%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG125+1 : 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 : n003.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 12:35:37 PM UTC 2026
% Result : ContradictoryAxioms 2.72s 1.35s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 18 unt; 5 def)
% Number of atoms : 157 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 154 ( 66 ~; 64 |; 14 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aElement0(X1)
& doDivides0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f46,axiom,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
fof(f47,axiom,
? [X0,X1] :
( aElement0(X0)
& aElement0(X1)
& xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2416) ).
fof(f48,axiom,
doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(f49,axiom,
doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(f59,plain,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(ennf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aElement0(X1)
& doDivides0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f82,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f83,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f82]) ).
fof(f88,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f89,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f88]) ).
fof(f96,plain,
( aElement0(sK3)
& aElement0(sK4)
& xu = sdtpldt0(sdtasdt0(xa,sK3),sdtasdt0(xb,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f47]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aElement0(X1)
| ~ doDivides0(X1,X0) )
& ( ( aElement0(X1)
& doDivides0(X1,X0) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aElement0(X1)
| ~ doDivides0(X1,X0) )
& ( ( aElement0(X1)
& doDivides0(X1,X0) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f116]) ).
fof(f121,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f122,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(cnf_transformation,[],[f59]) ).
fof(f137,plain,
xu = sdtpldt0(sdtasdt0(xa,sK3),sdtasdt0(xb,sK4)),
inference(cnf_transformation,[],[f96]) ).
fof(f138,plain,
aElement0(sK4),
inference(cnf_transformation,[],[f96]) ).
fof(f139,plain,
aElement0(sK3),
inference(cnf_transformation,[],[f96]) ).
fof(f140,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f48]) ).
fof(f141,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f49]) ).
fof(f187,plain,
! [X0,X1] :
( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f194,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f197,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f221,definition,
( spl26_1
<=> aDivisorOf0(xu,xb) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f223,plain,
( ~ aDivisorOf0(xu,xb)
| spl26_1 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f225,definition,
( spl26_2
<=> aDivisorOf0(xu,xa) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f228,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f136,f225,f221]) ).
fof(f239,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa)
| ~ aElement0(xa) ),
inference(resolution,[],[f140,f187]) ).
fof(f240,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa) ),
inference(forward_subsumption_resolution,[],[f239,f122]) ).
fof(f242,definition,
( spl26_5
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[spl26_5])],[avatar_definition]) ).
fof(f243,plain,
( aElement0(xu)
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f244,plain,
( ~ aElement0(xu)
| spl26_5 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,plain,
( spl26_2
| ~ spl26_5 ),
inference(avatar_split_clause,[],[f240,f242,f225]) ).
fof(f246,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xb)
| ~ aElement0(xb) ),
inference(resolution,[],[f141,f187]) ).
fof(f288,plain,
( aElement0(xu)
| ~ aElement0(sdtasdt0(xa,sK3))
| ~ aElement0(sdtasdt0(xb,sK4)) ),
inference(superposition,[],[f194,f137]) ).
fof(f290,plain,
( ~ aElement0(sdtasdt0(xa,sK3))
| ~ aElement0(sdtasdt0(xb,sK4))
| spl26_5 ),
inference(forward_subsumption_resolution,[],[f288,f244]) ).
fof(f292,definition,
( spl26_8
<=> aElement0(sdtasdt0(xb,sK4)) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f294,plain,
( ~ aElement0(sdtasdt0(xb,sK4))
| spl26_8 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl26_9
<=> aElement0(sdtasdt0(xa,sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
fof(f298,plain,
( ~ aElement0(sdtasdt0(xa,sK3))
| spl26_9 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f303,plain,
( ~ spl26_8
| ~ spl26_9
| spl26_5 ),
inference(avatar_split_clause,[],[f290,f242,f296,f292]) ).
fof(f306,plain,
( ~ aElement0(xb)
| ~ aElement0(sK4)
| spl26_8 ),
inference(resolution,[],[f294,f197]) ).
