%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM490+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 : n001.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 12:24:31 PM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 24 unt; 3 def)
% Number of atoms : 198 ( 27 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 229 ( 104 ~; 101 |; 11 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(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(f46,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1951) ).
fof(f47,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f49,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(flattening,[],[f48]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f53]) ).
fof(f76,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f77,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,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(f79,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f78]) ).
fof(f123,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtmndt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f186,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f187,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f188,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f192,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f193,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f197,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f46]) ).
fof(f198,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f199,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f145]) ).
fof(f200,plain,
! [X2,X0] :
( ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f148]) ).
fof(f201,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f147]) ).
fof(f287,definition,
( spl4_5
<=> aNaturalNumber0(sdtasdt0(xr,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f288,plain,
( aNaturalNumber0(sdtasdt0(xr,xm))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f289,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| spl4_5 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f291,definition,
( spl4_6
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f292,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl4_6 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f296,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| spl4_5 ),
inference(resolution,[],[f289,f123]) ).
fof(f300,plain,
( ~ aNaturalNumber0(xr)
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f299,f187]) ).
fof(f361,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f296,f123]) ).
fof(f362,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f361,f188]) ).
fof(f363,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f362,f187]) ).
fof(f364,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f386,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(resolution,[],[f201,f192]) ).
fof(f397,plain,
( ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(forward_subsumption_resolution,[],[f386,f186]) ).
fof(f398,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(forward_subsumption_resolution,[],[f397,f188]) ).
fof(f399,plain,
aNaturalNumber0(xr),
inference(forward_demodulation,[],[f398,f193]) ).
fof(f400,plain,
( $false
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f399,f300]) ).
fof(f401,plain,
spl4_5,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f670,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f199,f197]) ).
fof(f683,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f670,f288]) ).
fof(f689,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ spl4_5
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f683,f297]) ).
fof(f2414,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl4_6 ),
inference(resolution,[],[f293,f123]) ).
fof(f2415,plain,
( ~ aNaturalNumber0(xm)
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f2414,f186]) ).
fof(f2416,plain,
( $false
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f2415,f187]) ).
fof(f2417,plain,
spl4_6,
inference(avatar_contradiction_clause,[],[f2416]) ).
fof(f2420,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f689,f292]) ).
fof(f2543,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
inference(superposition,[],[f200,f197]) ).
fof(f2561,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f2543,f2420]) ).
fof(f2572,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f2561,f292]) ).
fof(f2580,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f2572,f297]) ).
fof(f2584,plain,
( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f2580,f288]) ).
fof(f2585,plain,
( $false
| ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f2584,f198]) ).
fof(f2586,plain,
( ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f2585]) ).
cnf(s7,plain,
spl4_7,
inference(sat_conversion,[],[f364]) ).
cnf(s8,plain,
spl4_5,
inference(sat_conversion,[],[f401]) ).
cnf(s48,plain,
spl4_6,
inference(sat_conversion,[],[f2417]) ).
cnf(s55,plain,
( ~ spl4_5
| ~ spl4_6
| ~ spl4_7 ),
inference(sat_conversion,[],[f2586]) ).
cnf(s59,plain,
~ spl4_7,
inference(rat,[],[s55,s48,s8]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s7,s59]) ).
fof(f2587,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 20:16:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 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
% 0.16/0.51 % (3921023)Will run a generic schedule for satisfiability detection.
% 0.16/0.51 % (3921028)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2922621540_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.51 % TRYING [1]
% 0.16/0.51 % TRYING [2]
% 0.16/0.51 % (3921029)% WARNING: option uhcvi not known.
% 0.16/0.51 % TRYING [3]
% 0.16/0.51 % (3921029)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=390849457:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.51 % (3921030)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2707028785:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.51 % (3921033)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1373629706:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51 % (3921031)dis+10_1_sil=32000:sp=arity:random_seed=3309979927:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.51 % (3921032)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2702084572:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.51 % (3921034)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2929217110:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.51 % TRYING [4]
% 0.16/0.51 % TRYING [5]
% 0.16/0.51 % TRYING [6]
% 0.16/0.51 % (3921032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3921023-3921032"...
% 0.16/0.51 % (3921031)Instruction limit reached!
% 0.16/0.51 % (3921031)------------------------------
% 0.16/0.51 % (3921031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.51 % (3921031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.51 % (3921031)CaDiCaL version: 2.1.3
% 0.16/0.51 % (3921031)Termination reason: Instruction limit
% 0.16/0.51 % (3921031)Termination phase: Saturation
% 0.16/0.51 % (3921031)Time elapsed: 0.061 s
% 0.16/0.51 % (3921031)Peak memory usage: 12 MB
% 0.16/0.51 % (3921031)Instructions burned: 104 (million)
% 0.16/0.51 % (3921032)...printing done.
% 0.16/0.51 % (3921032)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (3921032)------------------------------
% 0.16/0.52 % (3921032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3921032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3921032)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3921032)Termination reason: Refutation
% 0.16/0.52 % (3921032)Time elapsed: 0.062 s
% 0.16/0.52 % (3921032)Peak memory usage: 14 MB
% 0.16/0.52 % (3921032)Instructions burned: 105 (million)
% 0.16/0.52 % (3921023)Success in time 0.109 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------