_relation_of(sK0),identity_relation_of_type(sK0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
? [X0] :
( ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129',prove_relset_1_29) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Apr 30 17:35:40 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.cB7YIURQ60/Vampire---4.8_14129
% 0.60/0.76 % (14389)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 (2996ds/83Mi)
% 0.60/0.76 % (14383)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 (2996ds/34Mi)
% 0.60/0.76 % (14385)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.76 % (14384)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 (2996ds/51Mi)
% 0.60/0.76 % (14386)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.76 % (14388)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.76 % (14390)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 (2996ds/56Mi)
% 0.60/0.76 % (14389)First to succeed.
% 0.60/0.76 % (14386)Refutation not found, incomplete strategy% (14386)------------------------------
% 0.60/0.76 % (14386)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76 % (14386)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76 % (14388)Refutation not found, incomplete strategy% (14388)------------------------------
% 0.60/0.76 % (14388)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76
% 0.60/0.76 % (14386)Memory used [KB]: 1022
% 0.60/0.76 % (14386)Time elapsed: 0.003 s
% 0.60/0.76 % (14386)Instructions burned: 2 (million)
% 0.60/0.76 % (14386)------------------------------
% 0.60/0.76 % (14386)------------------------------
% 0.60/0.76 % (14388)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76
% 0.60/0.76 % (14388)Memory used [KB]: 1023
% 0.60/0.76 % (14388)Time elapsed: 0.003 s
% 0.60/0.76 % (14388)Instructions burned: 2 (million)
% 0.60/0.76 % (14388)------------------------------
% 0.60/0.76 % (14388)------------------------------
% 0.60/0.76 % (14383)Refutation not found, incomplete strategy% (14383)------------------------------
% 0.60/0.76 % (14383)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76 % (14383)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76
% 0.60/0.76 % (14383)Memory used [KB]: 1052
% 0.60/0.76 % (14383)Time elapsed: 0.003 s
% 0.60/0.76 % (14383)Instructions burned: 3 (million)
% 0.60/0.76 % (14383)------------------------------
% 0.60/0.76 % (14383)------------------------------
% 0.60/0.76 % (14390)Refutation not found, incomplete strategy% (14390)------------------------------
% 0.60/0.76 % (14390)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76 % (14390)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76
% 0.60/0.76 % (14390)Memory used [KB]: 1023
% 0.60/0.76 % (14390)Time elapsed: 0.003 s
% 0.60/0.76 % (14390)Instructions burned: 2 (million)
% 0.60/0.76 % (14390)------------------------------
% 0.60/0.76 % (14390)------------------------------
% 0.60/0.77 % (14389)Refutation found. Thanks to Tanya!
% 0.60/0.77 % SZS status Theorem for Vampire---4
% 0.60/0.77 % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.77 % (14389)------------------------------
% 0.60/0.77 % (14389)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.77 % (14389)Termination reason: Refutation
% 0.60/0.77
% 0.60/0.77 % (14389)Memory used [KB]: 1057
% 0.60/0.77 % (14389)Time elapsed: 0.004 s
% 0.60/0.77 % (14389)Instructions burned: 7 (million)
% 0.60/0.77 % (14389)------------------------------
% 0.60/0.77 % (14389)------------------------------
% 0.60/0.77 % (14379)Success in time 0.389 s
% 0.60/0.77 % Vampire---4.8 exiting
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