%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM521+3 : 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 : n007.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 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 16 unt; 4 def)
% Number of atoms : 133 ( 25 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 144 ( 64 ~; 52 |; 22 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 15 !; 6 ?)
% 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,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xm )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
~ ( xn != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
| sdtlseqdt0(xn,xp) )
& xm != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xp )
| sdtlseqdt0(xm,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f51,plain,
~ ( xn != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
| sdtlseqdt0(xn,xp) )
& xm != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xm,X1) )
| sdtlseqdt0(xm,xp) ) ),
inference(rectify,[],[f44]) ).
fof(f82,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f87,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f88,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f87]) ).
fof(f121,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xn) ),
inference(ennf_transformation,[],[f42]) ).
fof(f122,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xm) ),
inference(ennf_transformation,[],[f43]) ).
fof(f123,plain,
( xn = xp
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| xp != sdtpldt0(xn,X0) )
& ~ sdtlseqdt0(xn,xp) )
| xm = xp
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xm,X1) )
& ~ sdtlseqdt0(xm,xp) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f182,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f220,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f221,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f222,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f121]) ).
fof(f249,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f122]) ).
fof(f251,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| xm = xp
| ~ sdtlseqdt0(xm,xp) ),
inference(cnf_transformation,[],[f123]) ).
fof(f273,definition,
( spl11_1
<=> sdtlseqdt0(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f275,plain,
( ~ sdtlseqdt0(xm,xp)
| spl11_1 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f277,definition,
( spl11_2
<=> xm = xp ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f279,plain,
( xm = xp
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl11_3
<=> sdtlseqdt0(xn,xp) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f285,definition,
( spl11_4
<=> xn = xp ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f287,plain,
( xn = xp
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f251,f285,f281,f277,f273]) ).
fof(f323,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ spl11_2 ),
inference(superposition,[],[f249,f279]) ).
fof(f330,plain,
( ~ aNaturalNumber0(xm)
| ~ spl11_2 ),
inference(resolution,[],[f323,f182]) ).
fof(f331,plain,
( $false
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f330,f221]) ).
fof(f332,plain,
~ spl11_2,
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f337,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ spl11_4 ),
inference(superposition,[],[f247,f287]) ).
fof(f366,plain,
( ~ aNaturalNumber0(xn)
| ~ spl11_4 ),
inference(resolution,[],[f337,f182]) ).
fof(f367,plain,
( $false
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f366,f222]) ).
fof(f368,plain,
~ spl11_4,
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f437,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f185,f249]) ).
fof(f438,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f185,f247]) ).
fof(f443,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f438,f220]) ).
fof(f444,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f437,f275]) ).
fof(f447,plain,
sdtlseqdt0(xn,xp),
inference(forward_subsumption_resolution,[],[f443,f222]) ).
fof(f448,plain,
( ~ aNaturalNumber0(xp)
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f444,f221]) ).
fof(f452,plain,
spl11_3,
inference(avatar_split_clause,[],[f447,f281]) ).
fof(f453,plain,
( $false
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f448,f220]) ).
fof(f454,plain,
spl11_1,
inference(avatar_contradiction_clause,[],[f453]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f288]) ).
cnf(s9,plain,
~ spl11_2,
inference(sat_conversion,[],[f332]) ).
cnf(s10,plain,
~ spl11_4,
inference(sat_conversion,[],[f368]) ).
cnf(s12,plain,
spl11_3,
inference(sat_conversion,[],[f452]) ).
cnf(s13,plain,
spl11_1,
inference(sat_conversion,[],[f454]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s10,s12,s9,s13]) ).
fof(f455,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM521+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:17:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.46 % (1754445)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (1754455)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=438047599:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (1754450)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1172515548_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (1754452)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1485589372:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (1754456)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1083187658:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (1754453)dis+10_1_sil=32000:sp=arity:random_seed=2337984535:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (1754454)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3308100196:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (1754451)% WARNING: option uhcvi not known.
% 0.10/0.46 % (1754453) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1754445-1754453"...
% 0.10/0.46 % Detected minimum model sizes of [3]
% 0.10/0.46 % (1754451)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3933109230:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % Detected maximum model sizes of [max]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (1754453)...printing done.
% 0.10/0.46 % (1754456) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1754445-1754456"...
% 0.10/0.46 % (1754453)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status ContradictoryAxioms for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (1754453)------------------------------
% 0.10/0.46 % (1754453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (1754453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (1754453)CaDiCaL version: 2.1.3
% 0.10/0.46 % (1754453)Termination reason: Refutation
% 0.10/0.46 % (1754453)Time elapsed: 0.008 s
% 0.10/0.46 % (1754453)Peak memory usage: 12 MB
% 0.10/0.46 % (1754453)Instructions burned: 11 (million)
% 0.10/0.46 % (1754445)Success in time 0.042 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------