%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM475+2 : 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 : n014.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 12:24:27 PM UTC 2026
% Result : Theorem 1.44s 0.66s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 26 unt; 1 def)
% Number of atoms : 127 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 40 ~; 45 |; 23 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f37,axiom,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f40,axiom,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xq
& xr = sdtmndt0(xq,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(f41,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1459) ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(rectify,[],[f35]) ).
fof(f45,plain,
xn != sdtasdt0(xl,xr),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f49]) ).
fof(f64,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f64]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f157,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f158,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f159,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f162,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f168,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[],[f37]) ).
fof(f171,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f38]) ).
fof(f178,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f40]) ).
fof(f179,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f41]) ).
fof(f180,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[],[f45]) ).
fof(f193,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| aNaturalNumber0(X0)
| aNaturalNumber0(X1) ),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f206,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| aNaturalNumber0(X1)
| aNaturalNumber0(X0)
| aNaturalNumber0(X2)
| X1 = X2 ),
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f243,plain,
~ aNaturalNumber0(xl),
inference(consistent_polarity_flipping,[],[f159]) ).
fof(f244,plain,
~ aNaturalNumber0(xm),
inference(consistent_polarity_flipping,[],[f158]) ).
fof(f245,plain,
~ aNaturalNumber0(xn),
inference(consistent_polarity_flipping,[],[f157]) ).
fof(f252,plain,
~ aNaturalNumber0(xr),
inference(consistent_polarity_flipping,[],[f178]) ).
fof(f256,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,sK2),
inference(superposition,[],[f171,f162]) ).
fof(f556,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,sdtasdt0(xl,xr)),
inference(forward_demodulation,[],[f179,f168]) ).
fof(f557,plain,
sdtasdt0(xl,sK2) = sdtpldt0(xm,sdtasdt0(xl,xr)),
inference(forward_demodulation,[],[f556,f162]) ).
fof(f564,definition,
( spl5_11
<=> aNaturalNumber0(sdtasdt0(xl,xr)) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f565,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| spl5_11 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f566,plain,
( aNaturalNumber0(sdtasdt0(xl,xr))
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f743,plain,
! [X0] :
( sdtasdt0(xl,xq) != sdtpldt0(xm,X0)
| aNaturalNumber0(X0)
| aNaturalNumber0(xm)
| aNaturalNumber0(xn)
| xn = X0 ),
inference(superposition,[],[f206,f171]) ).
fof(f764,plain,
! [X0] :
( sdtasdt0(xl,xq) != sdtpldt0(xm,X0)
| aNaturalNumber0(X0)
| aNaturalNumber0(xn)
| xn = X0 ),
inference(forward_subsumption_resolution,[],[f743,f244]) ).
fof(f789,plain,
! [X0] :
( sdtasdt0(xl,xq) != sdtpldt0(xm,X0)
| aNaturalNumber0(X0)
| xn = X0 ),
inference(forward_subsumption_resolution,[],[f764,f245]) ).
fof(f1011,plain,
( aNaturalNumber0(xl)
| aNaturalNumber0(xr)
| ~ spl5_11 ),
inference(resolution,[],[f566,f193]) ).
fof(f1012,plain,
( aNaturalNumber0(xr)
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f1011,f243]) ).
fof(f1013,plain,
( $false
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f1012,f252]) ).
fof(f1014,plain,
~ spl5_11,
inference(avatar_contradiction_clause,[],[f1013]) ).
fof(f12008,plain,
( sdtasdt0(xl,xq) != sdtasdt0(xl,sK2)
| aNaturalNumber0(sdtasdt0(xl,xr))
| xn = sdtasdt0(xl,xr) ),
inference(superposition,[],[f789,f557]) ).
fof(f12009,plain,
( aNaturalNumber0(sdtasdt0(xl,xr))
| xn = sdtasdt0(xl,xr) ),
inference(forward_subsumption_resolution,[],[f12008,f256]) ).
fof(f12011,plain,
( xn = sdtasdt0(xl,xr)
| spl5_11 ),
inference(forward_subsumption_resolution,[],[f12009,f565]) ).
fof(f12013,plain,
( $false
| spl5_11 ),
inference(forward_subsumption_resolution,[],[f12011,f180]) ).
fof(f12014,plain,
spl5_11,
inference(avatar_contradiction_clause,[],[f12013]) ).
cnf(s21,plain,
~ spl5_11,
inference(sat_conversion,[],[f1014]) ).
cnf(s443,plain,
spl5_11,
inference(sat_conversion,[],[f12014]) ).
cnf(s446,plain,
$false,
inference(rat,[],[s21,s443]) ).
fof(f12016,plain,
$false,
inference(avatar_sat_refutation,[],[s446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+2 : 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 : n014.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 20:05:16 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
% 1.44/0.66 % (1130016)Will run a generic schedule for satisfiability detection.
% 1.44/0.66 % (1130021)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2296123641_2999 on theBenchmark for (2999ds/0Mi)
% 1.44/0.66 % TRYING [1]
% 1.44/0.66 % TRYING [2]
% 1.44/0.66 % TRYING [3]
% 1.44/0.66 % (1130022)% WARNING: option uhcvi not known.
