TSTP Solution File: NUM500+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n014.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 03:31:38 EDT 2024
% Result : Theorem 0.63s 0.83s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 8 unt; 1 typ; 0 def)
% Number of atoms : 436 ( 78 equ)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 281 ( 91 ~; 93 |; 87 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 191 ( 191 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 9 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 58 ( 32 !; 25 ?; 12 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_9,type,
sQ16_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f563,plain,
$false,
inference(avatar_sat_refutation,[],[f533,f550,f562]) ).
tff(f562,plain,
~ spl17_14,
inference(avatar_contradiction_clause,[],[f561]) ).
tff(f561,plain,
( $false
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f560,f210]) ).
tff(f210,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
tff(f45,axiom,
( ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) )
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/tmp/tmp.Gb0fGq4HUm/Vampire---4.8_12564',m__2306) ).
tff(f560,plain,
( ~ aNaturalNumber0(xk)
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f559,f326]) ).
tff(f326,plain,
~ sQ16_eqProxy($i,sz00,xk),
inference(equality_proxy_replacement,[],[f213,f300]) ).
tff(f300,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ16_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ16_eqProxy])]) ).
tff(f213,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
( ( sz10 != xk )
& ( sz00 != xk ) ),
inference(ennf_transformation,[],[f46]) ).
tff(f46,axiom,
~ ( ( sz10 = xk )
| ( sz00 = xk ) ),
file('/export/starexec/sandbox2/tmp/tmp.Gb0fGq4HUm/Vampire---4.8_12564',m__2315) ).
tff(f559,plain,
( sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| ~ spl17_14 ),
inference(subsumption_resolution,[],[f558,f325]) ).
tff(f325,plain,
~ sQ16_eqProxy($i,sz10,xk),
inference(equality_proxy_replacement,[],[f214,f300]) ).
tff(f214,plain,
sz10 != xk,
inference(cnf_transformation,[],[f62]) ).
tff(f558,plain,
( sQ16_eqProxy($i,sz10,xk)
| sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| ~ spl17_14 ),
inference(resolution,[],[f555,f368]) ).
tff(f368,plain,
! [X0: $i] :
( isPrime0(sK13(X0))
| sQ16_eqProxy($i,sz10,X0)
| sQ16_eqProxy($i,sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f268,f300]) ).
tff(f268,plain,
! [X0: $i] :
( isPrime0(sK13(X0))
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0] :
( ( isPrime0(sK13(X0))
& doDivides0(sK13(X0),X0)
& aNaturalNumber0(sK13(X0)) )
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f106,f158]) ).
tff(f158,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK13(X0))
& doDivides0(sK13(X0),X0)
& aNaturalNumber0(sK13(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f106,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
tff(f105,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0] :
( ( ( sz10 != X0 )
& ( sz00 != X0 )
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Gb0fGq4HUm/Vampire---4.8_12564',mPrimDiv) ).
tff(f555,plain,
( ~ isPrime0(sK13(xk))
| ~ spl17_14 ),
inference(resolution,[],[f532,f223]) ).
tff(f223,plain,
! [X0: $i] :
( ~ sP2(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ( ( sK10(X0) != X0 )
& ( sz10 != sK10(X0) )
& doDivides0(sK10(X0),X0)
& ( sdtasdt0(sK10(X0),sK11(X0)) = X0 )
& aNaturalNumber0(sK11(X0))
& aNaturalNumber0(sK10(X0)) )
| ( sz10 = X0 )
| ( sz00 = X0 ) ) )
| ~ sP2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f149,f151,f150]) ).
tff(f150,plain,
! [X0] :
( ? [X1] :
( ( X0 != X1 )
& ( sz10 != X1 )
& doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( ( sK10(X0) != X0 )
& ( sz10 != sK10(X0) )
& doDivides0(sK10(X0),X0)
& ? [X2] :
( ( sdtasdt0(sK10(X0),X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f151,plain,
! [X0] :
( ? [X2] :
( ( sdtasdt0(sK10(X0),X2) = X0 )
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(sK10(X0),sK11(X0)) = X0 )
& aNaturalNumber0(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f149,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( ( X0 != X1 )
& ( sz10 != X1 )
& doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 ) ) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( ( X0 != X1 )
& ( sz10 != X1 )
& doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 ) ) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f532,plain,
( sP2(sK13(xk))
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f530]) ).
tff(f530,plain,
( spl17_14
<=> sP2(sK13(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
tff(f550,plain,
spl17_13,
inference(avatar_contradiction_clause,[],[f549]) ).
tff(f549,plain,
( $false
| spl17_13 ),
inference(subsumption_resolution,[],[f548,f210]) ).
tff(f548,plain,
( ~ aNaturalNumber0(xk)
| spl17_13 ),
inference(subsumption_resolution,[],[f547,f326]) ).
tff(f547,plain,
( sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| spl17_13 ),
inference(subsumption_resolution,[],[f546,f325]) ).
tff(f546,plain,
( sQ16_eqProxy($i,sz10,xk)
| sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| spl17_13 ),
inference(resolution,[],[f528,f370]) ).
tff(f370,plain,
! [X0: $i] :
( aNaturalNumber0(sK13(X0))
| sQ16_eqProxy($i,sz10,X0)
| sQ16_eqProxy($i,sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f266,f300]) ).
