%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM489+1 : 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 : n002.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 12:15:25 PM UTC 2026
% Result : Theorem 2.43s 1.22s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 1 def)
% Number of atoms : 72 ( 23 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 84 ( 38 ~; 31 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f45,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
xn != sdtpldt0(xp,xr),
inference(flattening,[],[f46]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f107]) ).
fof(f120,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f108]) ).
fof(f121,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f124,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f128,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f129,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f132,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f47]) ).
fof(f187,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f192,definition,
~ sP5(xn),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f193,plain,
sP5(sdtpldt0(xp,xr)),
inference(inequality_splitting,[],[f132,f192]) ).
fof(f211,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f376,plain,
sP5(sdtpldt0(xp,sdtmndt0(xn,xp))),
inference(superposition,[],[f193,f129]) ).
fof(f377,plain,
( sP5(xn)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f376,f211]) ).
fof(f378,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f377,f192]) ).
fof(f379,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f378,f128]) ).
fof(f380,plain,
~ aNaturalNumber0(xn),
inference(forward_subsumption_resolution,[],[f379,f122]) ).
fof(f381,plain,
$false,
inference(forward_subsumption_resolution,[],[f380,f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 20:12:37 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.43/1.22 % (3846029)Detected formulas, will run a generic FOF schedule.
% 2.43/1.22 % (3846037)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3501911096:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.43/1.22 % (3846037)First to succeed.
% 2.43/1.22 % (3846037)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3846029"
% 2.43/1.22 % (3846038)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3563688262:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.43/1.22 % (3846039)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1302505011:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.43/1.22 % (3846034)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=3576086007:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.43/1.22 % (3846035)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=521236995:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.43/1.22 % (3846036)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=2731039472:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.43/1.22 % (3846038)Also succeeded, but the first one will report.
% 2.43/1.22 % (3846040)dis-21_1_sil=8000:lcm=predicate:random_seed=2566959850: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)
% 2.43/1.22 % (3846039)Also succeeded, but the first one will report.
% 2.43/1.22 % (3846040)Instruction limit reached!
% 2.43/1.22 % (3846040)------------------------------
% 2.43/1.22 % (3846040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.22 % (3846040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.22 % (3846040)CaDiCaL version: 2.1.3
% 2.43/1.22 % (3846040)Termination reason: Instruction limit
% 2.43/1.22 % (3846040)Termination phase: Saturation
% 2.43/1.22 % (3846040)Time elapsed: 0.082 s
% 2.43/1.22 % (3846040)Peak memory usage: 90 MB
% 2.43/1.22 % (3846040)Instructions burned: 130 (million)
% 2.43/1.22 % (3846037)Refutation found. Thanks to Tanya!
% 2.43/1.22 % SZS status Theorem for theBenchmark
% 2.43/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/1.22 % (3846037)------------------------------
% 2.43/1.22 % (3846037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.22 % (3846037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.22 % (3846037)CaDiCaL version: 2.1.3
% 2.43/1.22 % (3846037)Termination reason: Refutation
% 2.43/1.22 % (3846037)Time elapsed: 0.004 s
% 2.43/1.22 % (3846037)Peak memory usage: 89 MB
% 2.43/1.22 % (3846037)Instructions burned: 8 (million)
% 2.43/1.22 % (3846037)------------------------------
% 2.43/1.22 % (3846037)------------------------------
% 2.43/1.22 % (3846029)Success in time 0.268 s
% 2.43/1.22 % Vampire exiting
%------------------------------------------------------------------------------