%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG086+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 : n009.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 12:35:27 PM UTC 2026
% Result : Theorem 2.69s 1.33s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 1 def)
% Number of atoms : 51 ( 11 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 49 ( 14 ~; 7 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 18 ( 6 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xy )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f27,conjecture,
? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& xx = sdtpldt0(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& xx = sdtpldt0(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& xy = sdtpldt0(X2,X3) )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(rectify,[],[f26]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xx ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
( aElementOf0(sK2,xI)
& aElementOf0(sK3,xJ)
& xx = sdtpldt0(sK2,sK3)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(sK4,xI)
& aElementOf0(sK5,xJ)
& xy = sdtpldt0(sK4,sK5)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f30]) ).
fof(f83,plain,
xx = sdtpldt0(sK2,sK3),
inference(cnf_transformation,[],[f61]) ).
fof(f84,plain,
aElementOf0(sK3,xJ),
inference(cnf_transformation,[],[f61]) ).
fof(f85,plain,
aElementOf0(sK2,xI),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xx ),
inference(cnf_transformation,[],[f37]) ).
fof(f115,definition,
~ sP13(xx),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f116,plain,
! [X0,X1] :
( sP13(sdtpldt0(X0,X1))
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(inequality_splitting,[],[f86,f115]) ).
fof(f264,plain,
~ sP13(sdtpldt0(sK2,sK3)),
inference(superposition,[],[f115,f83]) ).
fof(f266,plain,
( ~ aElementOf0(sK3,xJ)
| ~ aElementOf0(sK2,xI) ),
inference(resolution,[],[f264,f116]) ).
fof(f267,plain,
~ aElementOf0(sK2,xI),
inference(forward_subsumption_resolution,[],[f266,f84]) ).
fof(f269,plain,
$false,
inference(forward_subsumption_resolution,[],[f267,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG086+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 23:12:00 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.69/1.33 % (2513454)Detected formulas, will run a generic FOF schedule.
% 2.69/1.33 % (2513462)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2954676106:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.33 % (2513462)First to succeed.
% 2.69/1.33 % (2513462)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2513454"
% 2.69/1.33 % (2513465)dis-21_1_sil=8000:lcm=predicate:random_seed=1942687386: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)
% 2.69/1.33 % (2513460)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=4095011661:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.33 % (2513464)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3426537685:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.33 % (2513461)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=2461818782:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.33 % (2513459)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=403714497:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.33 % (2513463)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1324763253:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.33 % (2513463)Also succeeded, but the first one will report.
% 2.69/1.33 % (2513464)Also succeeded, but the first one will report.
% 2.69/1.33 % (2513465)Also succeeded, but the first one will report.
% 2.69/1.33 % (2513462)Refutation found. Thanks to Tanya!
% 2.69/1.33 % SZS status Theorem for theBenchmark
% 2.69/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.33 % (2513462)------------------------------
% 2.69/1.33 % (2513462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.33 % (2513462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.33 % (2513462)CaDiCaL version: 2.1.3
% 2.69/1.33 % (2513462)Termination reason: Refutation
% 2.69/1.33 % (2513462)Time elapsed: 0.004 s
% 2.69/1.33 % (2513462)Peak memory usage: 89 MB
% 2.69/1.33 % (2513462)Instructions burned: 9 (million)
% 2.69/1.33 % (2513462)------------------------------
% 2.69/1.33 % (2513462)------------------------------
% 2.69/1.33 % (2513454)Success in time 0.294 s
% 2.69/1.33 % Vampire exiting
%------------------------------------------------------------------------------