%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM436+3 : 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 : n009.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 12:15:10 PM UTC 2026
% Result : Theorem 1.76s 1.12s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 15 unt; 6 def)
% Number of atoms : 233 ( 51 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 278 ( 115 ~; 103 |; 51 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 40 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(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(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(f65,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK1(X0,X1))
& sdtasdt0(X1,sK1(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f67]) ).
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(f99,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f105,plain,
sz00 != xq,
inference(cnf_transformation,[],[f23]) ).
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(f121,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ sP0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f125,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,X0)
| sP0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f126,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f99]) ).
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(f152,definition,
( spl3_6
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f154,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| spl3_6 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f121,f152,f129]) ).
fof(f230,definition,
( spl3_12
<=> aInteger0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f232,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| spl3_12 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f234,plain,
( sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(sdtasdt0(xq,xm))
| ~ spl3_4 ),
inference(superposition,[],[f144,f119]) ).
fof(f236,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f234]) ).
fof(f239,definition,
( spl3_13
<=> aInteger0(sdtasdt0(xq,xm)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f241,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| spl3_13 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,plain,
( ~ spl3_13
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f236,f143,f239]) ).
fof(f259,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xm)
| spl3_13 ),
inference(resolution,[],[f241,f77]) ).
fof(f261,plain,
( ~ aInteger0(xm)
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f259,f106]) ).
fof(f262,plain,
( $false
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f261,f117]) ).
fof(f263,plain,
spl3_13,
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f349,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f126,f77]) ).
fof(f362,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(superposition,[],[f349,f118]) ).
fof(f368,plain,
( ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(sdtasdt0(xp,xm))
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f362,f154]) ).
fof(f376,plain,
( sz00 = xq
| ~ aInteger0(sdtasdt0(xp,xm))
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f368,f106]) ).
fof(f390,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f376,f105]) ).
fof(f392,plain,
( ~ spl3_12
| spl3_6 ),
inference(avatar_split_clause,[],[f390,f152,f230]) ).
fof(f505,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm)
| spl3_12 ),
inference(resolution,[],[f232,f77]) ).
fof(f507,plain,
( ~ aInteger0(xm)
| spl3_12 ),
inference(forward_subsumption_resolution,[],[f505,f108]) ).
fof(f508,plain,
( $false
| spl3_12 ),
inference(forward_subsumption_resolution,[],[f507,f117]) ).
fof(f509,plain,
spl3_12,
inference(avatar_contradiction_clause,[],[f508]) ).
cnf(s3,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f145]) ).
cnf(s5,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
( ~ spl3_4
| ~ spl3_13 ),
inference(sat_conversion,[],[f243]) ).
cnf(s17,plain,
spl3_13,
inference(sat_conversion,[],[f263]) ).
cnf(s27,plain,
( spl3_6
| ~ spl3_12 ),
inference(sat_conversion,[],[f392]) ).
cnf(s31,plain,
spl3_12,
inference(sat_conversion,[],[f509]) ).
cnf(s32,plain,
spl3_6,
inference(rat,[],[s27,s31]) ).
cnf(s37,plain,
~ spl3_4,
inference(rat,[],[s16,s17]) ).
cnf(s39,plain,
~ spl3_1,
inference(rat,[],[s5,s32]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s3,s37,s39]) ).
fof(f510,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:54:45 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 1.76/1.12 % (2359853)Detected formulas, will run a generic FOF schedule.
% 1.76/1.12 % (2359863)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3503628635:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.76/1.12 % (2359863)First to succeed.
% 1.76/1.12 % (2359863)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2359853"
% 1.76/1.12 % (2359862)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=676664334:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.76/1.12 % (2359862)Also succeeded, but the first one will report.
% 1.76/1.12 % (2359861)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=401471204:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.76/1.12 % (2359859)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=1054757458:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.76/1.12 % (2359858)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=3523898316:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.76/1.12 % (2359860)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=1538835975:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.76/1.12 % (2359861)Also succeeded, but the first one will report.
% 1.76/1.12 % (2359864)dis-21_1_sil=8000:lcm=predicate:random_seed=2982110455: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)
% 1.76/1.12 % (2359864)Also succeeded, but the first one will report.
% 1.76/1.12 % (2359863)Refutation found. Thanks to Tanya!
% 1.76/1.12 % SZS status Theorem for theBenchmark
% 1.76/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.31 % (2359863)------------------------------
% 2.60/1.31 % (2359863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.31 % (2359863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.31 % (2359863)CaDiCaL version: 2.1.3
% 2.60/1.31 % (2359863)Termination reason: Refutation
% 2.60/1.31 % (2359863)Time elapsed: 0.007 s
% 2.60/1.31 % (2359863)Peak memory usage: 90 MB
% 2.60/1.31 % (2359863)Instructions burned: 15 (million)
% 2.60/1.31 % (2359863)------------------------------
% 2.60/1.31 % (2359863)------------------------------
% 2.60/1.31 % (2359853)Success in time 0.279 s
% 2.60/1.31 % Vampire exiting
%------------------------------------------------------------------------------