% 1.44/0.66 % (1130027)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4190853493:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.44/0.66 % (1130023)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2475354379:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.44/0.66 % (1130024)dis+10_1_sil=32000:sp=arity:random_seed=3699644194:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.44/0.66 % (1130025)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1165660454:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.44/0.66 % (1130026)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2359513784:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.44/0.66 % TRYING [4]
% 1.44/0.66 % (1130022)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2025582401:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.44/0.66 % TRYING [5]
% 1.44/0.66 % TRYING [6]
% 1.44/0.66 % (1130024)Instruction limit reached!
% 1.44/0.66 % (1130024)------------------------------
% 1.44/0.66 % (1130024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130024)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130024)Termination reason: Instruction limit
% 1.44/0.66 % (1130024)Termination phase: Saturation
% 1.44/0.66 % (1130024)Time elapsed: 0.059 s
% 1.44/0.66 % (1130024)Peak memory usage: 12 MB
% 1.44/0.66 % (1130024)Instructions burned: 103 (million)
% 1.44/0.66 % (1130025)Instruction limit reached!
% 1.44/0.66 % (1130025)------------------------------
% 1.44/0.66 % (1130025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130025)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130025)Termination reason: Instruction limit
% 1.44/0.66 % (1130025)Termination phase: Saturation
% 1.44/0.66 % (1130025)Time elapsed: 0.064 s
% 1.44/0.66 % (1130025)Peak memory usage: 13 MB
% 1.44/0.66 % (1130025)Instructions burned: 116 (million)
% 1.44/0.66 % (1130026)Instruction limit reached!
% 1.44/0.66 % (1130026)------------------------------
% 1.44/0.66 % (1130026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130026)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130026)Termination reason: Instruction limit
% 1.44/0.66 % (1130026)Termination phase: Saturation
% 1.44/0.66 % (1130026)Time elapsed: 0.074 s
% 1.44/0.66 % (1130026)Peak memory usage: 13 MB
% 1.44/0.66 % (1130026)Instructions burned: 132 (million)
% 1.44/0.66 % (1130035)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4216276360:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.44/0.66 % (1130036)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=917500667:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.44/0.66 % TRYING [1]
% 1.44/0.66 % TRYING [2]
% 1.44/0.66 % TRYING [3]
% 1.44/0.66 % (1130027)Instruction limit reached!
% 1.44/0.66 % (1130027)------------------------------
% 1.44/0.66 % (1130027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130027)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130027)Termination reason: Instruction limit
% 1.44/0.66 % (1130027)Termination phase: Saturation
% 1.44/0.66 % (1130027)Time elapsed: 0.093 s
% 1.44/0.66 % (1130027)Peak memory usage: 15 MB
% 1.44/0.66 % (1130027)Instructions burned: 159 (million)
% 1.44/0.66 % (1130037)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1199289717:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.44/0.66 % TRYING [4]
% 1.44/0.66 % (1130040)ott-21_1_sil=16000:fs=off:random_seed=3207321089:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.44/0.66 % TRYING [5]
% 1.44/0.66 % TRYING [7]
% 1.44/0.66 % (1130036)Instruction limit reached!
% 1.44/0.66 % (1130036)------------------------------
% 1.44/0.66 % (1130036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130036)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130036)Termination reason: Instruction limit
% 1.44/0.66 % (1130036)Termination phase: Saturation
% 1.44/0.66 % (1130036)Time elapsed: 0.063 s
% 1.44/0.66 % (1130036)Peak memory usage: 12 MB
% 1.44/0.66 % (1130036)Instructions burned: 131 (million)
% 1.44/0.66 % (1130043)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=715891304:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.44/0.66 % TRYING [6]
% 1.44/0.66 % (1130040)Instruction limit reached!
% 1.44/0.66 % (1130040)------------------------------
% 1.44/0.66 % (1130040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.66 % (1130040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.66 % (1130040)CaDiCaL version: 2.1.3
% 1.44/0.66 % (1130040)Termination reason: Instruction limit
% 1.44/0.66 % (1130040)Termination phase: Saturation
% 1.44/0.66 % (1130040)Time elapsed: 0.092 s
% 1.44/0.66 % (1130040)Peak memory usage: 13 MB
% 1.44/0.66 % (1130040)Instructions burned: 181 (million)
% 1.44/0.66 % (1130022) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1130016-1130022"...
% 1.44/0.66 % (1130022)...printing done.
% 1.44/0.66 % (1130022)Refutation found. Thanks to Tanya!
% 1.44/0.66 % SZS status Theorem for theBenchmark
% 1.44/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.67 % (1130022)------------------------------
% 1.44/0.67 % (1130022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.67 % (1130022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.67 % (1130022)CaDiCaL version: 2.1.3
% 1.44/0.67 % (1130022)Termination reason: Refutation
% 1.44/0.67 % (1130022)Time elapsed: 0.210 s
% 1.44/0.67 % (1130022)Peak memory usage: 16 MB
% 1.44/0.67 % (1130022)Instructions burned: 382 (million)
% 1.44/0.67 % (1130016)Success in time 0.251 s
% 1.44/0.67 % Vampire exiting
%------------------------------------------------------------------------------