%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG101+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 : n013.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 12:35:31 PM UTC 2026
% Result : Theorem 2.58s 1.25s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 35 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 31 ( 8 ~; 3 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 2 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xy )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
fof(f40,conjecture,
? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( aElement0(X1)
& xy = sdtasdt0(xc,X1) )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(rectify,[],[f39]) ).
fof(f46,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(xc,X0) != xx ),
inference(ennf_transformation,[],[f41]) ).
fof(f57,plain,
( aElement0(sK0)
& xx = sdtasdt0(xc,sK0)
& aElementOf0(xx,slsdtgt0(xc))
& aElement0(sK1)
& xy = sdtasdt0(xc,sK1)
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f42]) ).
fof(f69,plain,
xx = sdtasdt0(xc,sK0),
inference(cnf_transformation,[],[f57]) ).
fof(f70,plain,
aElement0(sK0),
inference(cnf_transformation,[],[f57]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(xc,X0) != xx
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f94,plain,
( xx != xx
| ~ aElement0(sK0) ),
inference(superposition,[],[f71,f69]) ).
fof(f95,plain,
~ aElement0(sK0),
inference(trivial_inequality_removal,[],[f94]) ).
fof(f96,plain,
$false,
inference(forward_subsumption_resolution,[],[f95,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG101+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.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 23:15:37 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.58/1.25 % (656269)Detected formulas, will run a generic FOF schedule.
% 2.58/1.25 % (656278)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1942664670:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.25 % (656278)First to succeed.
% 2.58/1.25 % (656278)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-656269"
% 2.58/1.25 % (656274)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=3679599033:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.25 % (656276)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=2547700322:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.25 % (656275)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=544354726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.25 % (656277)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=738259219:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.25 % (656280)dis-21_1_sil=8000:lcm=predicate:random_seed=2771905981: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)
% 2.58/1.25 % (656277)Also succeeded, but the first one will report.
% 2.58/1.25 % (656280)Also succeeded, but the first one will report.
% 2.58/1.25 % (656279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4098738972:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.25 % (656279)Also succeeded, but the first one will report.
% 2.58/1.25 % (656278)Refutation found. Thanks to Tanya!
% 2.58/1.25 % SZS status Theorem for theBenchmark
% 2.58/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.25 % (656278)------------------------------
% 2.58/1.25 % (656278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.25 % (656278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.25 % (656278)CaDiCaL version: 2.1.3
% 2.58/1.25 % (656278)Termination reason: Refutation
% 2.58/1.25 % (656278)Time elapsed: 0.001 s
% 2.58/1.25 % (656278)Peak memory usage: 88 MB
% 2.58/1.25 % (656278)Instructions burned: 1 (million)
% 2.58/1.25 % (656278)------------------------------
% 2.58/1.25 % (656278)------------------------------
% 2.58/1.25 % (656269)Success in time 0.303 s
% 2.58/1.25 % Vampire exiting
%------------------------------------------------------------------------------