%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM472+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 : n004.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 12:15:20 PM UTC 2026
% Result : Theorem 2.65s 1.33s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 13 unt; 1 def)
% Number of atoms : 92 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 106 ( 47 ~; 40 |; 13 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 28 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f39,conjecture,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(flattening,[],[f40]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f49]) ).
fof(f80,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f81,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f87,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f81]) ).
fof(f88,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtpldt0(X0,sK1(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f88]) ).
fof(f90,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f91,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f98,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f41]) ).
fof(f103,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f138,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f138]) ).
fof(f154,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[],[f98,f152]) ).
fof(f157,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f154,f90]) ).
fof(f159,definition,
( spl6_1
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f161,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl6_1 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f167,plain,
~ aNaturalNumber0(sdtpldt0(xm,xn)),
inference(forward_subsumption_resolution,[],[f157,f91]) ).
fof(f168,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f167,f159]) ).
fof(f169,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl6_1 ),
inference(resolution,[],[f161,f103]) ).
fof(f170,plain,
( ~ aNaturalNumber0(xn)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f169,f91]) ).
fof(f171,plain,
( $false
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f170,f90]) ).
fof(f172,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f171]) ).
cnf(s2,plain,
~ spl6_1,
inference(sat_conversion,[],[f168]) ).
cnf(s3,plain,
spl6_1,
inference(sat_conversion,[],[f172]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f173,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM472+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:04:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.65/1.33 % (3843961)Detected formulas, will run a generic FOF schedule.
% 2.65/1.33 % (3843969)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=255869121:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.33 % (3843969)First to succeed.
% 2.65/1.33 % (3843969)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3843961"
% 2.65/1.33 % (3843967)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=3663760810:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.33 % (3843966)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=916076116:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.33 % (3843968)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=4199098127:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.33 % (3843970)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2421101663:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.33 % (3843970)Also succeeded, but the first one will report.
% 2.65/1.33 % (3843971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=575251295:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.33 % (3843972)dis-21_1_sil=8000:lcm=predicate:random_seed=345820523: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)
% 2.65/1.33 % (3843972)Also succeeded, but the first one will report.
% 2.65/1.33 % (3843971)Also succeeded, but the first one will report.
% 2.65/1.33 % (3843969)Refutation found. Thanks to Tanya!
% 2.65/1.33 % SZS status Theorem for theBenchmark
% 2.65/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.33 % (3843969)------------------------------
% 2.65/1.33 % (3843969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.33 % (3843969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.33 % (3843969)CaDiCaL version: 2.1.3
% 2.65/1.33 % (3843969)Termination reason: Refutation
% 2.65/1.33 % (3843969)Time elapsed: 0.003 s
% 2.65/1.33 % (3843969)Peak memory usage: 90 MB
% 2.65/1.33 % (3843969)Instructions burned: 4 (million)
% 2.65/1.33 % (3843969)------------------------------
% 2.65/1.33 % (3843969)------------------------------
% 2.65/1.33 % (3843961)Success in time 0.287 s
% 2.65/1.33 % Vampire exiting
%------------------------------------------------------------------------------