TSTP Solution File: SEU110+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU110+1 : 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 : n003.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 09:20:17 EDT 2024
% Result : Theorem 0.58s 0.76s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 6 unt; 1 typ; 0 def)
% Number of atoms : 318 ( 13 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 249 ( 96 ~; 94 |; 45 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 115 ( 115 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 112 ( 100 !; 11 ?; 47 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_17,type,
sQ4_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f243,plain,
$false,
inference(subsumption_resolution,[],[f241,f59]) ).
tff(f59,plain,
~ subset(finite_subsets(sK0),finite_subsets(sK1)),
inference(cnf_transformation,[],[f47]) ).
tff(f47,plain,
( ~ subset(finite_subsets(sK0),finite_subsets(sK1))
& subset(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f40,f46]) ).
tff(f46,plain,
( ? [X0,X1] :
( ~ subset(finite_subsets(X0),finite_subsets(X1))
& subset(X0,X1) )
=> ( ~ subset(finite_subsets(sK0),finite_subsets(sK1))
& subset(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
? [X0,X1] :
( ~ subset(finite_subsets(X0),finite_subsets(X1))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
tff(f28,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(negated_conjecture,[],[f27]) ).
tff(f27,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.bD7IeCNTSa/Vampire---4.8_29839',t23_finsub_1) ).
tff(f241,plain,
subset(finite_subsets(sK0),finite_subsets(sK1)),
inference(resolution,[],[f237,f58]) ).
tff(f58,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f47]) ).
tff(f237,plain,
! [X0: $i,X1: $i] :
( ~ subset(X0,X1)
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(duplicate_literal_removal,[],[f234]) ).
tff(f234,plain,
! [X0: $i,X1: $i] :
( ~ subset(X0,X1)
| subset(finite_subsets(X0),finite_subsets(X1))
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(resolution,[],[f173,f105]) ).
tff(f105,plain,
! [X0: $i,X1: $i] :
( subset(sK3(finite_subsets(X0),X1),X0)
| subset(finite_subsets(X0),X1) ),
inference(resolution,[],[f99,f74]) ).
tff(f74,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f55,f56]) ).
tff(f56,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f55,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f54]) ).
tff(f54,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.bD7IeCNTSa/Vampire---4.8_29839',d3_tarski) ).
tff(f99,plain,
! [X3: $i,X0: $i] :
( ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(subsumption_resolution,[],[f78,f60]) ).
tff(f60,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(pure_predicate_removal,[],[f38]) ).
tff(f38,plain,
! [X0] :
( preboolean(finite_subsets(X0))
& ~ empty(finite_subsets(X0)) ),
inference(pure_predicate_removal,[],[f37]) ).
tff(f37,plain,
! [X0] :
( preboolean(finite_subsets(X0))
& cup_closed(finite_subsets(X0))
& ~ empty(finite_subsets(X0)) ),
inference(pure_predicate_removal,[],[f14]) ).
tff(f14,axiom,
! [X0] :
( preboolean(finite_subsets(X0))
& diff_closed(finite_subsets(X0))
& cup_closed(finite_subsets(X0))
& ~ empty(finite_subsets(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.bD7IeCNTSa/Vampire---4.8_29839',fc2_finsub_1) ).
tff(f78,plain,
! [X3: $i,X0: $i] :
( subset(X3,X0)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f62]) ).
tff(f62,plain,
! [X3: $i,X0: $i,X1: $i] :
( subset(X3,X0)
| ~ in(X3,X1)
| ( finite_subsets(X0) != X1 )
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0,X1] :
( ( ( ( finite_subsets(X0) = X1 )
| ( ( ~ finite(sK2(X0,X1))
| ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( ( finite(sK2(X0,X1))
& subset(sK2(X0,X1),X0) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| ( finite_subsets(X0) != X1 ) ) )
| ~ preboolean(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f50,f51]) ).
