%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM492+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:15:26 PM UTC 2026
% Result : Theorem 1.71s 1.31s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 25 unt; 3 def)
% Number of atoms : 180 ( 19 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 208 ( 96 ~; 85 |; 16 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X0,X1)
& doDivides0(X0,sdtpldt0(X1,X2)) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f46,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
fof(f48,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& doDivides0(xp,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2001) ).
fof(f49,conjecture,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f53,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f56]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f81]) ).
fof(f108,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f109,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f108]) ).
fof(f123,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f123]) ).
fof(f139,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f163,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f190,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f203,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f204,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f209,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f210,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f214,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f46]) ).
fof(f216,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f48]) ).
fof(f218,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f53]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f163]) ).
fof(f267,definition,
( spl4_5
<=> aNaturalNumber0(sdtasdt0(xr,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f269,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| spl4_5 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f271,definition,
( spl4_6
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f272,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl4_6 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f279,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| spl4_5 ),
inference(resolution,[],[f269,f139]) ).
fof(f280,plain,
( ~ aNaturalNumber0(xr)
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f279,f204]) ).
fof(f509,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl4_6 ),
inference(resolution,[],[f273,f139]) ).
fof(f510,plain,
( ~ aNaturalNumber0(xm)
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f509,f203]) ).
fof(f511,plain,
( $false
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f510,f204]) ).
fof(f512,plain,
spl4_6,
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f525,plain,
! [X0] :
( ~ doDivides0(xp,X0)
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(resolution,[],[f190,f218]) ).
fof(f1278,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f221,f209]) ).
fof(f1285,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f1278,f203]) ).
fof(f1290,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(forward_subsumption_resolution,[],[f1285,f205]) ).
fof(f1297,plain,
aNaturalNumber0(xr),
inference(forward_demodulation,[],[f1290,f210]) ).
fof(f1298,plain,
( $false
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f1297,f280]) ).
fof(f1299,plain,
spl4_5,
inference(avatar_contradiction_clause,[],[f1298]) ).
fof(f1304,plain,
! [X0] :
( ~ doDivides0(xp,X0)
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(forward_subsumption_resolution,[],[f525,f203]) ).
fof(f1323,definition,
( spl4_59
<=> ! [X0] :
( ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm))) ) ),
introduced(definition,[new_symbols(definition,[spl4_59])],[avatar_definition]) ).
fof(f1324,plain,
( ! [X0] :
( ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0) )
| ~ spl4_59 ),
inference(avatar_component_clause,[],[f1323]) ).
fof(f1325,plain,
( ~ spl4_5
| spl4_59 ),
inference(avatar_split_clause,[],[f1304,f1323,f267]) ).
fof(f1409,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ spl4_59 ),
inference(superposition,[],[f1324,f214]) ).
fof(f1411,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ spl4_59 ),
inference(forward_subsumption_resolution,[],[f1409,f207]) ).
fof(f1414,plain,
( ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ spl4_6
| ~ spl4_59 ),
inference(forward_subsumption_resolution,[],[f1411,f272]) ).
fof(f1415,plain,
( $false
| ~ spl4_6
| ~ spl4_59 ),
inference(forward_subsumption_resolution,[],[f1414,f216]) ).
fof(f1416,plain,
( ~ spl4_6
| ~ spl4_59 ),
inference(avatar_contradiction_clause,[],[f1415]) ).
cnf(s22,plain,
spl4_6,
inference(sat_conversion,[],[f512]) ).
cnf(s61,plain,
spl4_5,
inference(sat_conversion,[],[f1299]) ).
cnf(s64,plain,
( ~ spl4_5
| spl4_59 ),
inference(sat_conversion,[],[f1325]) ).
cnf(s76,plain,
( ~ spl4_6
| ~ spl4_59 ),
inference(sat_conversion,[],[f1416]) ).
cnf(s77,plain,
spl4_59,
inference(rat,[],[s64,s61]) ).
cnf(s79,plain,
~ spl4_6,
inference(rat,[],[s76,s77]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s22,s79]) ).
fof(f1417,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM492+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:12:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.71/1.31 % (2693739)Detected formulas, will run a generic FOF schedule.
