%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM436+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 : n005.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 12:24:18 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 14 unt; 6 def)
% Number of atoms : 156 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 181 ( 83 ~; 63 |; 29 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
fof(f26,axiom,
( sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb))
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1071) ).
fof(f27,conjecture,
( ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
~ ( ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [X1] :
( aInteger0(X1)
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
inference(rectify,[],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f34]) ).
fof(f62,plain,
( ( ! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0) )
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
| ( ! [X1] :
( ~ aInteger0(X1)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,definition,
( ( ! [X1] :
( ~ aInteger0(X1)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f64,plain,
( ( ! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0) )
& ~ aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xp) )
| sP0 ),
inference(definition_folding,[],[f62,f63]) ).
fof(f71,plain,
( ( ! [X1] :
( ~ aInteger0(X1)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X1) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) )
| ~ sP0 ),
inference(nnf_transformation,[],[f63]) ).
fof(f72,plain,
( ( ! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) )
| ~ sP0 ),
inference(rectify,[],[f71]) ).
fof(f77,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f106,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f108,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f117,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f118,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f119,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f122,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f125,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| sP0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f129,definition,
( spl3_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f143,definition,
( spl3_4
<=> ! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f144,plain,
( ! [X0] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| ~ aInteger0(X0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f125,f143,f129]) ).
fof(f157,definition,
( spl3_7
<=> ! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0] :
( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0)
| ~ aInteger0(X0) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( ~ spl3_1
| spl3_7 ),
inference(avatar_split_clause,[],[f122,f157,f129]) ).
fof(f327,definition,
( spl3_10
<=> aInteger0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f329,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| spl3_10 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f332,plain,
( sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(sdtasdt0(xq,xm))
| ~ spl3_4 ),
inference(superposition,[],[f144,f119]) ).
fof(f334,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f332]) ).
fof(f337,definition,
( spl3_11
<=> aInteger0(sdtasdt0(xq,xm)) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f339,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| spl3_11 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f341,plain,
( ~ spl3_11
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f334,f143,f337]) ).
fof(f355,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xm)
| spl3_11 ),
inference(resolution,[],[f339,f77]) ).
fof(f356,plain,
( ~ aInteger0(xm)
| spl3_11 ),
inference(forward_subsumption_resolution,[],[f355,f106]) ).
fof(f357,plain,
( $false
| spl3_11 ),
inference(forward_subsumption_resolution,[],[f356,f117]) ).
fof(f358,plain,
spl3_11,
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f370,plain,
( sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(sdtasdt0(xp,xm))
| ~ spl3_7 ),
inference(superposition,[],[f158,f118]) ).
fof(f371,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f370]) ).
fof(f372,plain,
( ~ spl3_10
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f371,f157,f327]) ).
fof(f373,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm)
| spl3_10 ),
inference(resolution,[],[f329,f77]) ).
fof(f374,plain,
( ~ aInteger0(xm)
| spl3_10 ),
inference(forward_subsumption_resolution,[],[f373,f108]) ).
fof(f375,plain,
( $false
| spl3_10 ),
inference(forward_subsumption_resolution,[],[f374,f117]) ).
fof(f376,plain,
spl3_10,
inference(avatar_contradiction_clause,[],[f375]) ).
cnf(s3,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f145]) ).
cnf(s6,plain,
( ~ spl3_1
| spl3_7 ),
inference(sat_conversion,[],[f159]) ).
cnf(s13,plain,
( ~ spl3_4
| ~ spl3_11 ),
inference(sat_conversion,[],[f341]) ).
cnf(s14,plain,
spl3_11,
inference(sat_conversion,[],[f358]) ).
cnf(s15,plain,
( ~ spl3_7
| ~ spl3_10 ),
inference(sat_conversion,[],[f372]) ).
cnf(s16,plain,
spl3_10,
inference(sat_conversion,[],[f376]) ).
cnf(s17,plain,
~ spl3_7,
inference(rat,[],[s15,s16]) ).
cnf(s18,plain,
~ spl3_4,
inference(rat,[],[s13,s14]) ).
cnf(s20,plain,
~ spl3_1,
inference(rat,[],[s6,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s3,s18,s20]) ).
fof(f377,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+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 : n005.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 19:54:31 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 % (130128)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (130133)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3418777116_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % (130134)% WARNING: option uhcvi not known.
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (130134)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3552194377:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (130135)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3342174662:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (130136)dis+10_1_sil=32000:sp=arity:random_seed=1321117080:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (130137)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3751779153:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % (130139)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=320032380:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (130138)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1923009647:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (130136) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-130128-130136"...
% 0.16/0.46 % (130134) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-130128-130134"...
% 0.16/0.46 % (130135) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-130128-130135"...
% 0.16/0.46 % (130136)...printing done.
% 0.16/0.46 % (130134)...printing done.
% 0.16/0.46 % (130135)...printing done.
% 0.16/0.46 % (130136)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 % (130136)------------------------------
% 0.16/0.46 % (130136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (130136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (130136)CaDiCaL version: 2.1.3
% 0.16/0.46 % (130136)Termination reason: Refutation
% 0.16/0.46 % (130136)Time elapsed: 0.008 s
% 0.16/0.46 % (130136)Peak memory usage: 12 MB
% 0.16/0.46 % (130136)Instructions burned: 11 (million)
% 0.16/0.46 % (130128)Success in time 0.043 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------