tff(f51,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) )
=> ( ( ~ finite(sK2(X0,X1))
| ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( ( finite(sK2(X0,X1))
& subset(sK2(X0,X1),X0) )
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f50,plain,
! [X0,X1] :
( ( ( ( finite_subsets(X0) = X1 )
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| ( finite_subsets(X0) != X1 ) ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f49]) ).
tff(f49,plain,
! [X0,X1] :
( ( ( ( finite_subsets(X0) = X1 )
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| ( finite_subsets(X0) != X1 ) ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f48]) ).
tff(f48,plain,
! [X0,X1] :
( ( ( ( finite_subsets(X0) = X1 )
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| ( finite_subsets(X0) != X1 ) ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1 )
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( ( finite_subsets(X0) = X1 )
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bD7IeCNTSa/Vampire---4.8_29839',d5_finsub_1) ).
tff(f173,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ subset(sK3(finite_subsets(X0),finite_subsets(X1)),X2)
| ~ subset(X2,X1)
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(resolution,[],[f160,f71]) ).
tff(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f43]) ).
tff(f43,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
tff(f26,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.bD7IeCNTSa/Vampire---4.8_29839',t1_xboole_1) ).
tff(f160,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK3(finite_subsets(X0),finite_subsets(X1)),X1)
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(duplicate_literal_removal,[],[f158]) ).
tff(f158,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK3(finite_subsets(X0),finite_subsets(X1)),X1)
| subset(finite_subsets(X0),finite_subsets(X1))
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(resolution,[],[f114,f97]) ).
tff(f97,plain,
! [X0: $i,X1: $i] :
( finite(sK3(finite_subsets(X0),X1))
| subset(finite_subsets(X0),X1) ),
inference(resolution,[],[f92,f74]) ).
tff(f92,plain,
! [X3: $i,X0: $i] :
( ~ in(X3,finite_subsets(X0))
| finite(X3) ),
inference(subsumption_resolution,[],[f77,f60]) ).
tff(f77,plain,
! [X3: $i,X0: $i] :
( finite(X3)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f63]) ).
tff(f63,plain,
! [X3: $i,X0: $i,X1: $i] :
( finite(X3)
| ~ in(X3,X1)
| ( finite_subsets(X0) != X1 )
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f52]) ).
tff(f114,plain,
! [X0: $i,X1: $i] :
( ~ finite(sK3(X0,finite_subsets(X1)))
| ~ subset(sK3(X0,finite_subsets(X1)),X1)
| subset(X0,finite_subsets(X1)) ),
inference(resolution,[],[f107,f75]) ).
tff(f75,plain,
! [X0: $i,X1: $i] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tff(f107,plain,
! [X3: $i,X0: $i] :
( in(X3,finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0) ),
inference(subsumption_resolution,[],[f76,f60]) ).
tff(f76,plain,
! [X3: $i,X0: $i] :
( in(X3,finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f64]) ).
tff(f64,plain,
! [X3: $i,X0: $i,X1: $i] :
( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0)
| ( finite_subsets(X0) != X1 )
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14 % 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
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:33:20 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35 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.bD7IeCNTSa/Vampire---4.8_29839
% 0.58/0.74 % (30105)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.74 % (30104)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)
% 0.58/0.74 % (30106)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)
% 0.58/0.74 % (30108)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)
% 0.58/0.74 % (30107)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)
% 0.58/0.74 % (30109)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)
% 0.58/0.74 % (30110)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)
% 0.58/0.74 % (30103)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)
% 0.58/0.76 % (30103)First to succeed.
% 0.58/0.76 % (30103)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30091"
% 0.58/0.76 % (30103)Refutation found. Thanks to Tanya!
% 0.58/0.76 % SZS status Theorem for Vampire---4
% 0.58/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.76 % (30103)------------------------------
% 0.58/0.76 % (30103)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.76 % (30103)Termination reason: Refutation
% 0.58/0.76
% 0.58/0.76 % (30103)Memory used [KB]: 1126
% 0.58/0.76 % (30103)Time elapsed: 0.015 s
% 0.58/0.76 % (30103)Instructions burned: 27 (million)
% 0.58/0.76 % (30091)Success in time 0.403 s
% 0.58/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------