%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:15:16 PM UTC 2026
% Result : Theorem 3.43s 1.46s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 10 unt; 3 def)
% Number of atoms : 57 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 17 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f20,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__718) ).
fof(f21,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xm )
| sdtlseqdt0(xm,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xm )
| sdtlseqdt0(xm,xm) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f32,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f53,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xm,X0) )
& ~ sdtlseqdt0(xm,xm) ),
inference(ennf_transformation,[],[f22]) ).
fof(f59,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f67,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f89,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f20]) ).
fof(f91,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xm,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f96,definition,
! [X0,X1] :
( sQ1_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
fof(f100,plain,
! [X0] :
( sQ1_eqProxy(sdtpldt0(X0,sz00),X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f67,f96]) ).
fof(f120,plain,
! [X0] :
( ~ sQ1_eqProxy(xm,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f91,f96]) ).
fof(f122,plain,
! [X0,X1] :
( sQ1_eqProxy(X1,X0)
| ~ sQ1_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f96]) ).
fof(f123,plain,
! [X0] :
( ~ sQ1_eqProxy(sdtpldt0(xm,X0),xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f122,f120]) ).
fof(f126,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[],[f100,f123]) ).
fof(f128,definition,
( spl2_1
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f129,plain,
( ~ aNaturalNumber0(sz00)
| spl2_1 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,definition,
( spl2_2
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f132,plain,
( ~ aNaturalNumber0(xm)
| spl2_2 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f126,f131,f128]) ).
fof(f134,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f129,f59]) ).
fof(f135,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f136,plain,
( $false
| spl2_2 ),
inference(resolution,[],[f132,f89]) ).
fof(f137,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f136]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f133]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f135]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f137]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f138,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 19:58:11 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/1.46 % (1743510)Detected formulas, will run a generic FOF schedule.
% 3.43/1.46 % (1743517)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=1865510033:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.46 % (1743515)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=3252784461:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.46 % (1743516)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=3496598785:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.46 % (1743521)dis-21_1_sil=8000:lcm=predicate:random_seed=4102958790: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)
% 3.43/1.46 % (1743518)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3236957331:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.46 % (1743519)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3828383182:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.46 % (1743520)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2723882319:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.46 % (1743521)First to succeed.
% 3.43/1.46 % (1743520)Also succeeded, but the first one will report.
% 3.43/1.46 % (1743521)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1743510"
% 3.43/1.46 % (1743518)Instruction limit reached!
% 3.43/1.46 % (1743518)------------------------------
% 3.43/1.46 % (1743518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.46 % (1743518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.46 % (1743518)CaDiCaL version: 2.1.3
% 3.43/1.46 % (1743518)Termination reason: Instruction limit
% 3.43/1.46 % (1743518)Termination phase: Saturation
% 3.43/1.46 % (1743518)Time elapsed: 0.066 s
% 3.43/1.46 % (1743518)Peak memory usage: 89 MB
% 3.43/1.46 % (1743518)Instructions burned: 111 (million)
% 3.43/1.46 % (1743519)Instruction limit reached!
% 3.43/1.46 % (1743519)------------------------------
% 3.43/1.46 % (1743519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.46 % (1743519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.46 % (1743519)CaDiCaL version: 2.1.3
% 3.43/1.46 % (1743519)Termination reason: Instruction limit
% 3.43/1.46 % (1743519)Termination phase: Saturation
% 3.43/1.46 % (1743519)Time elapsed: 0.066 s
% 3.43/1.46 % (1743519)Peak memory usage: 88 MB
% 3.43/1.46 % (1743519)Instructions burned: 120 (million)
% 3.43/1.46 % (1743529)lrs+10_1_sil=8000:sp=occurrence:random_seed=3333619864:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.43/1.46 % (1743530)lrs+10_1_sil=32000:urr=on:br=off:random_seed=115257873:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.43/1.46 % (1743521)Refutation found. Thanks to Tanya!
% 3.43/1.46 % SZS status Theorem for theBenchmark
% 3.43/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.46 % (1743521)------------------------------
% 3.43/1.46 % (1743521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.46 % (1743521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.46 % (1743521)CaDiCaL version: 2.1.3
% 3.43/1.46 % (1743521)Termination reason: Refutation
% 3.43/1.46 % (1743521)Time elapsed: 0.003 s
% 3.43/1.46 % (1743521)Peak memory usage: 89 MB
% 3.43/1.46 % (1743521)Instructions burned: 2 (million)
% 3.43/1.46 % (1743521)------------------------------
% 3.43/1.46 % (1743521)------------------------------
% 3.43/1.46 % (1743510)Success in time 0.401 s
% 3.43/1.46 % Vampire exiting
%------------------------------------------------------------------------------