TSTP Solution File: SET790+4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET790+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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n029.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 09:08:30 EDT 2024
% Result : Theorem 0.55s 0.75s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 10 unt; 1 typ; 0 def)
% Number of atoms : 290 ( 18 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 239 ( 87 ~; 68 |; 49 &)
% ( 7 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 91 ( 91 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 111 ( 96 !; 14 ?; 28 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_13,type,
sQ4_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f83,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f74,f82]) ).
tff(f82,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f81]) ).
tff(f81,plain,
( $false
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f80,f40]) ).
tff(f40,plain,
member(sK2,sK1),
inference(resolution,[],[f33,f27]) ).
tff(f27,plain,
least(sK2,sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
( ( sK2 != sK3 )
& least(sK3,sK0,sK1)
& least(sK2,sK0,sK1)
& order(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f24,f23]) ).
tff(f23,plain,
( ? [X0,X1,X2] :
( ? [X3] :
( ( X2 != X3 )
& least(X3,X0,X1) )
& least(X2,X0,X1)
& order(X0,X1) )
=> ( ? [X3] :
( ( sK2 != X3 )
& least(X3,sK0,sK1) )
& least(sK2,sK0,sK1)
& order(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f24,plain,
( ? [X3] :
( ( sK2 != X3 )
& least(X3,sK0,sK1) )
=> ( ( sK2 != sK3 )
& least(sK3,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f19,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( X2 != X3 )
& least(X3,X0,X1) )
& least(X2,X0,X1)
& order(X0,X1) ),
inference(flattening,[],[f18]) ).
tff(f18,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( X2 != X3 )
& least(X3,X0,X1) )
& least(X2,X0,X1)
& order(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,plain,
~ ! [X0,X1,X2] :
( ( least(X2,X0,X1)
& order(X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> ( X2 = X3 ) ) ),
inference(rectify,[],[f12]) ).
tff(f12,negated_conjecture,
~ ! [X0,X1,X5] :
( ( least(X5,X0,X1)
& order(X0,X1) )
=> ! [X2] :
( least(X2,X0,X1)
=> ( X2 = X5 ) ) ),
inference(negated_conjecture,[],[f11]) ).
tff(f11,conjecture,
! [X0,X1,X5] :
( ( least(X5,X0,X1)
& order(X0,X1) )
=> ! [X2] :
( least(X2,X0,X1)
=> ( X2 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',thIV2) ).
tff(f33,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) )
& member(X2,X1) )
| ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
tff(f16,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
tff(f15,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0,X1,X5] :
( least(X5,X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X5,X2) )
& member(X5,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',least) ).
tff(f80,plain,
( ~ member(sK2,sK1)
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f79,f26]) ).
tff(f26,plain,
order(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
tff(f79,plain,
( ~ order(sK0,sK1)
| ~ member(sK2,sK1)
| ~ spl5_2 ),
inference(resolution,[],[f55,f41]) ).
tff(f41,plain,
member(sK3,sK1),
inference(resolution,[],[f33,f28]) ).
tff(f28,plain,
least(sK3,sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
tff(f55,plain,
( ! [X0: $i] :
( ~ member(sK3,X0)
| ~ order(sK0,X0)
| ~ member(sK2,X0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f54]) ).
tff(f54,plain,
( spl5_2
<=> ! [X0] :
( ~ member(sK3,X0)
| ~ order(sK0,X0)
| ~ member(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
tff(f74,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f73]) ).
tff(f73,plain,
( $false
| spl5_1 ),
inference(subsumption_resolution,[],[f72,f41]) ).
tff(f72,plain,
( ~ member(sK3,sK1)
| spl5_1 ),
inference(resolution,[],[f62,f27]) ).
tff(f62,plain,
( ! [X0: $i] :
( ~ least(sK2,sK0,X0)
| ~ member(sK3,X0) )
| spl5_1 ),
inference(resolution,[],[f52,f34]) ).
