%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n004.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 12:15:21 PM UTC 2026
% Result : Theorem 3.94s 1.53s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 28 unt; 8 def)
% Number of atoms : 154 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 149 ( 67 ~; 60 |; 11 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% 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(f37,axiom,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
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(f47,plain,
xn != sdtasdt0(xl,xr),
inference(flattening,[],[f43]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f66,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(f67,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,[],[f66]) ).
fof(f117,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f131,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f167,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f169,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f179,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f37]) ).
fof(f188,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f40]) ).
fof(f189,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f41]) ).
fof(f190,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[],[f47]) ).
fof(f201,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ sQ5_eqProxy(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| sQ5_eqProxy(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(equality_proxy_replacement,[],[f131,f201,f201]) ).
fof(f251,plain,
sQ5_eqProxy(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
inference(equality_proxy_replacement,[],[f189,f201]) ).
fof(f252,plain,
~ sQ5_eqProxy(xn,sdtasdt0(xl,xr)),
inference(equality_proxy_replacement,[],[f190,f201]) ).
fof(f254,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f201]) ).
fof(f270,plain,
~ sQ5_eqProxy(sdtasdt0(xl,xr),xn),
inference(resolution,[],[f254,f252]) ).
fof(f285,definition,
( spl6_5
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f286,plain,
( ~ aNaturalNumber0(xp)
| spl6_5 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f293,plain,
( $false
| spl6_5 ),
inference(resolution,[],[f286,f179]) ).
fof(f294,plain,
spl6_5,
inference(avatar_contradiction_clause,[],[f293]) ).
fof(f301,definition,
( spl6_8
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f302,plain,
( ~ aNaturalNumber0(xl)
| spl6_8 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f314,plain,
( $false
| spl6_8 ),
inference(resolution,[],[f302,f169]) ).
fof(f315,plain,
spl6_8,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f320,definition,
( spl6_12
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
fof(f321,plain,
( ~ aNaturalNumber0(xn)
| spl6_12 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f323,plain,
( $false
| spl6_12 ),
inference(resolution,[],[f321,f167]) ).
fof(f324,plain,
spl6_12,
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f392,definition,
( spl6_16
<=> aNaturalNumber0(sdtasdt0(xl,xr)) ),
introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition]) ).
fof(f393,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| spl6_16 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f431,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr)
| spl6_16 ),
inference(resolution,[],[f393,f117]) ).
fof(f433,definition,
( spl6_26
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[spl6_26])],[avatar_definition]) ).
fof(f434,plain,
( ~ aNaturalNumber0(xr)
| spl6_26 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f435,plain,
( ~ spl6_26
| ~ spl6_8
| spl6_16 ),
inference(avatar_split_clause,[],[f431,f392,f301,f433]) ).
fof(f436,plain,
( $false
| spl6_26 ),
inference(resolution,[],[f434,f188]) ).
fof(f437,plain,
spl6_26,
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f2805,plain,
( sQ5_eqProxy(sdtasdt0(xl,xr),xn)
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f215,f251]) ).
fof(f2818,definition,
( spl6_286
<=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
introduced(definition,[new_symbols(definition,[spl6_286])],[avatar_definition]) ).
fof(f2819,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xp))
| spl6_286 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f2821,definition,
( spl6_287
<=> sQ5_eqProxy(sdtasdt0(xl,xr),xn) ),
introduced(definition,[new_symbols(definition,[spl6_287])],[avatar_definition]) ).
fof(f2822,plain,
( sQ5_eqProxy(sdtasdt0(xl,xr),xn)
| ~ spl6_287 ),
inference(avatar_component_clause,[],[f2821]) ).
fof(f2823,plain,
( ~ spl6_12
| ~ spl6_16
| ~ spl6_286
| spl6_287 ),
inference(avatar_split_clause,[],[f2805,f2821,f2818,f392,f320]) ).
fof(f2824,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| spl6_286 ),
inference(resolution,[],[f2819,f117]) ).
fof(f2825,plain,
( ~ spl6_5
| ~ spl6_8
| spl6_286 ),
inference(avatar_split_clause,[],[f2824,f2818,f301,f285]) ).
fof(f2826,plain,
( $false
| ~ spl6_287 ),
inference(resolution,[],[f2822,f270]) ).
fof(f2827,plain,
~ spl6_287,
inference(avatar_contradiction_clause,[],[f2826]) ).
cnf(s6,plain,
spl6_5,
inference(sat_conversion,[],[f294]) ).
cnf(s9,plain,
spl6_8,
inference(sat_conversion,[],[f315]) ).
