%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG125+4 : 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 : n019.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 2.50s 1.26s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 1 def)
% Number of atoms : 71 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 88 ( 37 ~; 21 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 6 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
~ ( ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xa )
| doDivides0(xu,xa)
| aDivisorOf0(xu,xa) )
& ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xb )
| doDivides0(xu,xb)
| aDivisorOf0(xu,xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2383) ).
fof(f48,axiom,
~ ~ ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xa )
& doDivides0(xu,xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).
fof(f49,axiom,
~ ~ ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xb )
& doDivides0(xu,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
fof(f57,plain,
~ ( ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xa )
| doDivides0(xu,xa)
| aDivisorOf0(xu,xa) )
& ( ? [X1] :
( aElement0(X1)
& xb = sdtasdt0(xu,X1) )
| doDivides0(xu,xb)
| aDivisorOf0(xu,xb) ) ),
inference(rectify,[],[f46]) ).
fof(f58,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xa )
& doDivides0(xu,xa) ),
inference(flattening,[],[f48]) ).
fof(f59,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xb )
& doDivides0(xu,xb) ),
inference(flattening,[],[f49]) ).
fof(f73,plain,
( ( ! [X0] :
( ~ aElement0(X0)
| xa != sdtasdt0(xu,X0) )
& ~ doDivides0(xu,xa)
& ~ aDivisorOf0(xu,xa) )
| ( ! [X1] :
( ~ aElement0(X1)
| xb != sdtasdt0(xu,X1) )
& ~ doDivides0(xu,xb)
& ~ aDivisorOf0(xu,xb) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f112,definition,
( ( ! [X1] :
( ~ aElement0(X1)
| xb != sdtasdt0(xu,X1) )
& ~ doDivides0(xu,xb)
& ~ aDivisorOf0(xu,xb) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f113,plain,
( ( ! [X0] :
( ~ aElement0(X0)
| xa != sdtasdt0(xu,X0) )
& ~ doDivides0(xu,xa)
& ~ aDivisorOf0(xu,xa) )
| sP2 ),
inference(definition_folding,[],[f73,f112]) ).
fof(f131,plain,
( ( ! [X1] :
( ~ aElement0(X1)
| xb != sdtasdt0(xu,X1) )
& ~ doDivides0(xu,xb)
& ~ aDivisorOf0(xu,xb) )
| ~ sP2 ),
inference(nnf_transformation,[],[f112]) ).
fof(f132,plain,
( ( ! [X0] :
( ~ aElement0(X0)
| xb != sdtasdt0(xu,X0) )
& ~ doDivides0(xu,xb)
& ~ aDivisorOf0(xu,xb) )
| ~ sP2 ),
inference(rectify,[],[f131]) ).
fof(f134,plain,
( aElement0(sK25)
& xa = sdtasdt0(xu,sK25)
& doDivides0(xu,xa) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X0,sK25)],[f58]) ).
fof(f135,plain,
( aElement0(sK26)
& xb = sdtasdt0(xu,sK26)
& doDivides0(xu,xb) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X0,sK26)],[f59]) ).
fof(f230,plain,
( ~ doDivides0(xu,xb)
| ~ sP2 ),
inference(cnf_transformation,[],[f132]) ).
fof(f233,plain,
( ~ doDivides0(xu,xa)
| sP2 ),
inference(cnf_transformation,[],[f113]) ).
fof(f238,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[],[f134]) ).
fof(f241,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[],[f135]) ).
fof(f322,plain,
sP2,
inference(forward_subsumption_resolution,[],[f233,f238]) ).
fof(f324,plain,
~ sP2,
inference(forward_subsumption_resolution,[],[f230,f241]) ).
fof(f325,plain,
$false,
inference(forward_subsumption_resolution,[],[f324,f322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG125+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:23:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.50/1.26 % (3520341)Detected formulas, will run a generic FOF schedule.
% 2.50/1.26 % (3520350)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=838241685:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.26 % (3520350)First to succeed.
% 2.50/1.26 % (3520350)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3520341"
% 2.50/1.26 % (3520346)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=397702593:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.26 % (3520348)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=1282131184:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.26 % (3520349)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2910139138:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.26 % (3520347)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=87142686:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.26 % (3520349)Also succeeded, but the first one will report.
% 2.50/1.26 % (3520351)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3608252031:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.26 % (3520352)dis-21_1_sil=8000:lcm=predicate:random_seed=748791642: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)
% 2.50/1.26 % (3520352)Also succeeded, but the first one will report.
% 2.50/1.26 % (3520351)Also succeeded, but the first one will report.
% 2.50/1.26 % (3520350)Refutation found. Thanks to Tanya!
% 2.50/1.26 % SZS status ContradictoryAxioms for theBenchmark
% 2.50/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.27 % (3520350)------------------------------
% 2.50/1.27 % (3520350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.27 % (3520350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.27 % (3520350)CaDiCaL version: 2.1.3
% 2.50/1.27 % (3520350)Termination reason: Refutation
% 2.50/1.27 % (3520350)Time elapsed: 0.003 s
% 2.50/1.27 % (3520350)Peak memory usage: 88 MB
% 2.50/1.27 % (3520350)Instructions burned: 6 (million)
% 2.50/1.27 % (3520350)------------------------------
% 2.50/1.27 % (3520350)------------------------------
% 2.50/1.27 % (3520341)Success in time 0.284 s
% 2.50/1.27 % Vampire exiting
%------------------------------------------------------------------------------