%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG089+1 : 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 12:35:28 PM UTC 2026
% Result : Theorem 2.65s 1.34s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 70 ( 1 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 28 ~; 18 |; 15 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f25,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f26,axiom,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f27,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/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,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f36,plain,
! [X0] :
( aIdeal0(X0)
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f37,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0] :
( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f68,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f69,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
fof(f70,plain,
aElement0(xz),
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f75,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f81,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f37]) ).
fof(f82,plain,
! [X3,X0,X1] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f141,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(resolution,[],[f82,f81]) ).
fof(f148,plain,
( ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(forward_subsumption_resolution,[],[f141,f70]) ).
fof(f149,plain,
( ~ aIdeal0(xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(forward_subsumption_resolution,[],[f148,f74]) ).
fof(f150,plain,
~ aElementOf0(sdtasdt0(xz,xk),xI),
inference(forward_subsumption_resolution,[],[f149,f68]) ).
fof(f151,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[],[f150,f82]) ).
fof(f152,plain,
( ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI) ),
inference(forward_subsumption_resolution,[],[f151,f70]) ).
fof(f153,plain,
~ aIdeal0(xI),
inference(forward_subsumption_resolution,[],[f152,f75]) ).
fof(f154,plain,
$false,
inference(forward_subsumption_resolution,[],[f153,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:12:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.65/1.34 % (2514284)Detected formulas, will run a generic FOF schedule.
% 2.65/1.34 % (2514293)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3899321449:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.34 % (2514293)First to succeed.
% 2.65/1.34 % (2514293)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2514284"
% 2.65/1.34 % (2514292)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3400886415:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.34 % (2514289)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=2052667301:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.34 % (2514290)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=1419321227:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.34 % (2514291)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=1950480991:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.34 % (2514295)dis-21_1_sil=8000:lcm=predicate:random_seed=2318892059: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)
% 2.65/1.34 % (2514294)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1671913172:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.34 % (2514292)Also succeeded, but the first one will report.
% 2.65/1.34 % (2514295)Also succeeded, but the first one will report.
% 2.65/1.34 % (2514294)Also succeeded, but the first one will report.
% 2.65/1.34 % (2514293)Refutation found. Thanks to Tanya!
% 2.65/1.34 % SZS status Theorem for theBenchmark
% 2.65/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.34 % (2514293)------------------------------
% 2.65/1.34 % (2514293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2514293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2514293)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2514293)Termination reason: Refutation
% 2.65/1.34 % (2514293)Time elapsed: 0.002 s
% 2.65/1.34 % (2514293)Peak memory usage: 88 MB
% 2.65/1.34 % (2514293)Instructions burned: 4 (million)
% 2.65/1.34 % (2514293)------------------------------
% 2.65/1.34 % (2514293)------------------------------
% 2.65/1.34 % (2514284)Success in time 0.292 s
% 2.65/1.34 % Vampire exiting
%------------------------------------------------------------------------------