%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM565+3 : 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 : n012.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 12:15:46 PM UTC 2026
% Result : Theorem 2.32s 0.93s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 94 ( 36 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 101 ( 30 ~; 15 |; 44 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f80,conjecture,
! [X0] :
( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
=> ( ( aSet0(slcrc0)
& ~ ? [X1] : aElementOf0(X1,slcrc0) )
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f81,negated_conjecture,
~ ! [X0] :
( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
=> ( ( aSet0(slcrc0)
& ~ ? [X1] : aElementOf0(X1,slcrc0) )
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
fof(f85,plain,
~ ! [X0] :
( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
=> ( ( aSet0(slcrc0)
& ~ ? [X2] : aElementOf0(X2,slcrc0) )
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(rectify,[],[f81]) ).
fof(f102,plain,
? [X0] :
( sdtlpdtrp0(xc,X0) != sdtlpdtrp0(xc,slcrc0)
& aSet0(slcrc0)
& ! [X2] : ~ aElementOf0(X2,slcrc0)
& aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
inference(ennf_transformation,[],[f85]) ).
fof(f103,plain,
? [X0] :
( sdtlpdtrp0(xc,X0) != sdtlpdtrp0(xc,slcrc0)
& aSet0(slcrc0)
& ! [X2] : ~ aElementOf0(X2,slcrc0)
& aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
inference(flattening,[],[f102]) ).
fof(f120,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f180,plain,
? [X0] :
( sdtlpdtrp0(xc,X0) != sdtlpdtrp0(xc,slcrc0)
& aSet0(slcrc0)
& ! [X1] : ~ aElementOf0(X1,slcrc0)
& aSet0(X0)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = sz00
& aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
inference(rectify,[],[f103]) ).
fof(f181,plain,
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK14)
& aSet0(slcrc0)
& ! [X1] : ~ aElementOf0(X1,slcrc0)
& aSet0(sK14)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,sK14) )
& aSubsetOf0(sK14,xS)
& sz00 = sbrdtbr0(sK14)
& aElementOf0(sK14,slbdtsldtrb0(xS,sz00)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f180]) ).
fof(f187,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f258,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f265,plain,
sz00 = sbrdtbr0(sK14),
inference(cnf_transformation,[],[f181]) ).
fof(f268,plain,
aSet0(sK14),
inference(cnf_transformation,[],[f181]) ).
fof(f271,plain,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK14),
inference(cnf_transformation,[],[f181]) ).
fof(f287,plain,
! [X0] :
( slcrc0 = X0
| sz00 != sbrdtbr0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f340,plain,
xK = sbrdtbr0(sK14),
inference(definition_unfolding,[],[f265,f258]) ).
fof(f343,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f287,f258]) ).
fof(f406,plain,
( xK != xK
| slcrc0 = sK14
| ~ aSet0(sK14) ),
inference(superposition,[],[f343,f340]) ).
fof(f407,plain,
( slcrc0 = sK14
| ~ aSet0(sK14) ),
inference(trivial_inequality_removal,[],[f406]) ).
fof(f408,plain,
slcrc0 = sK14,
inference(forward_subsumption_resolution,[],[f407,f268]) ).
fof(f413,plain,
sdtlpdtrp0(xc,sK14) != sdtlpdtrp0(xc,sK14),
inference(superposition,[],[f271,f408]) ).
fof(f419,plain,
$false,
inference(trivial_inequality_removal,[],[f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM565+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 20:30:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.32/0.93 % (2711193)Detected formulas, will run a generic FOF schedule.
% 2.32/0.93 % (2711203)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2249667609:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/0.93 % (2711202)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3216197100:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/0.93 % (2711204)dis-21_1_sil=8000:lcm=predicate:random_seed=142767290: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)
% 2.32/0.93 % (2711198)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=1655006469:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/0.93 % (2711201)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3594231207:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/0.93 % (2711199)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=3701149861:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/0.93 % (2711200)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=2539905578:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/0.93 % (2711202)First to succeed.
% 2.32/0.93 % (2711202)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2711193"
% 2.32/0.93 % (2711203)Also succeeded, but the first one will report.
% 2.32/0.93 % (2711201)Also succeeded, but the first one will report.
% 2.32/0.93 % (2711204)Instruction limit reached!
% 2.32/0.93 % (2711204)------------------------------
% 2.32/0.93 % (2711204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2711204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2711204)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2711204)Termination reason: Instruction limit
% 2.32/0.93 % (2711204)Termination phase: Saturation
% 2.32/0.93 % (2711204)Time elapsed: 0.034 s
% 2.32/0.93 % (2711204)Peak memory usage: 89 MB
% 2.32/0.93 % (2711204)Instructions burned: 130 (million)
% 2.32/0.93 % (2711202)Refutation found. Thanks to Tanya!
% 2.32/0.93 % SZS status Theorem for theBenchmark
% 2.32/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.94 % (2711202)------------------------------
% 2.32/0.94 % (2711202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.94 % (2711202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.94 % (2711202)CaDiCaL version: 2.1.3
% 2.32/0.94 % (2711202)Termination reason: Refutation
% 2.32/0.94 % (2711202)Time elapsed: 0.004 s
% 2.32/0.94 % (2711202)Peak memory usage: 88 MB
% 2.32/0.94 % (2711202)Instructions burned: 8 (million)
% 2.32/0.94 % (2711202)------------------------------
% 2.32/0.94 % (2711202)------------------------------
% 2.32/0.94 % (2711193)Success in time 0.298 s
% 2.32/0.94 % Vampire exiting
%------------------------------------------------------------------------------