%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:24:15 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 15 unt; 2 def)
% Number of atoms : 68 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 23 ~; 18 |; 10 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f20,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f34,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,plain,
( ! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(ennf_transformation,[],[f22]) ).
fof(f55,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f65,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f86,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f89,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
~ aInteger0(sz00),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f101,plain,
! [X0] :
( aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(consistent_polarity_flipping,[],[f65]) ).
fof(f109,plain,
! [X0] :
( aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f121,plain,
~ aInteger0(xa),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f122,plain,
~ aInteger0(xq),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f123,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa))
| aInteger0(X0) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f159,plain,
sz00 = sdtasdt0(xq,sz00),
inference(resolution,[],[f109,f122]) ).
fof(f160,plain,
( sz00 != sdtpldt0(xa,smndt0(xa))
| aInteger0(sz00) ),
inference(superposition,[],[f123,f159]) ).
fof(f162,definition,
( spl1_3
<=> aInteger0(sz00) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f164,plain,
( aInteger0(sz00)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f166,definition,
( spl1_4
<=> sz00 = sdtpldt0(xa,smndt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f169,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f160,f166,f162]) ).
fof(f221,plain,
sz00 = sdtpldt0(xa,smndt0(xa)),
inference(resolution,[],[f101,f121]) ).
fof(f223,plain,
spl1_4,
inference(avatar_split_clause,[],[f221,f166]) ).
fof(f224,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f164,f92]) ).
fof(f225,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f224]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f169]) ).
cnf(s3,plain,
spl1_4,
inference(sat_conversion,[],[f223]) ).
cnf(s4,plain,
~ spl1_3,
inference(sat_conversion,[],[f225]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s3,s4]) ).
fof(f226,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.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 19:50:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.46 % (3367706)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3367711)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=150547832_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (3367712)% WARNING: option uhcvi not known.
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % (3367712)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3900384819:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (3367713)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2302971043:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3367714)dis+10_1_sil=32000:sp=arity:random_seed=2815609387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3367715)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=635177756:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3367717)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1682841377:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (3367716)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=315167952:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3367717) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3367706-3367717"...
% 0.16/0.46 % (3367717)...printing done.
% 0.16/0.46 % (3367713) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3367706-3367713"...
% 0.16/0.46 % (3367717)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3367717)------------------------------
% 0.16/0.46 % (3367717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (3367717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (3367717)CaDiCaL version: 2.1.3
% 0.16/0.46 % (3367717)Termination reason: Refutation
% 0.16/0.46 % (3367717)Time elapsed: 0.005 s
% 0.16/0.46 % (3367717)Peak memory usage: 12 MB
% 0.16/0.46 % (3367717)Instructions burned: 6 (million)
% 0.16/0.46 % (3367706)Success in time 0.044 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------