tff(f266,plain,
! [X0: $i] :
( aNaturalNumber0(sK13(X0))
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f159]) ).
tff(f528,plain,
( ~ aNaturalNumber0(sK13(xk))
| spl17_13 ),
inference(avatar_component_clause,[],[f526]) ).
tff(f526,plain,
( spl17_13
<=> aNaturalNumber0(sK13(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
tff(f533,plain,
( ~ spl17_13
| spl17_14 ),
inference(avatar_split_clause,[],[f524,f530,f526]) ).
tff(f524,plain,
( sP2(sK13(xk))
| ~ aNaturalNumber0(sK13(xk)) ),
inference(subsumption_resolution,[],[f523,f210]) ).
tff(f523,plain,
( ~ aNaturalNumber0(xk)
| sP2(sK13(xk))
| ~ aNaturalNumber0(sK13(xk)) ),
inference(subsumption_resolution,[],[f522,f326]) ).
tff(f522,plain,
( sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| sP2(sK13(xk))
| ~ aNaturalNumber0(sK13(xk)) ),
inference(subsumption_resolution,[],[f521,f325]) ).
tff(f521,plain,
( sQ16_eqProxy($i,sz10,xk)
| sQ16_eqProxy($i,sz00,xk)
| ~ aNaturalNumber0(xk)
| sP2(sK13(xk))
| ~ aNaturalNumber0(sK13(xk)) ),
inference(resolution,[],[f369,f225]) ).
tff(f225,plain,
! [X0: $i] :
( ~ doDivides0(X0,xk)
| sP2(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0] :
( sP2(X0)
| ( ~ doDivides0(X0,xk)
& ! [X1] :
( ( sdtasdt0(X0,X1) != xk )
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f131]) ).
tff(f131,plain,
! [X0] :
( sP2(X0)
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( ( xk != sdtasdt0(X0,X3) )
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f64,f130]) ).
tff(f64,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( ( X0 != X1 )
& ( sz10 != X1 )
& doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 ) ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( ( xk != sdtasdt0(X0,X3) )
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
tff(f63,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( ( X0 != X1 )
& ( sz10 != X1 )
& doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| ( sz10 = X0 )
| ( sz00 = X0 ) ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( ( xk != sdtasdt0(X0,X3) )
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f53]) ).
tff(f53,plain,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( ( X0 = X1 )
| ( sz10 = X1 ) ) )
& ( sz10 != X0 )
& ( sz00 != X0 ) ) )
& ( doDivides0(X0,xk)
| ? [X3] :
( ( xk = sdtasdt0(X0,X3) )
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X0) ),
inference(rectify,[],[f49]) ).
tff(f49,negated_conjecture,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( ( X0 = X1 )
| ( sz10 = X1 ) ) )
& ( sz10 != X0 )
& ( sz00 != X0 ) ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( ( sdtasdt0(X0,X1) = xk )
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
inference(negated_conjecture,[],[f48]) ).
tff(f48,conjecture,
? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( ( sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( ( X0 = X1 )
| ( sz10 = X1 ) ) )
& ( sz10 != X0 )
& ( sz00 != X0 ) ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( ( sdtasdt0(X0,X1) = xk )
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.Gb0fGq4HUm/Vampire---4.8_12564',m__) ).
tff(f369,plain,
! [X0: $i] :
( doDivides0(sK13(X0),X0)
| sQ16_eqProxy($i,sz10,X0)
| sQ16_eqProxy($i,sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f267,f300]) ).
tff(f267,plain,
! [X0: $i] :
( doDivides0(sK13(X0),X0)
| ( sz10 = X0 )
| ( sz00 = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.13 % 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
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Apr 30 16:47:33 EDT 2024
% 0.14/0.33 % CPUTime :
% 0.14/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.34 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.Gb0fGq4HUm/Vampire---4.8_12564
% 0.63/0.82 % (12682)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.63/0.82 % (12680)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.63/0.82 % (12679)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.63/0.82 % (12681)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 (2995ds/34Mi)
% 0.63/0.82 % (12677)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 (2995ds/34Mi)
% 0.63/0.82 % (12683)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 (2995ds/83Mi)
% 0.63/0.82 % (12684)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 (2995ds/56Mi)
% 0.63/0.82 % (12678)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 (2995ds/51Mi)
% 0.63/0.83 % (12677)First to succeed.
% 0.63/0.83 % (12677)Refutation found. Thanks to Tanya!
% 0.63/0.83 % SZS status Theorem for Vampire---4
% 0.63/0.83 % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.83 % (12677)------------------------------
% 0.63/0.83 % (12677)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.83 % (12677)Termination reason: Refutation
% 0.63/0.83
% 0.63/0.83 % (12677)Memory used [KB]: 1217
% 0.63/0.83 % (12677)Time elapsed: 0.011 s
% 0.63/0.83 % (12677)Instructions burned: 17 (million)
% 0.63/0.83 % (12677)------------------------------
% 0.63/0.83 % (12677)------------------------------
% 0.63/0.83 % (12674)Success in time 0.491 s
% 0.63/0.83 % Vampire---4.8 exiting
%------------------------------------------------------------------------------