%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM466+2 : 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 : n001.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 12:15:18 PM UTC 2026
% Result : Theorem 0.27s 2.04s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 1 def)
% Number of atoms : 129 ( 31 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 144 ( 49 ~; 39 |; 51 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 33 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(f32,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1218) ).
fof(f33,conjecture,
( ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xm,X0) )
& doDivides0(xm,xn) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
| doDivides0(xl,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f34,negated_conjecture,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xm,X0) )
& doDivides0(xm,xn) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
| doDivides0(xl,xn) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn) )
=> ( ? [X2] :
( aNaturalNumber0(X2)
& xn = sdtasdt0(xl,X2) )
| doDivides0(xl,xn) ) ),
inference(rectify,[],[f34]) ).
fof(f37,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| xn != sdtasdt0(xl,X2) )
& ~ doDivides0(xl,xn)
& ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn) ),
inference(ennf_transformation,[],[f35]) ).
fof(f38,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| xn != sdtasdt0(xl,X2) )
& ~ doDivides0(xl,xn)
& ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn) ),
inference(flattening,[],[f37]) ).
fof(f39,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(f40,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0) )
& ~ doDivides0(xl,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X2] :
( aNaturalNumber0(X2)
& xn = sdtasdt0(xm,X2) )
& doDivides0(xm,xn) ),
inference(rectify,[],[f38]) ).
fof(f48,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0) )
& ~ doDivides0(xl,xn)
& aNaturalNumber0(sK0)
& xm = sdtasdt0(xl,sK0)
& doDivides0(xl,xm)
& aNaturalNumber0(sK1)
& xn = sdtasdt0(xm,sK1)
& doDivides0(xm,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X2,sK1)],[f47]) ).
fof(f54,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
xn = sdtasdt0(xm,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f57,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f59,plain,
xm = sdtasdt0(xl,sK0),
inference(cnf_transformation,[],[f48]) ).
fof(f60,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f48]) ).
fof(f62,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f69,definition,
~ sP3(xn),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f70,plain,
! [X0] :
( sP3(sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f62,f69]) ).
fof(f79,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f63,f59]) ).
fof(f80,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f79,f54]) ).
fof(f81,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f80,f60]) ).
fof(f138,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sK0,X0))
| sP3(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f70,f81]) ).
fof(f182,plain,
! [X0] :
( sP3(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f138,f65]) ).
fof(f189,plain,
! [X0] :
( sP3(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f193,plain,
! [X0] :
( sP3(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f189,f60]) ).
fof(f194,plain,
( sP3(xn)
| ~ aNaturalNumber0(sK1) ),
inference(superposition,[],[f193,f56]) ).
fof(f204,plain,
~ aNaturalNumber0(sK1),
inference(forward_subsumption_resolution,[],[f194,f69]) ).
fof(f205,plain,
$false,
inference(forward_subsumption_resolution,[],[f204,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n001.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 20:09:16 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.27/2.04 % (3918037)Detected formulas, will run a generic FOF schedule.
% 0.27/2.04 % (3918047)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1653798006:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.27/2.04 % (3918042)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=4165513758:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.27/2.04 % (3918044)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=1376770287:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.27/2.04 % (3918045)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4044820845:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.27/2.04 % (3918043)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=3113273413:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.27/2.04 % (3918045)First to succeed.
% 0.27/2.04 % (3918045)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3918037"
% 0.27/2.04 % (3918047)Instruction limit reached!
% 0.27/2.04 % (3918047)------------------------------
% 0.27/2.04 % (3918047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.04 % (3918047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.04 % (3918047)CaDiCaL version: 2.1.3
% 0.27/2.04 % (3918047)Termination reason: Instruction limit
% 0.27/2.04 % (3918047)Termination phase: Saturation
% 0.27/2.04 % (3918047)Time elapsed: 0.071 s
% 0.27/2.04 % (3918047)Peak memory usage: 90 MB
% 0.27/2.04 % (3918047)Instructions burned: 140 (million)
% 0.27/2.04 % (3918048)dis-21_1_sil=8000:lcm=predicate:random_seed=2660344477: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)
% 0.27/2.04 % (3918046)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=852893890:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.27/2.04 % (3918046)Also succeeded, but the first one will report.
% 0.27/2.04 % (3918048)Instruction limit reached!
% 0.27/2.04 % (3918048)------------------------------
% 0.27/2.04 % (3918048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.04 % (3918048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.04 % (3918048)CaDiCaL version: 2.1.3
% 0.27/2.04 % (3918048)Termination reason: Instruction limit
% 0.27/2.04 % (3918048)Termination phase: Saturation
% 0.27/2.04 % (3918048)Time elapsed: 0.129 s
% 0.27/2.04 % (3918048)Peak memory usage: 90 MB
% 0.27/2.04 % (3918048)Instructions burned: 130 (million)
% 0.27/2.04 % (3918056)lrs+10_1_sil=8000:sp=occurrence:random_seed=2972466683:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.27/2.04 % (3918059)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1666923856:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 0.27/2.04 % (3918056)Instruction limit reached!
% 0.27/2.04 % (3918056)------------------------------
% 0.27/2.04 % (3918056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.04 % (3918056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.04 % (3918056)CaDiCaL version: 2.1.3
% 0.27/2.04 % (3918056)Termination reason: Instruction limit
% 0.27/2.04 % (3918056)Termination phase: Saturation
% 0.27/2.04 % (3918056)Time elapsed: 0.134 s
% 0.27/2.04 % (3918056)Peak memory usage: 91 MB
% 0.27/2.04 % (3918056)Instructions burned: 287 (million)
% 0.27/2.04 % (3918045)Refutation found. Thanks to Tanya!
% 0.27/2.04 % SZS status Theorem for theBenchmark
% 0.27/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/2.04 % (3918045)------------------------------
% 0.27/2.04 % (3918045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.04 % (3918045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.04 % (3918045)CaDiCaL version: 2.1.3
% 0.27/2.04 % (3918045)Termination reason: Refutation
% 0.27/2.04 % (3918045)Time elapsed: 0.008 s
% 0.27/2.04 % (3918045)Peak memory usage: 89 MB
% 0.27/2.04 % (3918045)Instructions burned: 5 (million)
% 0.27/2.04 % (3918045)------------------------------
% 0.27/2.04 % (3918045)------------------------------
% 0.27/2.04 % (3918037)Success in time 0.695 s
% 0.27/2.04 % Vampire exiting
%------------------------------------------------------------------------------