%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 12:24:39 PM UTC 2026
% Result : ContradictoryAxioms 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 19 unt; 4 def)
% Number of atoms : 101 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 48 ~; 38 |; 9 &)
% ( 4 <=>; 2 =>; 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 : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
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(f78,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f83,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f84,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f83]) ).
fof(f115,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(ennf_transformation,[],[f44]) ).
fof(f162,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f165,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f200,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f201,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f206,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f207,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f43]) ).
fof(f208,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(cnf_transformation,[],[f115]) ).
fof(f225,definition,
( spl4_1
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f229,definition,
( spl4_2
<=> xm = xp ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f231,plain,
( xm = xp
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f233,definition,
( spl4_3
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f237,definition,
( spl4_4
<=> xn = xp ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f239,plain,
( xn = xp
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f208,f237,f233,f229,f225]) ).
fof(f313,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f165,f206]) ).
fof(f314,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f165,f207]) ).
fof(f318,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f313,f200]) ).
fof(f322,plain,
sdtlseqdt0(xn,xp),
inference(forward_subsumption_resolution,[],[f318,f202]) ).
fof(f327,plain,
spl4_3,
inference(avatar_split_clause,[],[f322,f233]) ).
fof(f330,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f314,f200]) ).
fof(f332,plain,
sdtlseqdt0(xm,xp),
inference(forward_subsumption_resolution,[],[f330,f201]) ).
fof(f334,plain,
spl4_1,
inference(avatar_split_clause,[],[f332,f225]) ).
fof(f338,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ spl4_4 ),
inference(superposition,[],[f206,f239]) ).
fof(f370,plain,
( ~ aNaturalNumber0(xn)
| ~ spl4_4 ),
inference(resolution,[],[f338,f162]) ).
fof(f371,plain,
( $false
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f370,f202]) ).
fof(f372,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f377,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ spl4_2 ),
inference(superposition,[],[f207,f231]) ).
fof(f399,plain,
( ~ aNaturalNumber0(xm)
| ~ spl4_2 ),
inference(resolution,[],[f377,f162]) ).
fof(f400,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f399,f201]) ).
fof(f401,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f400]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f240]) ).
cnf(s7,plain,
spl4_3,
inference(sat_conversion,[],[f327]) ).
cnf(s10,plain,
spl4_1,
inference(sat_conversion,[],[f334]) ).
cnf(s12,plain,
~ spl4_4,
inference(sat_conversion,[],[f372]) ).
cnf(s13,plain,
~ spl4_2,
inference(sat_conversion,[],[f401]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s12,s7,s13,s10]) ).
fof(f402,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM521+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 20:19:34 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % (3716995)Will run a generic schedule for satisfiability detection.
% 0.19/0.46 % (3717000)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2657601466_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.46 % TRYING [1]
% 0.19/0.46 % TRYING [2]
% 0.19/0.46 % (3717001)% WARNING: option uhcvi not known.
% 0.19/0.46 % TRYING [3]
% 0.19/0.46 % (3717001)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1693953453:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.46 % (3717002)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3283013260:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.46 % (3717003)dis+10_1_sil=32000:sp=arity:random_seed=998493571:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.46 % (3717005)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4077521696:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.46 % (3717004)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3117312995:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.46 % (3717006)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=875435253:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.46 % TRYING [4]
% 0.19/0.46 % (3717003) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3716995-3717003"...
% 0.19/0.46 % (3717004) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3716995-3717004"...
% 0.19/0.46 % (3717001) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3716995-3717001"...
% 0.19/0.46 % (3717006) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3716995-3717006"...
% 0.19/0.46 % (3717003)...printing done.
% 0.19/0.46 % (3717004)...printing done.
% 0.19/0.46 % (3717001)...printing done.
% 0.19/0.46 % (3717003)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status ContradictoryAxioms for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (3717003)------------------------------
% 0.19/0.47 % (3717003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.47 % (3717003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.47 % (3717003)CaDiCaL version: 2.1.3
% 0.19/0.47 % (3717003)Termination reason: Refutation
% 0.19/0.47 % (3717003)Time elapsed: 0.007 s
% 0.19/0.47 % (3717003)Peak memory usage: 12 MB
% 0.19/0.47 % (3717003)Instructions burned: 9 (million)
% 0.19/0.47 % (3716995)Success in time 0.049 s
% 0.19/0.47 % Vampire exiting
%------------------------------------------------------------------------------