tff(f34,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f52,plain,
( ~ apply(sK0,sK2,sK3)
| spl5_1 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f50,plain,
( spl5_1
<=> apply(sK0,sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
tff(f56,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f48,f54,f50]) ).
tff(f48,plain,
! [X0: $i] :
( ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ apply(sK0,sK2,sK3) ),
inference(subsumption_resolution,[],[f47,f40]) ).
tff(f47,plain,
! [X0: $i] :
( ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1)
| ~ apply(sK0,sK2,sK3) ),
inference(resolution,[],[f46,f28]) ).
tff(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ least(sK3,X0,X2)
| ~ member(sK3,X1)
| ~ member(sK2,X1)
| ~ order(X0,X1)
| ~ member(sK2,X2)
| ~ apply(X0,sK2,sK3) ),
inference(resolution,[],[f44,f34]) ).
tff(f44,plain,
! [X0: $i,X1: $i] :
( ~ apply(X0,sK3,sK2)
| ~ apply(X0,sK2,sK3)
| ~ member(sK3,X1)
| ~ member(sK2,X1)
| ~ order(X0,X1) ),
inference(resolution,[],[f37,f36]) ).
tff(f36,plain,
~ sQ4_eqProxy($i,sK2,sK3),
inference(equality_proxy_replacement,[],[f29,f35]) ).
tff(f35,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ4_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).
tff(f29,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f25]) ).
tff(f37,plain,
! [X0: $i,X1: $i,X6: $i,X5: $i] :
( sQ4_eqProxy($i,X5,X6)
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) ),
inference(equality_proxy_replacement,[],[f31,f35]) ).
tff(f31,plain,
! [X0: $i,X1: $i,X6: $i,X5: $i] :
( ( X5 = X6 )
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tff(f21,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) )
& ! [X5,X6] :
( ( X5 = X6 )
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(flattening,[],[f20]) ).
tff(f20,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) )
& ! [X5,X6] :
( ( X5 = X6 )
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
! [X0,X1] :
( 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,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> ( X5 = X6 ) ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
tff(f14,plain,
! [X0,X1] :
( 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,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> ( X5 = X6 ) ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0,X1] :
( 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) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> ( X2 = X3 ) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',order) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % 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
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 16:36:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 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.Mtn525P960/Vampire---4.8_31623
% 0.55/0.75 % (31967)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)
% 0.55/0.75 % (31969)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.75 % (31970)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)
% 0.55/0.75 % (31971)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)
% 0.55/0.75 % (31968)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)
% 0.55/0.75 % (31972)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)
% 0.55/0.75 % (31973)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)
% 0.55/0.75 % (31974)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)
% 0.55/0.75 % (31972)Also succeeded, but the first one will report.
% 0.55/0.75 % (31970)Also succeeded, but the first one will report.
% 0.55/0.75 % (31967)First to succeed.
% 0.55/0.75 % (31974)Also succeeded, but the first one will report.
% 0.55/0.75 % (31968)Also succeeded, but the first one will report.
% 0.55/0.75 % (31971)Also succeeded, but the first one will report.
% 0.55/0.75 % (31973)Also succeeded, but the first one will report.
% 0.55/0.75 % (31967)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31874"
% 0.55/0.75 % (31969)Also succeeded, but the first one will report.
% 0.55/0.75 % (31967)Refutation found. Thanks to Tanya!
% 0.55/0.75 % SZS status Theorem for Vampire---4
% 0.55/0.75 % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.75 % (31967)------------------------------
% 0.55/0.75 % (31967)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.75 % (31967)Termination reason: Refutation
% 0.55/0.75
% 0.55/0.75 % (31967)Memory used [KB]: 1083
% 0.55/0.75 % (31967)Time elapsed: 0.004 s
% 0.55/0.75 % (31967)Instructions burned: 6 (million)
% 0.55/0.75 % (31874)Success in time 0.382 s
% 0.55/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------