%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM505+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 : n010.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 12:15:29 PM UTC 2026
% Result : Theorem 2.70s 1.38s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 15 unt; 0 def)
% Number of atoms : 239 ( 86 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 304 ( 123 ~; 115 |; 51 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
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(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f50,conjecture,
( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f57,plain,
( ( xp = xk
| ~ sdtlseqdt0(xk,xp) )
& ~ sdtlseqdt0(xp,xk) ),
inference(ennf_transformation,[],[f51]) ).
fof(f94,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f95,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f94]) ).
fof(f104,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f105,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f107,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f106]) ).
fof(f112,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f115]) ).
fof(f127,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f105]) ).
fof(f128,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f116]) ).
fof(f132,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f134,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f137,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f138,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f145,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f155,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f57]) ).
fof(f156,plain,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f57]) ).
fof(f190,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f201,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f206,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f210,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f213,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f215,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f224,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f201]) ).
fof(f228,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f213]) ).
fof(f232,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[],[f224,f215]) ).
fof(f249,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk ),
inference(resolution,[],[f206,f156]) ).
fof(f250,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk ),
inference(forward_subsumption_resolution,[],[f249,f155]) ).
fof(f252,plain,
( xp = xk
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f250,f133]) ).
fof(f284,plain,
( ~ sdtlseqdt0(xk,xk)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f155,f252]) ).
fof(f287,plain,
~ aNaturalNumber0(xk),
inference(forward_subsumption_resolution,[],[f284,f210]) ).
fof(f502,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f228,f145]) ).
fof(f503,plain,
( sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f502,f287]) ).
fof(f504,plain,
( sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f503,f137]) ).
fof(f505,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f504,f133]) ).
fof(f506,plain,
( sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f505,f190]) ).
fof(f507,plain,
( sz00 = xp
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f506,f135]) ).
fof(f508,plain,
sz00 = xp,
inference(forward_subsumption_resolution,[],[f507,f134]) ).
fof(f527,plain,
~ isPrime0(xp),
inference(superposition,[],[f232,f508]) ).
fof(f533,plain,
$false,
inference(forward_subsumption_resolution,[],[f527,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM505+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n010.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 20:14:02 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.70/1.38 % (1279207)Detected formulas, will run a generic FOF schedule.
% 2.70/1.38 % (1279304)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2789591598:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.38 % (1279304)First to succeed.
% 2.70/1.38 % (1279304)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1279207"
% 2.70/1.38 % (1279300)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=2022176896:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.38 % (1279302)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=2801361628:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.38 % (1279301)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=674532989:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.38 % (1279303)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2752672949:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.38 % (1279303)Also succeeded, but the first one will report.
% 2.70/1.38 % (1279306)dis-21_1_sil=8000:lcm=predicate:random_seed=3044395764: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)
% 2.70/1.38 % (1279305)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4284851690:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.38 % (1279305)Also succeeded, but the first one will report.
% 2.70/1.38 % (1279306)Instruction limit reached!
% 2.70/1.38 % (1279306)------------------------------
% 2.70/1.38 % (1279306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.38 % (1279306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.38 % (1279306)CaDiCaL version: 2.1.3
% 2.70/1.38 % (1279306)Termination reason: Instruction limit
% 2.70/1.38 % (1279306)Termination phase: Saturation
% 2.70/1.38 % (1279306)Time elapsed: 0.080 s
% 2.70/1.38 % (1279306)Peak memory usage: 90 MB
% 2.70/1.38 % (1279306)Instructions burned: 130 (million)
% 2.70/1.38 % (1279304)Refutation found. Thanks to Tanya!
% 2.70/1.38 % SZS status Theorem for theBenchmark
% 2.70/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.38 % (1279304)------------------------------
% 2.70/1.38 % (1279304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.38 % (1279304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.38 % (1279304)CaDiCaL version: 2.1.3
% 2.70/1.38 % (1279304)Termination reason: Refutation
% 2.70/1.38 % (1279304)Time elapsed: 0.005 s
% 2.70/1.38 % (1279304)Peak memory usage: 88 MB
% 2.70/1.38 % (1279304)Instructions burned: 12 (million)
% 2.70/1.38 % (1279304)------------------------------
% 2.70/1.38 % (1279304)------------------------------
% 2.70/1.38 % (1279207)Success in time 0.298 s
% 2.70/1.38 % Vampire exiting
%------------------------------------------------------------------------------