%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM501+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 : n026.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 12:15:28 PM UTC 2026
% Result : Theorem 2.62s 1.28s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 9 unt; 1 def)
% Number of atoms : 171 ( 46 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 207 ( 80 ~; 69 |; 53 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 56 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xr = sdtasdt0(X0,X1) )
| doDivides0(X0,xr) ) )
=> ( X0 = sz10
| X0 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X0) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X0) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f54,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = xr )
| doDivides0(X1,xr) ) )
=> ( sz10 = X1
| xr = X1 ) )
& isPrime0(xr) ),
inference(rectify,[],[f48]) ).
fof(f64,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(ennf_transformation,[],[f54]) ).
fof(f65,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X0) )
& ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f50]) ).
fof(f90,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f91,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f93,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f92]) ).
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(f142,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(sK9)
& xk = sdtasdt0(xr,sK9)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f65]) ).
fof(f156,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f196,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f208,plain,
xk = sdtasdt0(xr,sK9),
inference(cnf_transformation,[],[f142]) ).
fof(f209,plain,
aNaturalNumber0(sK9),
inference(cnf_transformation,[],[f142]) ).
fof(f210,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f142]) ).
fof(f212,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f237,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f238,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f239,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f308,definition,
~ sP29(sdtasdt0(xn,xm)),
introduced(definition,[new_symbols(definition,[sP29])],[inequality_splitting_name_introduction]) ).
fof(f309,plain,
! [X0] :
( sP29(sdtasdt0(xr,X0))
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f212,f308]) ).
fof(f336,plain,
! [X0] :
( sP29(sdtasdt0(X0,xr))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f309,f238]) ).
fof(f344,plain,
! [X0] :
( sP29(sdtasdt0(X0,xr))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literal_removal,[],[f336]) ).
fof(f353,plain,
! [X0] :
( sP29(sdtasdt0(X0,xr))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f344,f210]) ).
fof(f373,plain,
! [X0,X1] :
( sP29(sdtasdt0(X0,sdtasdt0(X1,xr)))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f353,f237]) ).
fof(f376,plain,
! [X0,X1] :
( sP29(sdtasdt0(X0,sdtasdt0(X1,xr)))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f373,f210]) ).
fof(f378,plain,
! [X0,X1] :
( sP29(sdtasdt0(X0,sdtasdt0(X1,xr)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f376,f239]) ).
fof(f390,plain,
! [X0,X1] :
( sP29(sdtasdt0(X1,sdtasdt0(xr,X0)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f378,f238]) ).
fof(f403,plain,
! [X0,X1] :
( sP29(sdtasdt0(X1,sdtasdt0(xr,X0)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literal_removal,[],[f390]) ).
fof(f410,plain,
! [X0,X1] :
( sP29(sdtasdt0(X1,sdtasdt0(xr,X0)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f403,f210]) ).
fof(f1067,plain,
! [X0] :
( sP29(sdtasdt0(X0,xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK9) ),
inference(superposition,[],[f410,f208]) ).
fof(f1112,plain,
! [X0] :
( sP29(sdtasdt0(X0,xk))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1067,f209]) ).
fof(f1293,plain,
~ sP29(sdtasdt0(xp,xk)),
inference(superposition,[],[f308,f196]) ).
fof(f2149,plain,
~ aNaturalNumber0(xp),
inference(resolution,[],[f1112,f1293]) ).
fof(f2607,plain,
$false,
inference(forward_subsumption_resolution,[],[f2149,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM501+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n026.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 20:16:27 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.43 Running first-order theorem proving
% 0.09/0.43 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
% 2.62/1.28 % (3180718)Detected formulas, will run a generic FOF schedule.
% 2.62/1.28 % (3180726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3110022071:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.28 % (3180726)First to succeed.
% 2.62/1.28 % (3180726)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3180718"
% 2.62/1.28 % (3180727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1923978707:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.28 % (3180723)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=644953162:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.28 % (3180728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2595717603:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.28 % (3180729)dis-21_1_sil=8000:lcm=predicate:random_seed=1463406831: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)
% 2.62/1.28 % (3180724)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=3094291705:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.28 % (3180725)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=1885299096:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.28 % (3180727)Also succeeded, but the first one will report.
% 2.62/1.28 % (3180729)Instruction limit reached!
% 2.62/1.28 % (3180729)------------------------------
% 2.62/1.28 % (3180729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3180729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3180729)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3180729)Termination reason: Instruction limit
% 2.62/1.28 % (3180729)Termination phase: Saturation
% 2.62/1.28 % (3180729)Time elapsed: 0.080 s
% 2.62/1.28 % (3180729)Peak memory usage: 91 MB
% 2.62/1.28 % (3180729)Instructions burned: 130 (million)
% 2.62/1.28 % (3180728)Instruction limit reached!
% 2.62/1.28 % (3180728)------------------------------
% 2.62/1.28 % (3180728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3180728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3180728)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3180728)Termination reason: Instruction limit
% 2.62/1.28 % (3180728)Termination phase: Saturation
% 2.62/1.28 % (3180728)Time elapsed: 0.092 s
% 2.62/1.28 % (3180728)Peak memory usage: 90 MB
% 2.62/1.28 % (3180728)Instructions burned: 140 (million)
% 2.62/1.28 % (3180726)Refutation found. Thanks to Tanya!
% 2.62/1.28 % SZS status Theorem for theBenchmark
% 2.62/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.28 % (3180726)------------------------------
% 2.62/1.28 % (3180726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3180726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3180726)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3180726)Termination reason: Refutation
% 2.62/1.28 % (3180726)Time elapsed: 0.045 s
% 2.62/1.28 % (3180726)Peak memory usage: 89 MB
% 2.62/1.28 % (3180726)Instructions burned: 79 (million)
% 2.62/1.28 % (3180726)------------------------------
% 2.62/1.28 % (3180726)------------------------------
% 2.62/1.28 % (3180718)Success in time 0.312 s
% 2.62/1.28 % Vampire exiting
%------------------------------------------------------------------------------