%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM432+1 : 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 : n007.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 12:24:17 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 22 unt; 1 def)
% Number of atoms : 139 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 66 ~; 60 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f22,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
fof(f26,axiom,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__924) ).
fof(f27,conjecture,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(flattening,[],[f28]) ).
fof(f32,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f32]) ).
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(f53,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f19]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f54]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f64,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f87,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f91,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f22]) ).
fof(f92,plain,
sz00 != xq,
inference(cnf_transformation,[],[f22]) ).
fof(f93,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f22]) ).
fof(f95,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f22]) ).
fof(f99,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f24]) ).
fof(f101,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f102,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[],[f26]) ).
fof(f103,plain,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(cnf_transformation,[],[f29]) ).
fof(f105,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f82]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sz00 = X2 ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f112,plain,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f174,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtpldt0(xn,X0)) ),
inference(resolution,[],[f63,f99]) ).
fof(f229,definition,
( spl1_1
<=> aInteger0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f261,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f105,f64]) ).
fof(f272,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sz00 = xq
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(superposition,[],[f261,f102]) ).
fof(f374,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sz00 = xq ),
inference(resolution,[],[f107,f112]) ).
fof(f377,plain,
( ~ aInteger0(xc)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f374,f93]) ).
fof(f379,plain,
( ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f377,f91]) ).
fof(f381,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f379,f95]) ).
fof(f383,plain,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))),
inference(forward_subsumption_resolution,[],[f381,f92]) ).
fof(f721,plain,
aInteger0(sdtpldt0(xn,xm)),
inference(resolution,[],[f174,f101]) ).
fof(f731,plain,
( sz00 = xq
| ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f272,f383]) ).
fof(f732,plain,
spl1_1,
inference(avatar_split_clause,[],[f721,f229]) ).
fof(f734,plain,
( ~ aInteger0(xq)
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f731,f92]) ).
fof(f736,plain,
~ aInteger0(sdtpldt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f734,f93]) ).
fof(f746,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f736,f229]) ).
cnf(s23,plain,
spl1_1,
inference(sat_conversion,[],[f732]) ).
cnf(s25,plain,
~ spl1_1,
inference(sat_conversion,[],[f746]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s23,s25]) ).
fof(f747,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM432+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 19:51:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.17/0.48 % (1740320)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1740333)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=542963464:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1740332)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1740335)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=74594219:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1740331)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=652926628_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (1740332)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1398659647:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (1740334)dis+10_1_sil=32000:sp=arity:random_seed=3002851011:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1740336)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1115334401:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % (1740337)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=175217249:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (1740332) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1740320-1740332"...
% 0.17/0.48 % (1740332)...printing done.
% 0.17/0.48 % (1740332)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1740332)------------------------------
% 0.17/0.48 % (1740332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1740332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1740332)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1740332)Termination reason: Refutation
% 0.17/0.48 % (1740332)Time elapsed: 0.018 s
% 0.17/0.48 % (1740332)Peak memory usage: 13 MB
% 0.17/0.48 % (1740332)Instructions burned: 23 (million)
% 0.17/0.48 % (1740320)Success in time 0.056 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------