TSTP Solution File: SET662+3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET662+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 : 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 : Sun May 5 09:07:53 EDT 2024
% Result : Theorem 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 169 ( 67 ~; 59 |; 8 &)
% ( 12 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f131,plain,
$false,
inference(avatar_sat_refutation,[],[f94,f121,f130]) ).
fof(f130,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f129]) ).
fof(f129,plain,
( $false
| ~ spl8_2 ),
inference(subsumption_resolution,[],[f125,f49]) ).
fof(f49,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',p20) ).
fof(f125,plain,
( ~ ilf_type(cross_product(sK0,sK1),set_type)
| ~ spl8_2 ),
inference(resolution,[],[f93,f68]) ).
fof(f68,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',p13) ).
fof(f93,plain,
( empty(power_set(cross_product(sK0,sK1)))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f91,plain,
( spl8_2
<=> empty(power_set(cross_product(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f121,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f120,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[],[f119,f50]) ).
fof(f50,plain,
empty(empty_set),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',p5a) ).
fof(f119,plain,
( ~ empty(empty_set)
| spl8_1 ),
inference(subsumption_resolution,[],[f118,f49]) ).
fof(f118,plain,
( ~ ilf_type(empty_set,set_type)
| ~ empty(empty_set)
| spl8_1 ),
inference(subsumption_resolution,[],[f105,f49]) ).
fof(f105,plain,
( ~ ilf_type(sK6(empty_set,cross_product(sK0,sK1)),set_type)
| ~ ilf_type(empty_set,set_type)
| ~ empty(empty_set)
| spl8_1 ),
inference(resolution,[],[f96,f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',p11) ).
fof(f96,plain,
( member(sK6(empty_set,cross_product(sK0,sK1)),empty_set)
| spl8_1 ),
inference(unit_resulting_resolution,[],[f49,f49,f89,f72]) ).
fof(f72,plain,
! [X0,X1] :
( member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,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,[],[f40]) ).
fof(f40,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,[],[f13]) ).
fof(f13,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.ufYCEKSIWq/Vampire---4.8_5752',p12) ).
fof(f89,plain,
( ~ member(empty_set,power_set(cross_product(sK0,sK1)))
| spl8_1 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f87,plain,
( spl8_1
<=> member(empty_set,power_set(cross_product(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f94,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f85,f91,f87]) ).
fof(f85,plain,
( empty(power_set(cross_product(sK0,sK1)))
| ~ member(empty_set,power_set(cross_product(sK0,sK1))) ),
inference(subsumption_resolution,[],[f84,f49]) ).
fof(f84,plain,
( empty(power_set(cross_product(sK0,sK1)))
| ~ member(empty_set,power_set(cross_product(sK0,sK1)))
| ~ ilf_type(empty_set,set_type) ),
inference(subsumption_resolution,[],[f83,f49]) ).
fof(f83,plain,
( empty(power_set(cross_product(sK0,sK1)))
| ~ ilf_type(power_set(cross_product(sK0,sK1)),set_type)
| ~ member(empty_set,power_set(cross_product(sK0,sK1)))
| ~ ilf_type(empty_set,set_type) ),
inference(resolution,[],[f79,f75]) ).
fof(f75,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,[],[f45]) ).
fof(f45,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,[],[f44]) ).
fof(f44,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,[],[f15]) ).
fof(f15,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.ufYCEKSIWq/Vampire---4.8_5752',p14) ).
fof(f79,plain,
~ ilf_type(empty_set,member_type(power_set(cross_product(sK0,sK1)))),
inference(unit_resulting_resolution,[],[f49,f49,f77,f61]) ).
fof(f61,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,[],[f35]) ).
fof(f35,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/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',p7) ).
fof(f77,plain,
~ ilf_type(empty_set,subset_type(cross_product(sK0,sK1))),
inference(unit_resulting_resolution,[],[f49,f49,f47,f54]) ).
fof(f54,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,[],[f30]) ).
fof(f30,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,[],[f24]) ).
fof(f24,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,[],[f2]) ).
fof(f2,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.ufYCEKSIWq/Vampire---4.8_5752',p2) ).
fof(f47,plain,
~ ilf_type(empty_set,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(empty_set,relation_type(X0,X1))
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(empty_set,relation_type(X0,X1)) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(empty_set,relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.ufYCEKSIWq/Vampire---4.8_5752',prove_relset_1_25) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % 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 : n020.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 16:31:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 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.ufYCEKSIWq/Vampire---4.8_5752
% 0.57/0.75 % (6013)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)
% 0.57/0.75 % (6007)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)
% 0.57/0.75 % (6009)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75 % (6008)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)
% 0.57/0.75 % (6011)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 (2996ds/34Mi)
% 0.57/0.75 % (6010)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)
% 0.57/0.75 % (6013)First to succeed.
% 0.57/0.75 % (6013)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6002"
% 0.57/0.75 % (6010)Refutation not found, incomplete strategy% (6010)------------------------------
% 0.57/0.75 % (6010)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (6010)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (6010)Memory used [KB]: 1024
% 0.57/0.75 % (6010)Time elapsed: 0.003 s
% 0.57/0.75 % (6010)Instructions burned: 2 (million)
% 0.57/0.75 % (6010)------------------------------
% 0.57/0.75 % (6010)------------------------------
% 0.57/0.75 % (6013)Refutation found. Thanks to Tanya!
% 0.57/0.75 % SZS status Theorem for Vampire---4
% 0.57/0.75 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.75 % (6013)------------------------------
% 0.57/0.75 % (6013)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75 % (6013)Termination reason: Refutation
% 0.57/0.75
% 0.57/0.75 % (6013)Memory used [KB]: 1057
% 0.57/0.75 % (6013)Time elapsed: 0.003 s
% 0.57/0.75 % (6013)Instructions burned: 6 (million)
% 0.57/0.75 % (6002)Success in time 0.384 s
% 0.57/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------