%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM482+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 : 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 12:15:23 PM UTC 2026
% Result : Theorem 3.53s 1.46s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 10 unt; 1 def)
% Number of atoms : 123 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 147 ( 64 ~; 55 |; 19 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 38 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f41,conjecture,
( isPrime0(xk)
=> ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( isPrime0(xk)
=> ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f47]) ).
fof(f58,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f91,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f92,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f109,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) )
& isPrime0(xk) ),
inference(ennf_transformation,[],[f42]) ).
fof(f115,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f92]) ).
fof(f116,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f116]) ).
fof(f127,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f137,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f174,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f190,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f196,plain,
isPrime0(xk),
inference(cnf_transformation,[],[f109]) ).
fof(f197,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f204,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f174]) ).
fof(f212,definition,
( spl4_1
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f213,plain,
( aNaturalNumber0(sz10)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f229,plain,
spl4_1,
inference(avatar_split_clause,[],[f127,f212]) ).
fof(f442,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f204,f129]) ).
fof(f452,plain,
! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f442,f137]) ).
fof(f461,plain,
! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f452]) ).
fof(f469,plain,
( ! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f461,f213]) ).
fof(f575,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ spl4_1 ),
inference(resolution,[],[f469,f197]) ).
fof(f582,plain,
( ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ spl4_1 ),
inference(duplicate_literal_removal,[],[f575]) ).
fof(f583,plain,
( ~ isPrime0(xk)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f582,f190]) ).
fof(f584,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f583,f196]) ).
fof(f585,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f584]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f229]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f585]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6]) ).
fof(f586,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sun Sep 27 20:06:46 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 3.53/1.46 % (2725790)Detected formulas, will run a generic FOF schedule.
% 3.53/1.46 % (2725798)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2037539040:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.46 % (2725798)Instruction limit reached!
% 3.53/1.46 % (2725798)------------------------------
% 3.53/1.46 % (2725798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.46 % (2725798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.46 % (2725798)CaDiCaL version: 2.1.3
% 3.53/1.46 % (2725798)Termination reason: Instruction limit
% 3.53/1.46 % (2725798)Termination phase: Saturation
% 3.53/1.46 % (2725798)Time elapsed: 0.030 s
% 3.53/1.46 % (2725798)Peak memory usage: 88 MB
% 3.53/1.46 % (2725798)Instructions burned: 110 (million)
% 3.53/1.46 % (2725800)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=458949307:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.46 % (2725795)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=542283679:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.46 % (2725796)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=3245628057:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.46 % (2725797)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=2095159334:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.46 % (2725799)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=38810185:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.46 % (2725801)dis-21_1_sil=8000:lcm=predicate:random_seed=2769455686: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)
% 3.53/1.46 % (2725800)First to succeed.
% 3.53/1.46 % (2725799)Also succeeded, but the first one will report.
% 3.53/1.46 % (2725800)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2725790"
% 3.53/1.46 % (2725803)lrs+10_1_sil=8000:sp=occurrence:random_seed=1751064461:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.53/1.46 % (2725803)Also succeeded, but the first one will report.
% 3.53/1.46 % (2725801)Instruction limit reached!
% 3.53/1.46 % (2725801)------------------------------
% 3.53/1.46 % (2725801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.46 % (2725801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.46 % (2725801)CaDiCaL version: 2.1.3
% 3.53/1.46 % (2725801)Termination reason: Instruction limit
% 3.53/1.46 % (2725801)Termination phase: Saturation
% 3.53/1.46 % (2725801)Time elapsed: 0.078 s
% 3.53/1.46 % (2725801)Peak memory usage: 90 MB
% 3.53/1.46 % (2725801)Instructions burned: 129 (million)
% 3.53/1.46 % (2725811)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1195084219:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.53/1.46 % (2725811)Refutation not found, incomplete strategy
% 3.53/1.46 % (2725811)------------------------------
% 3.53/1.46 % (2725811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.46 % (2725811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.46 % (2725811)CaDiCaL version: 2.1.3
% 3.53/1.46 % (2725811)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.46 % (2725811)Time elapsed: 0.002 s
% 3.53/1.46 % (2725811)Peak memory usage: 89 MB
% 3.53/1.46 % (2725811)Instructions burned: 2 (million)
% 3.53/1.46 % (2725800)Refutation found. Thanks to Tanya!
% 3.53/1.46 % SZS status Theorem for theBenchmark
% 3.53/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.46 % (2725800)------------------------------
% 3.53/1.46 % (2725800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.46 % (2725800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.46 % (2725800)CaDiCaL version: 2.1.3
% 3.53/1.46 % (2725800)Termination reason: Refutation
% 3.53/1.46 % (2725800)Time elapsed: 0.013 s
% 3.53/1.46 % (2725800)Peak memory usage: 89 MB
% 3.53/1.46 % (2725800)Instructions burned: 14 (million)
% 3.53/1.46 % (2725800)------------------------------
% 3.53/1.46 % (2725800)------------------------------
% 3.53/1.46 % (2725790)Success in time 0.42 s
% 3.53/1.46 % Vampire exiting
%------------------------------------------------------------------------------