%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG089+2 : 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 : n010.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 12:35:28 PM UTC 2026
% Result : Theorem 2.51s 1.34s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 99 ( 7 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 101 ( 24 ~; 16 |; 49 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 30 ( 22 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,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/sandbox/benchmark/theBenchmark.p',m__870) ).
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/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(f27,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,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,[],[f25]) ).
fof(f33,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(f39,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,[],[f32]) ).
fof(f40,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,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)],[f33]) ).
fof(f73,plain,
! [X3,X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5)
| ~ aElementOf0(X3,xJ) ),
inference(cnf_transformation,[],[f39]) ).
fof(f77,plain,
! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f39]) ).
fof(f80,plain,
aElement0(xz),
inference(cnf_transformation,[],[f64]) ).
fof(f90,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f91,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f97,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f40]) ).
fof(f157,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(resolution,[],[f73,f97]) ).
fof(f160,plain,
( ~ aElementOf0(xl,xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(forward_subsumption_resolution,[],[f157,f80]) ).
fof(f161,plain,
~ aElementOf0(sdtasdt0(xz,xk),xI),
inference(forward_subsumption_resolution,[],[f160,f90]) ).
fof(f162,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI) ),
inference(resolution,[],[f77,f161]) ).
fof(f165,plain,
~ aElementOf0(xk,xI),
inference(forward_subsumption_resolution,[],[f162,f80]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f165,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 23:12:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.51/1.34 % (1411136)Detected formulas, will run a generic FOF schedule.
% 2.51/1.34 % (1411145)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=590416135:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.34 % (1411145)First to succeed.
% 2.51/1.34 % (1411145)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1411136"
% 2.51/1.34 % (1411142)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=2104218588:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.34 % (1411141)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=2766051907:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.34 % (1411143)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=1218834722:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.34 % (1411144)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2183613417:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.34 % (1411146)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2251694480:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.34 % (1411144)Also succeeded, but the first one will report.
% 2.51/1.34 % (1411147)dis-21_1_sil=8000:lcm=predicate:random_seed=2772361260: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)
% 2.51/1.34 % (1411147)Also succeeded, but the first one will report.
% 2.51/1.34 % (1411146)Also succeeded, but the first one will report.
% 2.51/1.34 % (1411145)Refutation found. Thanks to Tanya!
% 2.51/1.34 % SZS status Theorem for theBenchmark
% 2.51/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.34 % (1411145)------------------------------
% 2.51/1.34 % (1411145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.34 % (1411145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.34 % (1411145)CaDiCaL version: 2.1.3
% 2.51/1.34 % (1411145)Termination reason: Refutation
% 2.51/1.34 % (1411145)Time elapsed: 0.002 s
% 2.51/1.34 % (1411145)Peak memory usage: 88 MB
% 2.51/1.34 % (1411145)Instructions burned: 4 (million)
% 2.51/1.34 % (1411145)------------------------------
% 2.51/1.34 % (1411145)------------------------------
% 2.51/1.34 % (1411136)Success in time 0.269 s
% 2.51/1.34 % Vampire exiting
%------------------------------------------------------------------------------