%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:28 PM UTC 2026
% Result : Theorem 2.75s 1.28s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 14 unt; 7 def)
% Number of atoms : 245 ( 74 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 273 ( 91 ~; 96 |; 76 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 28 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f46,axiom,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(f48,conjecture,
? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f55,plain,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) )
=> ( sz10 = X2
| X0 = X2 ) ) )
| isPrime0(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f38]) ).
fof(f119,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f118]) ).
fof(f126,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f127,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f128,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(flattening,[],[f127]) ).
fof(f132,definition,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| sP2(X0) ),
inference(definition_folding,[],[f128,f132]) ).
fof(f148,plain,
! [X0] :
( ( aNaturalNumber0(sK6(X0))
& doDivides0(sK6(X0),X0)
& isPrime0(sK6(X0)) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f119]) ).
fof(f159,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f160,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
inference(rectify,[],[f159]) ).
fof(f161,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK14(X0)
& sK14(X0) != X0
& aNaturalNumber0(sK14(X0))
& aNaturalNumber0(sK15(X0))
& sdtasdt0(sK14(X0),sK15(X0)) = X0
& doDivides0(sK14(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0))],[f160]) ).
fof(f227,plain,
! [X0] :
( isPrime0(sK6(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f228,plain,
! [X0] :
( doDivides0(sK6(X0),X0)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f229,plain,
! [X0] :
( aNaturalNumber0(sK6(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f271,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f272,plain,
sz10 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f273,plain,
sz00 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f276,plain,
! [X0] :
( ~ sP2(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f283,plain,
! [X0] :
( sP2(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f297,definition,
! [X0,X1] :
( sQ16_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ16_eqProxy])],[equality_proxy_definition]) ).
fof(f345,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| ~ aNaturalNumber0(X0)
| sQ16_eqProxy(sz00,X0)
| aNaturalNumber0(sK6(X0)) ),
inference(equality_proxy_replacement,[],[f229,f297,f297]) ).
fof(f346,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| ~ aNaturalNumber0(X0)
| sQ16_eqProxy(sz00,X0)
| doDivides0(sK6(X0),X0) ),
inference(equality_proxy_replacement,[],[f228,f297,f297]) ).
fof(f347,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| ~ aNaturalNumber0(X0)
| sQ16_eqProxy(sz00,X0)
| isPrime0(sK6(X0)) ),
inference(equality_proxy_replacement,[],[f227,f297,f297]) ).
fof(f372,plain,
~ sQ16_eqProxy(sz00,xk),
inference(equality_proxy_replacement,[],[f273,f297]) ).
fof(f373,plain,
~ sQ16_eqProxy(sz10,xk),
inference(equality_proxy_replacement,[],[f272,f297]) ).
fof(f410,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f276,f283]) ).
fof(f445,definition,
( spl17_10
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition]) ).
fof(f446,plain,
( ~ aNaturalNumber0(xk)
| spl17_10 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
( $false
| spl17_10 ),
inference(resolution,[],[f446,f271]) ).
fof(f449,plain,
spl17_10,
inference(avatar_contradiction_clause,[],[f448]) ).
fof(f546,definition,
( spl17_27
<=> sQ16_eqProxy(sz00,xk) ),
introduced(definition,[new_symbols(definition,[spl17_27])],[avatar_definition]) ).
fof(f547,plain,
( sQ16_eqProxy(sz00,xk)
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f566,plain,
( $false
| ~ spl17_27 ),
inference(resolution,[],[f547,f372]) ).
fof(f567,plain,
~ spl17_27,
inference(avatar_contradiction_clause,[],[f566]) ).
fof(f589,plain,
( ~ aNaturalNumber0(xk)
| sQ16_eqProxy(sz00,xk)
| aNaturalNumber0(sK6(xk)) ),
inference(resolution,[],[f345,f373]) ).
fof(f592,definition,
( spl17_34
<=> aNaturalNumber0(sK6(xk)) ),
introduced(definition,[new_symbols(definition,[spl17_34])],[avatar_definition]) ).
fof(f594,plain,
( spl17_34
| spl17_27
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f589,f445,f546,f592]) ).
fof(f600,plain,
( ~ aNaturalNumber0(xk)
| sQ16_eqProxy(sz00,xk)
| isPrime0(sK6(xk)) ),
inference(resolution,[],[f347,f373]) ).
fof(f603,definition,
( spl17_36
<=> isPrime0(sK6(xk)) ),
introduced(definition,[new_symbols(definition,[spl17_36])],[avatar_definition]) ).