cnf(s12,plain,
spl6_12,
inference(sat_conversion,[],[f324]) ).
cnf(s26,plain,
( ~ spl6_8
| spl6_16
| ~ spl6_26 ),
inference(sat_conversion,[],[f435]) ).
cnf(s27,plain,
spl6_26,
inference(sat_conversion,[],[f437]) ).
cnf(s486,plain,
( ~ spl6_12
| ~ spl6_16
| ~ spl6_286
| spl6_287 ),
inference(sat_conversion,[],[f2823]) ).
cnf(s487,plain,
( ~ spl6_5
| ~ spl6_8
| spl6_286 ),
inference(sat_conversion,[],[f2825]) ).
cnf(s488,plain,
~ spl6_287,
inference(sat_conversion,[],[f2827]) ).
cnf(s489,plain,
( ~ spl6_12
| ~ spl6_16
| ~ spl6_286 ),
inference(rat,[],[s486,s488]) ).
cnf(s495,plain,
( ~ spl6_8
| spl6_16 ),
inference(rat,[],[s26,s27]) ).
cnf(s538,plain,
spl6_16,
inference(rat,[],[s495,s9]) ).
cnf(s577,plain,
~ spl6_286,
inference(rat,[],[s489,s12,s538]) ).
cnf(s585,plain,
~ spl6_5,
inference(rat,[],[s487,s9,s577]) ).
cnf(s588,plain,
$false,
inference(rat,[],[s6,s585]) ).
fof(f2828,plain,
$false,
inference(avatar_sat_refutation,[],[s588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:05:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.94/1.53 % (3845876)Detected formulas, will run a generic FOF schedule.
% 3.94/1.53 % (3845884)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3180999701:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.94/1.53 % (3845884)Instruction limit reached!
% 3.94/1.53 % (3845884)------------------------------
% 3.94/1.53 % (3845884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.53 % (3845884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.53 % (3845884)CaDiCaL version: 2.1.3
% 3.94/1.53 % (3845884)Termination reason: Instruction limit
% 3.94/1.53 % (3845884)Termination phase: Saturation
% 3.94/1.53 % (3845884)Time elapsed: 0.033 s
% 3.94/1.53 % (3845884)Peak memory usage: 89 MB
% 3.94/1.53 % (3845884)Instructions burned: 110 (million)
% 3.94/1.53 % (3845885)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2992085735:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.94/1.53 % (3845883)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=1598618448:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.94/1.53 % (3845882)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=2698147440:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.94/1.53 % (3845881)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=1818051902:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.94/1.53 % (3845887)dis-21_1_sil=8000:lcm=predicate:random_seed=3515269325: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)
% 3.94/1.53 % (3845886)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3707362191:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.94/1.53 % (3845887)First to succeed.
% 3.94/1.53 % (3845887)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3845876"
% 3.94/1.53 % (3845886)Also succeeded, but the first one will report.
% 3.94/1.53 % (3845885)Instruction limit reached!
% 3.94/1.53 % (3845885)------------------------------
% 3.94/1.53 % (3845885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.53 % (3845885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.53 % (3845885)CaDiCaL version: 2.1.3
% 3.94/1.53 % (3845885)Termination reason: Instruction limit
% 3.94/1.53 % (3845885)Termination phase: Saturation
% 3.94/1.53 % (3845885)Time elapsed: 0.068 s
% 3.94/1.53 % (3845885)Peak memory usage: 88 MB
% 3.94/1.53 % (3845885)Instructions burned: 121 (million)
% 3.94/1.53 % (3845889)lrs+10_1_sil=8000:sp=occurrence:random_seed=2858201667:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.94/1.53 % (3845889)Also succeeded, but the first one will report.
% 3.94/1.53 % (3845896)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3725073352:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.94/1.53 % (3845887)Refutation found. Thanks to Tanya!
% 3.94/1.53 % SZS status Theorem for theBenchmark
% 3.94/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.53 % (3845887)------------------------------
% 3.94/1.53 % (3845887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.53 % (3845887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.53 % (3845887)CaDiCaL version: 2.1.3
% 3.94/1.53 % (3845887)Termination reason: Refutation
% 3.94/1.53 % (3845887)Time elapsed: 0.035 s
% 3.94/1.53 % (3845887)Peak memory usage: 90 MB
% 3.94/1.53 % (3845887)Instructions burned: 51 (million)
% 3.94/1.53 % (3845887)------------------------------
% 3.94/1.53 % (3845887)------------------------------
% 3.94/1.53 % (3845876)Success in time 0.47 s
% 3.94/1.53 % Vampire exiting
%------------------------------------------------------------------------------