%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM521+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 : n017.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 12:15:34 PM UTC 2026
% Result : ContradictoryAxioms 3.51s 1.38s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 16 unt; 4 def)
% Number of atoms : 115 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 59 ~; 50 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
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,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
~ ( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f51,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(ennf_transformation,[],[f44]) ).
fof(f101,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f102,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f101]) ).
fof(f119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f120,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f121,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f125,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f126,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f43]) ).
fof(f127,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(cnf_transformation,[],[f51]) ).
fof(f179,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f201,definition,
( spl10_1
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f202,plain,
( sdtlseqdt0(xm,xp)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( ~ sdtlseqdt0(xm,xp)
| spl10_1 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f205,definition,
( spl10_2
<=> xm = xp ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f207,plain,
( xm = xp
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl10_3
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f210,plain,
( sdtlseqdt0(xn,xp)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f213,definition,
( spl10_4
<=> xn = xp ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f215,plain,
( xn = xp
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,plain,
( ~ spl10_1
| spl10_2
| ~ spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f127,f213,f209,f205,f201]) ).
fof(f221,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f125,f179]) ).
fof(f222,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f221,f121]) ).
fof(f223,plain,
sdtlseqdt0(xn,xp),
inference(forward_subsumption_resolution,[],[f222,f119]) ).
fof(f224,plain,
spl10_3,
inference(avatar_split_clause,[],[f223,f209]) ).
fof(f225,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f126,f179]) ).
fof(f226,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f225,f203]) ).
fof(f227,plain,
( ~ aNaturalNumber0(xp)
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f226,f120]) ).
fof(f228,plain,
( $false
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f227,f119]) ).
fof(f229,plain,
spl10_1,
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f242,plain,
( sdtlseqdt0(xp,xp)
| ~ spl10_1
| ~ spl10_2 ),
inference(superposition,[],[f202,f207]) ).
fof(f243,plain,
( ~ sdtlseqdt0(xp,xp)
| ~ spl10_2 ),
inference(superposition,[],[f126,f207]) ).
fof(f246,plain,
( $false
| ~ spl10_1
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f242,f243]) ).
fof(f247,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f254,plain,
( sdtlseqdt0(xp,xp)
| ~ spl10_3
| ~ spl10_4 ),
inference(superposition,[],[f210,f215]) ).
fof(f255,plain,
( ~ sdtlseqdt0(xp,xp)
| ~ spl10_4 ),
inference(superposition,[],[f125,f215]) ).
fof(f258,plain,
( $false
| ~ spl10_3
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f254,f255]) ).
fof(f259,plain,
( ~ spl10_3
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[],[f258]) ).
cnf(s1,plain,
( ~ spl10_1
| spl10_2
| ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f216]) ).
cnf(s2,plain,
spl10_3,
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
spl10_1,
inference(sat_conversion,[],[f229]) ).
cnf(s5,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f247]) ).
cnf(s6,plain,
( ~ spl10_3
| ~ spl10_4 ),
inference(sat_conversion,[],[f259]) ).
cnf(s7,plain,
~ spl10_2,
inference(rat,[],[s5,s3]) ).
cnf(s9,plain,
~ spl10_4,
inference(rat,[],[s6,s2]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s2,s7,s3]) ).
fof(f260,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM521+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:14:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.51/1.38 % (2909204)Detected formulas, will run a generic FOF schedule.
% 3.51/1.38 % (2909210)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=789832448:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.38 % (2909209)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=2307325251:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.38 % (2909212)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4229725935:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.38 % (2909211)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=1428306720:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.38 % (2909213)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3297069438:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.38 % (2909212)First to succeed.
% 3.51/1.38 % (2909213)Also succeeded, but the first one will report.
% 3.51/1.38 % (2909212)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2909204"
% 3.51/1.38 % (2909215)dis-21_1_sil=8000:lcm=predicate:random_seed=2148279546: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)
% 3.51/1.38 % (2909214)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2106645619:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.38 % (2909214)Also succeeded, but the first one will report.
% 3.51/1.38 % (2909215)Instruction limit reached!
% 3.51/1.38 % (2909215)------------------------------
% 3.51/1.38 % (2909215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (2909215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (2909215)CaDiCaL version: 2.1.3
% 3.51/1.38 % (2909215)Termination reason: Instruction limit
% 3.51/1.38 % (2909215)Termination phase: Saturation
% 3.51/1.38 % (2909215)Time elapsed: 0.081 s
% 3.51/1.38 % (2909215)Peak memory usage: 90 MB
% 3.51/1.38 % (2909215)Instructions burned: 130 (million)
% 3.51/1.38 % (2909212)Refutation found. Thanks to Tanya!
% 3.51/1.38 % SZS status ContradictoryAxioms for theBenchmark
% 3.51/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.38 % (2909212)------------------------------
% 3.51/1.38 % (2909212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (2909212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (2909212)CaDiCaL version: 2.1.3
% 3.51/1.38 % (2909212)Termination reason: Refutation
% 3.51/1.38 % (2909212)Time elapsed: 0.006 s
% 3.51/1.38 % (2909212)Peak memory usage: 89 MB
% 3.51/1.38 % (2909212)Instructions burned: 7 (million)
% 3.51/1.38 % (2909212)------------------------------
% 3.51/1.38 % (2909212)------------------------------
% 3.51/1.38 % (2909204)Success in time 0.431 s
% 3.51/1.38 % Vampire exiting
%------------------------------------------------------------------------------