%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG105+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 : n016.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 12:35:32 PM UTC 2026
% Result : Theorem 2.78s 1.37s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 106 ( 26 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 116 ( 45 ~; 36 |; 33 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 22 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f40,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1979) ).
fof(f42,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
fof(f43,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2043) ).
fof(f44,conjecture,
( ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) )
& ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) )
& ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,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(f47,plain,
~ ( ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xz,xx) = sdtasdt0(xc,X1) )
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ) ),
inference(rectify,[],[f45]) ).
fof(f51,plain,
( ( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(xc,X0) != sdtpldt0(xx,xy) )
& ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) )
| ( ! [X1] :
( ~ aElement0(X1)
| sdtasdt0(xz,xx) != sdtasdt0(xc,X1) )
& ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f56]) ).
fof(f65,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f66,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f65]) ).
fof(f70,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)],[f46]) ).
fof(f77,plain,
aElement0(xz),
inference(cnf_transformation,[],[f70]) ).
fof(f85,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f87,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f88,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f42]) ).
fof(f89,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f43]) ).
fof(f93,plain,
! [X0,X1] :
( sdtasdt0(xz,xx) != sdtasdt0(xc,X1)
| sdtasdt0(xc,X0) != sdtpldt0(xx,xy)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f96,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f108,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f172,plain,
! [X0] :
( sdtasdt0(xz,xx) != sdtasdt0(xz,xx)
| sdtasdt0(xc,X0) != sdtpldt0(xx,xy)
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(X0) ),
inference(superposition,[],[f93,f89]) ).
fof(f177,plain,
! [X0] :
( sdtasdt0(xc,X0) != sdtpldt0(xx,xy)
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(X0) ),
inference(trivial_inequality_removal,[],[f172]) ).
fof(f188,plain,
( sdtpldt0(xx,xy) != sdtpldt0(xx,xy)
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(superposition,[],[f177,f88]) ).
fof(f195,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(trivial_inequality_removal,[],[f188]) ).
fof(f200,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| ~ aElement0(xu)
| ~ aElement0(xz) ),
inference(resolution,[],[f195,f96]) ).
fof(f201,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| ~ aElement0(xz) ),
inference(forward_subsumption_resolution,[],[f200,f85]) ).
fof(f202,plain,
~ aElement0(sdtpldt0(xu,xv)),
inference(forward_subsumption_resolution,[],[f201,f77]) ).
fof(f203,plain,
( ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(resolution,[],[f202,f108]) ).
fof(f204,plain,
~ aElement0(xv),
inference(forward_subsumption_resolution,[],[f203,f85]) ).
fof(f205,plain,
$false,
inference(forward_subsumption_resolution,[],[f204,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.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 23:22:29 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
% 2.78/1.37 % (3104478)Detected formulas, will run a generic FOF schedule.
% 2.78/1.37 % (3104487)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=642686748:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.37 % (3104487)First to succeed.
% 2.78/1.37 % (3104487)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3104478"
% 2.78/1.37 % (3104484)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=4281609595:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.37 % (3104483)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=3825366076:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.37 % (3104489)dis-21_1_sil=8000:lcm=predicate:random_seed=3185047953: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)
% 2.78/1.37 % (3104485)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=2240519015:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.37 % (3104488)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2938380791:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.37 % (3104486)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=604335524:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.37 % (3104486)Also succeeded, but the first one will report.
% 2.78/1.37 % (3104489)Also succeeded, but the first one will report.
% 2.78/1.37 % (3104488)Also succeeded, but the first one will report.
% 2.78/1.37 % (3104487)Refutation found. Thanks to Tanya!
% 2.78/1.37 % SZS status Theorem for theBenchmark
% 2.78/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.37 % (3104487)------------------------------
% 2.78/1.37 % (3104487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (3104487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (3104487)CaDiCaL version: 2.1.3
% 2.78/1.37 % (3104487)Termination reason: Refutation
% 2.78/1.37 % (3104487)Time elapsed: 0.003 s
% 2.78/1.37 % (3104487)Peak memory usage: 88 MB
% 2.78/1.37 % (3104487)Instructions burned: 6 (million)
% 2.78/1.37 % (3104487)------------------------------
% 2.78/1.37 % (3104487)------------------------------
% 2.78/1.37 % (3104478)Success in time 0.315 s
% 2.78/1.37 % Vampire exiting
%------------------------------------------------------------------------------