TSTP Solution File: SET640+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET640+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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -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 May 1 03:48:27 EDT 2024
% Result : Theorem 0.62s 0.82s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 13 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 228 ( 84 ~; 79 |; 17 &)
% ( 13 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 79 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f522,plain,
$false,
inference(avatar_sat_refutation,[],[f458,f493,f521]) ).
fof(f521,plain,
~ spl15_10,
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f520,plain,
( $false
| ~ spl15_10 ),
inference(subsumption_resolution,[],[f515,f56]) ).
fof(f56,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p19) ).
fof(f515,plain,
( ~ ilf_type(cross_product(sK1,sK2),set_type)
| ~ spl15_10 ),
inference(resolution,[],[f457,f81]) ).
fof(f81,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p12) ).
fof(f457,plain,
( empty(power_set(cross_product(sK1,sK2)))
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f455,plain,
( spl15_10
<=> empty(power_set(cross_product(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f493,plain,
~ spl15_9,
inference(avatar_contradiction_clause,[],[f492]) ).
fof(f492,plain,
( $false
| ~ spl15_9 ),
inference(subsumption_resolution,[],[f463,f113]) ).
fof(f113,plain,
~ member(sK4(sK3,cross_product(sK1,sK2)),cross_product(sK1,sK2)),
inference(unit_resulting_resolution,[],[f56,f56,f107,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,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,[],[f27]) ).
fof(f27,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,[],[f6]) ).
fof(f6,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p6) ).
fof(f107,plain,
~ subset(sK3,cross_product(sK1,sK2)),
inference(unit_resulting_resolution,[],[f56,f51,f56,f56,f52,f63]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p1) ).
fof(f52,plain,
~ subset(sK0,cross_product(sK1,sK2)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',prove_relset_1_2) ).
fof(f51,plain,
subset(sK0,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f463,plain,
( member(sK4(sK3,cross_product(sK1,sK2)),cross_product(sK1,sK2))
| ~ spl15_9 ),
inference(unit_resulting_resolution,[],[f112,f56,f56,f56,f453,f83]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(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,[],[f43]) ).
fof(f43,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,[],[f42]) ).
fof(f42,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,[],[f11]) ).
fof(f11,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p11) ).
fof(f453,plain,
( member(sK3,power_set(cross_product(sK1,sK2)))
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f451,plain,
( spl15_9
<=> member(sK3,power_set(cross_product(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f112,plain,
member(sK4(sK3,cross_product(sK1,sK2)),sK3),
inference(unit_resulting_resolution,[],[f56,f56,f107,f61]) ).
fof(f61,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f458,plain,
( spl15_9
| spl15_10 ),
inference(avatar_split_clause,[],[f449,f455,f451]) ).
fof(f449,plain,
( empty(power_set(cross_product(sK1,sK2)))
| member(sK3,power_set(cross_product(sK1,sK2))) ),
inference(subsumption_resolution,[],[f448,f56]) ).
fof(f448,plain,
( empty(power_set(cross_product(sK1,sK2)))
| member(sK3,power_set(cross_product(sK1,sK2)))
| ~ ilf_type(sK3,set_type) ),
inference(subsumption_resolution,[],[f447,f56]) ).
fof(f447,plain,
( empty(power_set(cross_product(sK1,sK2)))
| ~ ilf_type(power_set(cross_product(sK1,sK2)),set_type)
| member(sK3,power_set(cross_product(sK1,sK2)))
| ~ ilf_type(sK3,set_type) ),
inference(resolution,[],[f199,f89]) ).
fof(f89,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,[],[f47]) ).
fof(f47,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,[],[f46]) ).
fof(f46,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,[],[f13]) ).
fof(f13,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p13) ).
fof(f199,plain,
ilf_type(sK3,member_type(power_set(cross_product(sK1,sK2)))),
inference(unit_resulting_resolution,[],[f56,f56,f106,f73]) ).
fof(f73,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,[],[f36]) ).
fof(f36,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,[],[f8]) ).
fof(f8,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p8) ).
fof(f106,plain,
ilf_type(sK3,subset_type(cross_product(sK1,sK2))),
inference(unit_resulting_resolution,[],[f56,f56,f50,f65]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,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,[],[f22]) ).
fof(f22,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,[],[f4]) ).
fof(f4,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p4) ).
fof(f50,plain,
ilf_type(sK3,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % 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
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 17:11:32 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 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.BFVmAO6CVp/Vampire---4.8_30336
% 0.62/0.80 % (30559)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)
% 0.62/0.80 % (30560)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)
% 0.62/0.80 % (30554)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)
% 0.62/0.80 % (30556)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.80 % (30557)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)
% 0.62/0.80 % (30555)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)
% 0.62/0.80 % (30558)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)
% 0.62/0.80 % (30561)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)
% 0.62/0.81 % (30560)First to succeed.
% 0.62/0.82 % (30560)Refutation found. Thanks to Tanya!
% 0.62/0.82 % SZS status Theorem for Vampire---4
% 0.62/0.82 % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.82 % (30560)------------------------------
% 0.62/0.82 % (30560)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82 % (30560)Termination reason: Refutation
% 0.62/0.82
% 0.62/0.82 % (30560)Memory used [KB]: 1221
% 0.62/0.82 % (30560)Time elapsed: 0.014 s
% 0.62/0.82 % (30560)Instructions burned: 22 (million)
% 0.62/0.82 % (30560)------------------------------
% 0.62/0.82 % (30560)------------------------------
% 0.62/0.82 % (30520)Success in time 0.427 s
% 0.62/0.82 % Vampire---4.8 exiting
%------------------------------------------------------------------------------