% 1.71/1.31 % (2693745)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=4236814930:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.71/1.31 % (2693750)dis-21_1_sil=8000:lcm=predicate:random_seed=1223808941: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)
% 1.71/1.31 % (2693746)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=2966657299:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.71/1.31 % (2693744)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=3230140027:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.71/1.31 % (2693747)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3656761926:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.71/1.31 % (2693748)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1104215886:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.71/1.31 % (2693749)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2351471928:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.71/1.31 % (2693749)First to succeed.
% 1.71/1.31 % (2693749)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2693739"
% 1.71/1.31 % (2693747)Instruction limit reached!
% 1.71/1.31 % (2693747)------------------------------
% 1.71/1.31 % (2693747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.71/1.31 % (2693747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/1.31 % (2693747)CaDiCaL version: 2.1.3
% 1.71/1.31 % (2693747)Termination reason: Instruction limit
% 1.71/1.31 % (2693747)Termination phase: Saturation
% 1.71/1.31 % (2693747)Time elapsed: 0.064 s
% 1.71/1.31 % (2693747)Peak memory usage: 89 MB
% 1.71/1.31 % (2693747)Instructions burned: 110 (million)
% 1.71/1.31 % (2693748)Instruction limit reached!
% 1.71/1.31 % (2693748)------------------------------
% 1.71/1.31 % (2693748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.71/1.31 % (2693748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/1.31 % (2693748)CaDiCaL version: 2.1.3
% 1.71/1.31 % (2693748)Termination reason: Instruction limit
% 1.71/1.31 % (2693748)Termination phase: Saturation
% 1.71/1.31 % (2693748)Time elapsed: 0.074 s
% 1.71/1.31 % (2693748)Peak memory usage: 88 MB
% 1.71/1.31 % (2693748)Instructions burned: 120 (million)
% 1.71/1.31 % (2693750)Instruction limit reached!
% 1.71/1.31 % (2693750)------------------------------
% 1.71/1.31 % (2693750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.71/1.31 % (2693750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/1.31 % (2693750)CaDiCaL version: 2.1.3
% 1.71/1.31 % (2693750)Termination reason: Instruction limit
% 1.71/1.31 % (2693750)Termination phase: Saturation
% 1.71/1.31 % (2693750)Time elapsed: 0.080 s
% 1.71/1.31 % (2693750)Peak memory usage: 90 MB
% 1.71/1.31 % (2693750)Instructions burned: 130 (million)
% 1.71/1.31 % (2693758)lrs+10_1_sil=8000:sp=occurrence:random_seed=2080407732:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.71/1.31 % (2693760)lrs+1011_1_sil=32000:sp=occurrence:random_seed=32006808:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.71/1.31 % (2693759)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1333602492:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.71/1.31 % (2693749)Refutation found. Thanks to Tanya!
% 1.71/1.31 % SZS status Theorem for theBenchmark
% 1.71/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.41 % (2693749)------------------------------
% 3.72/1.41 % (2693749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.41 % (2693749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.41 % (2693749)CaDiCaL version: 2.1.3
% 3.72/1.41 % (2693749)Termination reason: Refutation
% 3.72/1.41 % (2693749)Time elapsed: 0.030 s
% 3.72/1.41 % (2693749)Peak memory usage: 90 MB
% 3.72/1.41 % (2693749)Instructions burned: 41 (million)
% 3.72/1.41 % (2693749)------------------------------
% 3.72/1.41 % (2693749)------------------------------
% 3.72/1.41 % (2693739)Success in time 0.449 s
% 3.72/1.41 % Vampire exiting
%------------------------------------------------------------------------------