fof(f604,plain,
( isPrime0(sK6(xk))
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f605,plain,
( spl17_36
| spl17_27
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f600,f445,f546,f603]) ).
fof(f610,plain,
( ~ doDivides0(sK6(xk),xk)
| ~ aNaturalNumber0(sK6(xk))
| ~ spl17_36 ),
inference(resolution,[],[f604,f410]) ).
fof(f614,definition,
( spl17_38
<=> doDivides0(sK6(xk),xk) ),
introduced(definition,[new_symbols(definition,[spl17_38])],[avatar_definition]) ).
fof(f616,plain,
( ~ spl17_34
| ~ spl17_38
| ~ spl17_36 ),
inference(avatar_split_clause,[],[f610,f603,f614,f592]) ).
fof(f712,plain,
( ~ aNaturalNumber0(xk)
| sQ16_eqProxy(sz00,xk)
| doDivides0(sK6(xk),xk) ),
inference(resolution,[],[f346,f373]) ).
fof(f715,plain,
( spl17_38
| spl17_27
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f712,f445,f546,f614]) ).
cnf(s8,plain,
spl17_10,
inference(sat_conversion,[],[f449]) ).
cnf(s26,plain,
~ spl17_27,
inference(sat_conversion,[],[f567]) ).
cnf(s34,plain,
( ~ spl17_10
| spl17_27
| spl17_34 ),
inference(sat_conversion,[],[f594]) ).
cnf(s36,plain,
( ~ spl17_10
| spl17_27
| spl17_36 ),
inference(sat_conversion,[],[f605]) ).
cnf(s38,plain,
( ~ spl17_34
| ~ spl17_36
| ~ spl17_38 ),
inference(sat_conversion,[],[f616]) ).
cnf(s48,plain,
( ~ spl17_10
| spl17_27
| spl17_38 ),
inference(sat_conversion,[],[f715]) ).
cnf(s57,plain,
spl17_38,
inference(rat,[],[s48,s26,s8]) ).
cnf(s59,plain,
spl17_36,
inference(rat,[],[s36,s26,s8]) ).
cnf(s60,plain,
spl17_34,
inference(rat,[],[s34,s26,s8]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s38,s57,s59,s60]) ).
fof(f720,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:13:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.28 % (2729458)Detected formulas, will run a generic FOF schedule.
% 2.75/1.28 % (2729465)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=369179604:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.28 % (2729466)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3671741887:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.28 % (2729464)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2335412640:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.28 % (2729467)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3818557480:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.28 % (2729469)dis-21_1_sil=8000:lcm=predicate:random_seed=1261449494:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.75/1.28 % (2729463)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2782805848:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.28 % (2729468)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1080591350:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.28 % (2729469)First to succeed.
% 2.75/1.28 % (2729469)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2729458"
% 2.75/1.28 % (2729467)Also succeeded, but the first one will report.
% 2.75/1.28 % (2729468)Also succeeded, but the first one will report.
% 2.75/1.28 % (2729466)Instruction limit reached!
% 2.75/1.28 % (2729466)------------------------------
% 2.75/1.28 % (2729466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.28 % (2729466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.28 % (2729466)CaDiCaL version: 2.1.3
% 2.75/1.28 % (2729466)Termination reason: Instruction limit
% 2.75/1.28 % (2729466)Termination phase: Saturation
% 2.75/1.28 % (2729466)Time elapsed: 0.061 s
% 2.75/1.28 % (2729466)Peak memory usage: 89 MB
% 2.75/1.28 % (2729466)Instructions burned: 110 (million)
% 2.75/1.28 % (2729477)lrs+10_1_sil=8000:sp=occurrence:random_seed=3446253042:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.75/1.28 % (2729477)Also succeeded, but the first one will report.
% 2.75/1.28 % (2729469)Refutation found. Thanks to Tanya!
% 2.75/1.28 % SZS status Theorem for theBenchmark
% 2.75/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.47 % (2729469)------------------------------
% 3.58/1.47 % (2729469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (2729469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (2729469)CaDiCaL version: 2.1.3
% 3.58/1.47 % (2729469)Termination reason: Refutation
% 3.58/1.47 % (2729469)Time elapsed: 0.009 s
% 3.58/1.47 % (2729469)Peak memory usage: 89 MB
% 3.58/1.47 % (2729469)Instructions burned: 11 (million)
% 3.58/1.47 % (2729469)------------------------------
% 3.58/1.47 % (2729469)------------------------------
% 3.58/1.47 % (2729458)Success in time 0.423 s
% 3.58/1.47 % Vampire exiting
%------------------------------------------------------------------------------