%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG101+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 : n017.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 3.44s 1.37s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 122 ( 38 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 162 ( 65 ~; 60 |; 32 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 40 !; 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/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f39,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
fof(f40,conjecture,
? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& sdtasdt0(xc,X0) = xx ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f45,plain,
! [X0] :
( ~ aElement0(X0)
| xx != sdtasdt0(xc,X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f46,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(f56,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,[],[f46]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f57]) ).
fof(f59,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))],[f58]) ).
fof(f61,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0] :
( xx != sdtasdt0(xc,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK2(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f67,plain,
! [X0,X1,X5] :
( aElement0(sK2(X0,X5))
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f84,plain,
! [X0,X5] :
( aElement0(sK2(X0,X5))
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f85,plain,
! [X0,X5] :
( sdtasdt0(X0,sK2(X0,X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f66]) ).
fof(f111,plain,
! [X0] :
( xx != X0
| ~ aElement0(sK2(xc,X0))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(superposition,[],[f65,f85]) ).
fof(f117,plain,
! [X0] :
( xx != X0
| ~ aElement0(sK2(xc,X0))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f111,f61]) ).
fof(f120,plain,
( ~ aElement0(sK2(xc,xx))
| ~ aElementOf0(xx,slsdtgt0(xc)) ),
inference(equality_resolution,[],[f117]) ).
fof(f121,plain,
~ aElement0(sK2(xc,xx)),
inference(forward_subsumption_resolution,[],[f120,f64]) ).
fof(f122,plain,
( ~ aElementOf0(xx,slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(resolution,[],[f121,f84]) ).
fof(f123,plain,
~ aElement0(xc),
inference(forward_subsumption_resolution,[],[f122,f64]) ).
fof(f124,plain,
$false,
inference(forward_subsumption_resolution,[],[f123,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG101+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 23:11:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.44/1.37 % (3060145)Detected formulas, will run a generic FOF schedule.
% 3.44/1.37 % (3060150)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=795877323:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.37 % (3060156)dis-21_1_sil=8000:lcm=predicate:random_seed=1978142581: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)
% 3.44/1.37 % (3060153)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1388208764:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.37 % (3060151)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=1110989136:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.37 % (3060152)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=78514104:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.37 % (3060155)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=200581430:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.37 % (3060154)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=844351742:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.37 % (3060154)First to succeed.
% 3.44/1.37 % (3060153)Also succeeded, but the first one will report.
% 3.44/1.37 % (3060154)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3060145"
% 3.44/1.37 % (3060156)Also succeeded, but the first one will report.
% 3.44/1.37 % (3060155)Also succeeded, but the first one will report.
% 3.44/1.37 % (3060154)Refutation found. Thanks to Tanya!
% 3.44/1.37 % SZS status Theorem for theBenchmark
% 3.44/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.37 % (3060154)------------------------------
% 3.44/1.37 % (3060154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.37 % (3060154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.37 % (3060154)CaDiCaL version: 2.1.3
% 3.44/1.37 % (3060154)Termination reason: Refutation
% 3.44/1.37 % (3060154)Time elapsed: 0.003 s
% 3.44/1.37 % (3060154)Peak memory usage: 88 MB
% 3.44/1.37 % (3060154)Instructions burned: 3 (million)
% 3.44/1.37 % (3060154)------------------------------
% 3.44/1.37 % (3060154)------------------------------
% 3.44/1.37 % (3060145)Success in time 0.423 s
% 3.44/1.37 % Vampire exiting
%------------------------------------------------------------------------------