fof(f307,plain,
( ~ aElement0(sK4)
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f306,f121]) ).
fof(f308,plain,
( $false
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f307,f138]) ).
fof(f309,plain,
spl26_8,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f310,plain,
( ~ aElement0(xa)
| ~ aElement0(sK3)
| spl26_9 ),
inference(resolution,[],[f298,f197]) ).
fof(f311,plain,
( ~ aElement0(sK3)
| spl26_9 ),
inference(forward_subsumption_resolution,[],[f310,f122]) ).
fof(f312,plain,
( $false
| spl26_9 ),
inference(forward_subsumption_resolution,[],[f311,f139]) ).
fof(f313,plain,
spl26_9,
inference(avatar_contradiction_clause,[],[f312]) ).
fof(f314,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xb)
| ~ spl26_5 ),
inference(forward_subsumption_resolution,[],[f246,f243]) ).
fof(f316,plain,
( ~ aElement0(xb)
| spl26_1
| ~ spl26_5 ),
inference(forward_subsumption_resolution,[],[f314,f223]) ).
fof(f318,plain,
( $false
| spl26_1
| ~ spl26_5 ),
inference(forward_subsumption_resolution,[],[f316,f121]) ).
fof(f319,plain,
( spl26_1
| ~ spl26_5 ),
inference(avatar_contradiction_clause,[],[f318]) ).
cnf(s1,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
( spl26_2
| ~ spl26_5 ),
inference(sat_conversion,[],[f245]) ).
cnf(s6,plain,
( spl26_5
| ~ spl26_8
| ~ spl26_9 ),
inference(sat_conversion,[],[f303]) ).
cnf(s7,plain,
spl26_8,
inference(sat_conversion,[],[f309]) ).
cnf(s8,plain,
spl26_9,
inference(sat_conversion,[],[f313]) ).
cnf(s9,plain,
( spl26_1
| ~ spl26_5 ),
inference(sat_conversion,[],[f319]) ).
cnf(s11,plain,
spl26_5,
inference(rat,[],[s6,s8,s7]) ).
cnf(s12,plain,
spl26_1,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
spl26_2,
inference(rat,[],[s3,s11]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s12]) ).
fof(f328,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n003.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 23:24:41 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.72/1.35 % (1043212)Detected formulas, will run a generic FOF schedule.
% 2.72/1.35 % (1043257)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1415313937:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.35 % (1043257)First to succeed.
% 2.72/1.35 % (1043257)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1043212"
% 2.72/1.35 % (1043259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1403235121:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.35 % (1043254)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=1966521116:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.35 % (1043255)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=3509911715:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.35 % (1043258)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3640781707:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.35 % (1043256)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=2194431294:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.35 % (1043260)dis-21_1_sil=8000:lcm=predicate:random_seed=3120533313: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)
% 2.72/1.35 % (1043258)Also succeeded, but the first one will report.
% 2.72/1.35 % (1043260)Also succeeded, but the first one will report.
% 2.72/1.35 % (1043259)Also succeeded, but the first one will report.
% 2.72/1.35 % (1043257)Refutation found. Thanks to Tanya!
% 2.72/1.35 % SZS status ContradictoryAxioms for theBenchmark
% 2.72/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.35 % (1043257)------------------------------
% 2.72/1.35 % (1043257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (1043257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (1043257)CaDiCaL version: 2.1.3
% 2.72/1.35 % (1043257)Termination reason: Refutation
% 2.72/1.35 % (1043257)Time elapsed: 0.005 s
% 2.72/1.35 % (1043257)Peak memory usage: 89 MB
% 2.72/1.35 % (1043257)Instructions burned: 9 (million)
% 2.72/1.35 % (1043257)------------------------------
% 2.72/1.35 % (1043257)------------------------------
% 2.72/1.35 % (1043212)Success in time 0.295 s
% 2.72/1.35 % Vampire exiting
%------------------------------------------------------------------------------