%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG099+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 : n017.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 3.54s 1.47s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 18 unt; 0 def)
% Number of atoms : 134 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 137 ( 49 ~; 40 |; 32 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 42 !; 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(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f28,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(f30,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(f31,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
fof(f32,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(f33,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1332) ).
fof(f34,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(f35,conjecture,
? [X0] :
( aElement0(X0)
& ( aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(X0,xx,xI) )
& ( aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& ( aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(X0,xx,xI) )
& ( aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) ) ) )
& aIdeal0(xJ) ),
inference(rectify,[],[f28]) ).
fof(f42,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ) )
& ! [X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5) ) )
| ~ aElementOf0(X3,xJ) )
& aIdeal0(xJ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f44,plain,
! [X0] :
( ~ aElement0(X0)
| ( ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
& ~ sdteqdtlpzmzozddtrp0(X0,xx,xI) )
| ( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
& ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f52,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f61]) ).
fof(f96,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f42]) ).
fof(f100,plain,
aSet0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f105,plain,
aElement0(xy),
inference(cnf_transformation,[],[f30]) ).
fof(f106,plain,
aElement0(xx),
inference(cnf_transformation,[],[f30]) ).
fof(f108,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f31]) ).
fof(f109,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f31]) ).
fof(f110,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[],[f32]) ).
fof(f111,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f33]) ).
fof(f112,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[],[f34]) ).
fof(f116,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f124,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f137,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f171,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ aElement0(xw) ),
inference(resolution,[],[f112,f116]) ).
fof(f173,plain,
~ aElement0(xw),
inference(forward_subsumption_resolution,[],[f171,f111]) ).
fof(f177,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolution,[],[f121,f109]) ).
fof(f178,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolution,[],[f121,f108]) ).
fof(f183,plain,
aElement0(xb),
inference(forward_subsumption_resolution,[],[f178,f96]) ).
fof(f184,plain,
aElement0(xa),
inference(forward_subsumption_resolution,[],[f177,f100]) ).
fof(f239,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(superposition,[],[f124,f110]) ).
fof(f240,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(forward_subsumption_resolution,[],[f239,f173]) ).
fof(f241,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xy)
| ~ aElement0(xa) ),
inference(resolution,[],[f240,f137]) ).
fof(f242,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xa) ),
inference(forward_subsumption_resolution,[],[f241,f105]) ).
fof(f243,plain,
~ aElement0(sdtasdt0(xx,xb)),
inference(forward_subsumption_resolution,[],[f242,f184]) ).
fof(f250,plain,
( ~ aElement0(xx)
| ~ aElement0(xb) ),
inference(resolution,[],[f243,f137]) ).
fof(f251,plain,
~ aElement0(xb),
inference(forward_subsumption_resolution,[],[f250,f106]) ).
fof(f252,plain,
$false,
inference(forward_subsumption_resolution,[],[f251,f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:10:51 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.54/1.47 % (3059727)Detected formulas, will run a generic FOF schedule.
% 3.54/1.47 % (3059738)dis-21_1_sil=8000:lcm=predicate:random_seed=2249668580: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)
% 3.54/1.47 % (3059738)Instruction limit reached!
% 3.54/1.47 % (3059738)------------------------------
% 3.54/1.47 % (3059738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.47 % (3059738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.47 % (3059738)CaDiCaL version: 2.1.3
% 3.54/1.47 % (3059738)Termination reason: Instruction limit
% 3.54/1.47 % (3059738)Termination phase: Saturation
% 3.54/1.47 % (3059738)Time elapsed: 0.037 s
% 3.54/1.47 % (3059738)Peak memory usage: 90 MB
% 3.54/1.47 % (3059738)Instructions burned: 133 (million)
% 3.54/1.47 % (3059732)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=354764893:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.47 % (3059733)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=129999593:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.47 % (3059734)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=2698054901:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.47 % (3059736)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2948844029:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.47 % (3059737)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1840690010:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.47 % (3059735)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=749572626:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.47 % (3059736)First to succeed.
% 3.54/1.47 % (3059737)Also succeeded, but the first one will report.
% 3.54/1.47 % (3059736)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3059727"
% 3.54/1.47 % (3059735)Also succeeded, but the first one will report.
% 3.54/1.47 % (3059746)lrs+10_1_sil=8000:sp=occurrence:random_seed=973099738:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.54/1.47 % (3059746)Also succeeded, but the first one will report.
% 3.54/1.47 % (3059748)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2983521101:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.54/1.47 % (3059736)Refutation found. Thanks to Tanya!
% 3.54/1.47 % SZS status Theorem for theBenchmark
% 3.54/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.47 % (3059736)------------------------------
% 3.54/1.47 % (3059736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.47 % (3059736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.47 % (3059736)CaDiCaL version: 2.1.3
% 3.54/1.47 % (3059736)Termination reason: Refutation
% 3.54/1.47 % (3059736)Time elapsed: 0.006 s
% 3.54/1.47 % (3059736)Peak memory usage: 88 MB
% 3.54/1.47 % (3059736)Instructions burned: 7 (million)
% 3.54/1.47 % (3059736)------------------------------
% 3.54/1.47 % (3059736)------------------------------
% 3.54/1.47 % (3059727)Success in time 0.418 s
% 3.54/1.47 % Vampire exiting
%------------------------------------------------------------------------------