%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG102+1 : 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 : n019.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 2.41s 1.23s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 7 unt; 1 def)
% Number of atoms : 125 ( 36 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 160 ( 62 ~; 61 |; 32 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 41 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f41,conjecture,
? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xy ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,plain,
! [X0] :
( ~ aElement0(X0)
| xy != sdtasdt0(xc,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK0(X0,X1) )
| ~ aElementOf0(sK0(X0,X1),X1) )
& ( ( aElement0(sK1(X0,X1))
& sK0(X0,X1) = sdtasdt0(X0,sK1(X0,X1)) )
| aElementOf0(sK0(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK2(X0,X5))
& sdtasdt0(X0,sK2(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f54]) ).
fof(f56,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f58,plain,
aElementOf0(xy,slsdtgt0(xc)),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
! [X0] :
( ~ aElement0(X0)
| xy != sdtasdt0(xc,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK2(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f64,plain,
! [X0,X1,X5] :
( aElement0(sK2(X0,X5))
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f73,definition,
~ sP3(xy),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f74,plain,
! [X0] :
( sP3(sdtasdt0(xc,X0))
| ~ aElement0(X0) ),
inference(inequality_splitting,[],[f62,f73]) ).
fof(f78,plain,
! [X0,X5] :
( ~ aElementOf0(X5,slsdtgt0(X0))
| aElement0(sK2(X0,X5))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f64]) ).
fof(f79,plain,
! [X0,X5] :
( sdtasdt0(X0,sK2(X0,X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f63]) ).
fof(f81,plain,
! [X0] :
( sP3(X0)
| ~ aElement0(sK2(xc,X0))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(superposition,[],[f74,f79]) ).
fof(f88,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElement0(sK2(xc,X0))
| sP3(X0) ),
inference(forward_subsumption_resolution,[],[f81,f56]) ).
fof(f111,plain,
( ~ aElement0(sK2(xc,xy))
| sP3(xy) ),
inference(resolution,[],[f58,f88]) ).
fof(f112,plain,
( aElement0(sK2(xc,xy))
| ~ aElement0(xc) ),
inference(resolution,[],[f58,f78]) ).
fof(f113,plain,
aElement0(sK2(xc,xy)),
inference(forward_subsumption_resolution,[],[f112,f56]) ).
fof(f114,plain,
~ aElement0(sK2(xc,xy)),
inference(forward_subsumption_resolution,[],[f111,f73]) ).
fof(f115,plain,
$false,
inference(forward_subsumption_resolution,[],[f114,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG102+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:16:19 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.41/1.23 % (3516262)Detected formulas, will run a generic FOF schedule.
% 2.41/1.23 % (3516270)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2756987773:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.41/1.23 % (3516270)First to succeed.
% 2.41/1.23 % (3516270)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3516262"
% 2.41/1.23 % (3516269)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=3167832947:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.41/1.23 % (3516271)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1254552411:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.41/1.23 % (3516271)Also succeeded, but the first one will report.
% 2.41/1.23 % (3516268)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=1853079036:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.41/1.23 % (3516267)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=2519205083:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.41/1.23 % (3516272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2457435658:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.41/1.23 % (3516273)dis-21_1_sil=8000:lcm=predicate:random_seed=4095288226: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)
% 2.41/1.23 % (3516273)Also succeeded, but the first one will report.
% 2.41/1.23 % (3516272)Also succeeded, but the first one will report.
% 2.41/1.23 % (3516270)Refutation found. Thanks to Tanya!
% 2.41/1.23 % SZS status Theorem for theBenchmark
% 2.41/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/1.23 % (3516270)------------------------------
% 2.41/1.23 % (3516270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.23 % (3516270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.23 % (3516270)CaDiCaL version: 2.1.3
% 2.41/1.23 % (3516270)Termination reason: Refutation
% 2.41/1.23 % (3516270)Time elapsed: 0.002 s
% 2.41/1.23 % (3516270)Peak memory usage: 89 MB
% 2.41/1.23 % (3516270)Instructions burned: 3 (million)
% 2.41/1.23 % (3516270)------------------------------
% 2.41/1.23 % (3516270)------------------------------
% 2.41/1.23 % (3516262)Success in time 0.27 s
% 2.41/1.23 % Vampire exiting
%------------------------------------------------------------------------------