%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG121+4 : 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 : 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 12:35:36 PM UTC 2026
% Result : Theorem 3.44s 1.26s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 91 ( 28 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 95 ( 24 ~; 20 |; 50 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 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 : 31 ( 11 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f43,axiom,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(f53,conjecture,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f54,negated_conjecture,
~ ( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| aElementOf0(xb,xI) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f57,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& xa = sdtasdt0(xa,X1) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X2] :
( aElement0(X2)
& sz00 = sdtasdt0(xb,X2) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X3] :
( aElement0(X3)
& xb = sdtasdt0(xb,X3) )
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(rectify,[],[f43]) ).
fof(f62,plain,
~ ( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& xb = sdtpldt0(X2,X3) )
| aElementOf0(xb,xI) ),
inference(rectify,[],[f54]) ).
fof(f74,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xb )
& ! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| xb != sdtpldt0(X2,X3) )
& ~ aElementOf0(xb,xI) ),
inference(ennf_transformation,[],[f62]) ).
fof(f78,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f131,plain,
( aElement0(sK12)
& sz00 = sdtasdt0(xa,sK12)
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(sK13)
& xa = sdtasdt0(xa,sK13)
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(sK14)
& sz00 = sdtasdt0(xb,sK14)
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(sK15)
& xb = sdtasdt0(xb,sK15)
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f57]) ).
fof(f166,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f204,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f131]) ).
fof(f213,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f131]) ).
fof(f258,plain,
! [X2,X3] :
( xb != sdtpldt0(X2,X3)
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f263,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f387,plain,
! [X0] :
( xb != X0
| ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(X0) ),
inference(superposition,[],[f258,f263]) ).
fof(f388,plain,
! [X0] :
( xb != X0
| ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f387,f213]) ).
fof(f389,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(equality_resolution,[],[f388]) ).
fof(f390,plain,
~ aElement0(xb),
inference(forward_subsumption_resolution,[],[f389,f204]) ).
fof(f391,plain,
$false,
inference(forward_subsumption_resolution,[],[f390,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG121+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n009.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 23:21:45 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.44/1.26 % (2519298)Detected formulas, will run a generic FOF schedule.
% 3.44/1.26 % (2519308)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=580292140:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.26 % (2519303)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=3941100340:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.26 % (2519305)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=1860429429:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.26 % (2519306)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3257157738:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.26 % (2519307)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1293364429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.26 % (2519309)dis-21_1_sil=8000:lcm=predicate:random_seed=3877093292: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)
% 3.44/1.26 % (2519304)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=2844253300:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.26 % (2519307)First to succeed.
% 3.44/1.26 % (2519309)Also succeeded, but the first one will report.
% 3.44/1.26 % (2519307)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2519298"
% 3.44/1.26 % (2519308)Also succeeded, but the first one will report.
% 3.44/1.26 % (2519306)Instruction limit reached!
% 3.44/1.26 % (2519306)------------------------------
% 3.44/1.26 % (2519306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.26 % (2519306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.26 % (2519306)CaDiCaL version: 2.1.3
% 3.44/1.26 % (2519306)Termination reason: Instruction limit
% 3.44/1.26 % (2519306)Termination phase: Saturation
% 3.44/1.26 % (2519306)Time elapsed: 0.068 s
% 3.44/1.26 % (2519306)Peak memory usage: 89 MB
% 3.44/1.26 % (2519306)Instructions burned: 110 (million)
% 3.44/1.26 % (2519317)lrs+10_1_sil=8000:sp=occurrence:random_seed=3178150341:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.44/1.26 % (2519307)Refutation found. Thanks to Tanya!
% 3.44/1.26 % SZS status Theorem for theBenchmark
% 3.44/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.26 % (2519307)------------------------------
% 3.44/1.26 % (2519307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.26 % (2519307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.26 % (2519307)CaDiCaL version: 2.1.3
% 3.44/1.26 % (2519307)Termination reason: Refutation
% 3.44/1.26 % (2519307)Time elapsed: 0.007 s
% 3.44/1.26 % (2519307)Peak memory usage: 88 MB
% 3.44/1.26 % (2519307)Instructions burned: 10 (million)
% 3.44/1.26 % (2519307)------------------------------
% 3.44/1.26 % (2519307)------------------------------
% 3.44/1.26 % (2519298)Success in time 0.432 s
% 3.44/1.26 % Vampire exiting
%------------------------------------------------------------------------------