TSTP Solution File: SET162+3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET162+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 : n017.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 09:04:28 EDT 2024
% Result : Theorem 0.55s 0.74s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 10 unt; 1 typ; 0 def)
% Number of atoms : 190 ( 17 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 115 ( 43 ~; 51 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 86 ( 86 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 63 ( 57 !; 5 ?; 32 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_4,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f129,plain,
$false,
inference(resolution,[],[f112,f40]) ).
tff(f40,plain,
~ sQ2_eqProxy($i,sK0,union(sK0,empty_set)),
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,empty_set),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
sK0 != union(sK0,empty_set),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
tff(f12,plain,
( ? [X0] : ( union(X0,empty_set) != X0 )
=> ( sK0 != union(sK0,empty_set) ) ),
introduced(choice_axiom,[]) ).
tff(f11,plain,
? [X0] : ( union(X0,empty_set) != X0 ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,negated_conjecture,
~ ! [X0] : ( union(X0,empty_set) = X0 ),
inference(negated_conjecture,[],[f9]) ).
tff(f9,conjecture,
! [X0] : ( union(X0,empty_set) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',prove_union_empty_set) ).
tff(f112,plain,
! [X0: $i] : sQ2_eqProxy($i,X0,union(X0,empty_set)),
inference(subsumption_resolution,[],[f107,f80]) ).
tff(f80,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1(X0,union(X0,X1)),X0)
| sQ2_eqProxy($i,X0,union(X0,X1)) ),
inference(factoring,[],[f62]) ).
tff(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ member(sK1(X0,union(X1,X2)),X1)
| ~ member(sK1(X0,union(X1,X2)),X0)
| sQ2_eqProxy($i,X0,union(X1,X2)) ),
inference(resolution,[],[f41,f32]) ).
tff(f32,plain,
! [X2: $i,X0: $i,X1: $i] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f20]) ).
tff(f20,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',union_defn) ).
tff(f41,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1(X0,X1),X1)
| sQ2_eqProxy($i,X0,X1)
| ~ member(sK1(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f26,f39]) ).
tff(f26,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
! [X0,X1] :
( ( ( X0 = X1 )
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ( X0 != X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f16]) ).
tff(f16,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
! [X0,X1] :
( ( ( X0 = X1 )
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ( X0 != X1 ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,plain,
! [X0,X1] :
( ( ( X0 = X1 )
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0,X1] :
( ( X0 = X1 )
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',equal_member_defn) ).
tff(f107,plain,
! [X0: $i] :
( member(sK1(X0,union(X0,empty_set)),X0)
| sQ2_eqProxy($i,X0,union(X0,empty_set)) ),
inference(duplicate_literal_removal,[],[f104]) ).
tff(f104,plain,
! [X0: $i] :
( member(sK1(X0,union(X0,empty_set)),X0)
| sQ2_eqProxy($i,X0,union(X0,empty_set))
| sQ2_eqProxy($i,X0,union(X0,empty_set)) ),
inference(resolution,[],[f84,f80]) ).
tff(f84,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,union(X1,empty_set)),X1)
| member(sK1(X0,union(X1,empty_set)),X0)
| sQ2_eqProxy($i,X0,union(X1,empty_set)) ),
inference(resolution,[],[f66,f34]) ).
tff(f34,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',empty_set_defn) ).
tff(f66,plain,
! [X2: $i,X0: $i,X1: $i] :
( member(sK1(X0,union(X1,X2)),X2)
| member(sK1(X0,union(X1,X2)),X0)
| member(sK1(X0,union(X1,X2)),X1)
| sQ2_eqProxy($i,X0,union(X1,X2)) ),
inference(resolution,[],[f42,f31]) ).
tff(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
tff(f42,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| sQ2_eqProxy($i,X0,X1)
| member(sK1(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f25,f39]) ).
tff(f25,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET162+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
% 0.15/0.36 % Computer : n017.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 : Fri May 3 16:57:38 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729
% 0.55/0.73 % (3062)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)
% 0.55/0.73 % (3065)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)
% 0.55/0.74 % (3062)First to succeed.
% 0.55/0.74 % (3065)Refutation not found, incomplete strategy% (3065)------------------------------
% 0.55/0.74 % (3065)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74 % (3065)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74
% 0.55/0.74 % (3065)Memory used [KB]: 980
% 0.55/0.74 % (3065)Time elapsed: 0.004 s
% 0.55/0.74 % (3065)Instructions burned: 3 (million)
% 0.55/0.74 % (3064)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.74 % (3065)------------------------------
% 0.55/0.74 % (3065)------------------------------
% 0.55/0.74 % (3066)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)
% 0.55/0.74 % (3063)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)
% 0.55/0.74 % (3067)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)
% 0.55/0.74 % (3062)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2970"
% 0.55/0.74 % (3062)Refutation found. Thanks to Tanya!
% 0.55/0.74 % SZS status Theorem for Vampire---4
% 0.55/0.74 % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.74 % (3062)------------------------------
% 0.55/0.74 % (3062)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74 % (3062)Termination reason: Refutation
% 0.55/0.74
% 0.55/0.74 % (3062)Memory used [KB]: 1054
% 0.55/0.74 % (3062)Time elapsed: 0.004 s
% 0.55/0.74 % (3062)Instructions burned: 7 (million)
% 0.55/0.74 % (2970)Success in time 0.372 s
% 0.55/0.74 % Vampire---4.8 exiting
%------------------------------------------------------------------------------