%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM500+1 : 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 : n010.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 0.57s 0.99s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 16 unt; 0 def)
% Number of atoms : 259 ( 103 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 321 ( 123 ~; 127 |; 59 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
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(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
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)
& doDivides0(X0,xk)
& isPrime0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f55,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f84,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f85,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f84]) ).
fof(f96,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f38]) ).
fof(f97,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f99,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f113,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f114,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f113]) ).
fof(f124,plain,
! [X0] :
( ( aNaturalNumber0(sK2(X0))
& doDivides0(sK2(X0),X0)
& isPrime0(sK2(X0)) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f97]) ).
fof(f125,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f126,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f114]) ).
fof(f130,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f132,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f133,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f136,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f143,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f144,plain,
sz10 != xk,
inference(cnf_transformation,[],[f54]) ).
fof(f145,plain,
sz00 != xk,
inference(cnf_transformation,[],[f54]) ).
fof(f148,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f175,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f183,plain,
! [X0] :
( isPrime0(sK2(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f184,plain,
! [X0] :
( doDivides0(sK2(X0),X0)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f185,plain,
! [X0] :
( aNaturalNumber0(sK2(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f188,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f205,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f207,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f216,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f188]) ).
fof(f220,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f205]) ).
fof(f224,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[],[f216,f207]) ).
fof(f308,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk
| ~ aNaturalNumber0(sK2(xk))
| ~ isPrime0(sK2(xk)) ),
inference(resolution,[],[f184,f148]) ).
fof(f309,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk
| ~ isPrime0(sK2(xk)) ),
inference(forward_subsumption_resolution,[],[f308,f185]) ).
fof(f310,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk ),
inference(forward_subsumption_resolution,[],[f309,f183]) ).
fof(f311,plain,
( ~ aNaturalNumber0(xk)
| sz10 = xk ),
inference(forward_subsumption_resolution,[],[f310,f145]) ).
fof(f312,plain,
~ aNaturalNumber0(xk),
inference(forward_subsumption_resolution,[],[f311,f144]) ).
fof(f488,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f220,f143]) ).
fof(f489,plain,
( sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f488,f312]) ).
fof(f490,plain,
( sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f489,f135]) ).
fof(f491,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f490,f131]) ).
fof(f492,plain,
( sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f491,f175]) ).
fof(f493,plain,
( sz00 = xp
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f492,f133]) ).
fof(f494,plain,
sz00 = xp,
inference(forward_subsumption_resolution,[],[f493,f132]) ).
fof(f502,plain,
~ isPrime0(xp),
inference(superposition,[],[f224,f494]) ).
fof(f508,plain,
$false,
inference(forward_subsumption_resolution,[],[f502,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:13:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.57/0.99 % (1278649)Detected formulas, will run a generic FOF schedule.
% 0.57/0.99 % (1278670)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2810848668:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.57/0.99 % (1278667)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=237667470:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.57/0.99 % (1278669)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2710787188:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.57/0.99 % (1278665)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=2205530969:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.57/0.99 % (1278668)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2662229321:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.57/0.99 % (1278671)dis-21_1_sil=8000:lcm=predicate:random_seed=765312472: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)
% 0.57/0.99 % (1278666)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=68330723:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.57/0.99 % (1278669)First to succeed.
% 0.57/0.99 % (1278669)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1278649"
% 0.57/0.99 % (1278670)Also succeeded, but the first one will report.
% 0.57/0.99 % (1278668)Also succeeded, but the first one will report.
% 0.57/0.99 % (1278671)Instruction limit reached!
% 0.57/0.99 % (1278671)------------------------------
% 0.57/0.99 % (1278671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.57/0.99 % (1278671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.99 % (1278671)CaDiCaL version: 2.1.3
% 0.57/0.99 % (1278671)Termination reason: Instruction limit
% 0.57/0.99 % (1278671)Termination phase: Saturation
% 0.57/0.99 % (1278671)Time elapsed: 0.079 s
% 0.57/0.99 % (1278671)Peak memory usage: 90 MB
% 0.57/0.99 % (1278671)Instructions burned: 130 (million)
% 0.57/0.99 % (1278679)lrs+10_1_sil=8000:sp=occurrence:random_seed=1132100930:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.57/0.99 % (1278679)Also succeeded, but the first one will report.
% 0.57/0.99 % (1278669)Refutation found. Thanks to Tanya!
% 0.57/0.99 % SZS status Theorem for theBenchmark
% 0.57/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 3.18/1.19 % (1278669)------------------------------
% 3.18/1.19 % (1278669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.19 % (1278669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.19 % (1278669)CaDiCaL version: 2.1.3
% 3.18/1.19 % (1278669)Termination reason: Refutation
% 3.18/1.19 % (1278669)Time elapsed: 0.008 s
% 3.18/1.19 % (1278669)Peak memory usage: 88 MB
% 3.18/1.19 % (1278669)Instructions burned: 12 (million)
% 3.18/1.19 % (1278669)------------------------------
% 3.18/1.19 % (1278669)------------------------------
% 3.18/1.19 % (1278649)Success in time 0.389 s
% 3.18/1.19 % Vampire exiting
%------------------------------------------------------------------------------