TSTP Solution File: SET002+3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET002+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 03:43:58 EDT 2024
% Result : Theorem 0.55s 0.76s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 9 unt; 1 typ; 0 def)
% Number of atoms : 69 ( 17 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 41 ( 20 ~; 12 |; 5 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 30 ( 27 !; 2 ?; 16 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_3,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f52,plain,
$false,
inference(subsumption_resolution,[],[f51,f37]) ).
tff(f37,plain,
! [X1: $i] : subset(X1,X1),
inference(equality_resolution,[],[f29]) ).
tff(f29,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
! [X0,X1] :
( ( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ( X0 != X1 ) ) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
! [X0,X1] :
( ( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0,X1] :
( ( X0 = X1 )
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.i4PSWuJrFY/Vampire---4.8_23836',equal_defn) ).
tff(f51,plain,
~ subset(sK0,sK0),
inference(resolution,[],[f50,f40]) ).
tff(f40,plain,
~ sQ2_eqProxy($i,sK0,union(sK0,sK0)),
inference(equality_proxy_replacement,[],[f22,f39]) ).
tff(f39,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ2_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ2_eqProxy])]) ).
tff(f22,plain,
sK0 != union(sK0,sK0),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
sK0 != union(sK0,sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f12]) ).
tff(f12,plain,
( ? [X0] : ( union(X0,X0) != X0 )
=> ( sK0 != union(sK0,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f10,plain,
? [X0] : ( union(X0,X0) != X0 ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X0] : ( union(X0,X0) = X0 ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X0] : ( union(X0,X0) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.i4PSWuJrFY/Vampire---4.8_23836',prove_idempotency_of_union) ).
tff(f50,plain,
! [X0: $i,X1: $i] :
( sQ2_eqProxy($i,X1,union(X0,X1))
| ~ subset(X0,X1) ),
inference(forward_literal_rewriting,[],[f45,f47]) ).
tff(f47,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ2_eqProxy(X0,X2,X1)
| ~ sQ2_eqProxy(X0,X1,X2) ),
inference(equality_proxy_axiom,[],[f39]) ).
tff(f45,plain,
! [X0: $i,X1: $i] :
( sQ2_eqProxy($i,union(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(equality_proxy_replacement,[],[f31,f39]) ).
tff(f31,plain,
! [X0: $i,X1: $i] :
( ( union(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tff(f11,plain,
! [X0,X1] :
( ( union(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> ( union(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.i4PSWuJrFY/Vampire---4.8_23836',subset_union) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET002+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.15 % 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 17:09:47 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.i4PSWuJrFY/Vampire---4.8_23836
% 0.55/0.76 % (24040)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)
% 0.55/0.76 % (24047)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)
% 0.55/0.76 % (24040)First to succeed.
% 0.55/0.76 % (24047)Refutation not found, incomplete strategy% (24047)------------------------------
% 0.55/0.76 % (24047)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.76 % (24047)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.76
% 0.55/0.76 % (24047)Memory used [KB]: 954
% 0.55/0.76 % (24047)Time elapsed: 0.003 s
% 0.55/0.76 % (24047)Instructions burned: 2 (million)
% 0.55/0.76 % (24047)------------------------------
% 0.55/0.76 % (24047)------------------------------
% 0.55/0.76 % (24042)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.76 % (24043)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)
% 0.55/0.76 % (24041)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)
% 0.55/0.76 % (24044)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)
% 0.55/0.76 % (24045)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)
% 0.55/0.76 % (24046)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)
% 0.55/0.76 % (24040)Refutation found. Thanks to Tanya!
% 0.55/0.76 % SZS status Theorem for Vampire---4
% 0.55/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.76 % (24040)------------------------------
% 0.55/0.76 % (24040)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.76 % (24040)Termination reason: Refutation
% 0.55/0.76
% 0.55/0.76 % (24040)Memory used [KB]: 976
% 0.55/0.76 % (24040)Time elapsed: 0.004 s
% 0.55/0.76 % (24040)Instructions burned: 3 (million)
% 0.55/0.76 % (24040)------------------------------
% 0.55/0.76 % (24040)------------------------------
% 0.55/0.76 % (24019)Success in time 0.391 s
% 0.55/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------