%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM606+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 : n005.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 12:15:58 PM UTC 2026
% Result : Theorem 2.69s 1.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 104 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 117 ( 42 ~; 27 |; 39 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 31 ( 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(f98,axiom,
( ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
fof(f100,axiom,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& ~ ( ~ ? [X0] : aElementOf0(X0,xQ)
| xQ = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(f101,conjecture,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) )
| aSubsetOf0(xQ,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f102,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) )
| aSubsetOf0(xQ,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f101]) ).
fof(f115,plain,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& ~ ( ~ ? [X1] : aElementOf0(X1,xQ)
| xQ = slcrc0 ) ),
inference(rectify,[],[f100]) ).
fof(f123,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f147,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f148,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f147]) ).
fof(f151,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) )
& aSubsetOf0(xO,xS) ),
inference(ennf_transformation,[],[f98]) ).
fof(f153,plain,
( ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& ? [X1] : aElementOf0(X1,xQ)
& slcrc0 != xQ ),
inference(ennf_transformation,[],[f115]) ).
fof(f154,plain,
( ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& ? [X1] : aElementOf0(X1,xQ)
& slcrc0 != xQ ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
( ? [X0] :
( ~ aElementOf0(X0,szNzAzT0)
& aElementOf0(X0,xQ) )
& ~ aSubsetOf0(xQ,szNzAzT0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f352,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK48(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK48(X0,X1),X1)
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(X2,sK48(X0,X1))],[f148]) ).
fof(f364,plain,
( ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aElementOf0(sK52,xQ)
& slcrc0 != xQ ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52)],[f154]) ).
fof(f365,plain,
( ~ aElementOf0(sK53,szNzAzT0)
& aElementOf0(sK53,xQ)
& ~ aSubsetOf0(xQ,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(X0,sK53)],[f155]) ).
fof(f414,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f123]) ).
fof(f624,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f352]) ).
fof(f657,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f151]) ).
fof(f665,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f364]) ).
fof(f667,plain,
aElementOf0(sK53,xQ),
inference(cnf_transformation,[],[f365]) ).
fof(f668,plain,
~ aElementOf0(sK53,szNzAzT0),
inference(cnf_transformation,[],[f365]) ).
fof(f988,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xd))
| ~ aElementOf0(X0,xS) ),
inference(forward_demodulation,[],[f414,f624]) ).
fof(f1123,plain,
~ aElementOf0(sK53,szDzozmdt0(xd)),
inference(superposition,[],[f668,f624]) ).
fof(f2075,plain,
aElementOf0(sK53,xO),
inference(resolution,[],[f665,f667]) ).
fof(f2122,plain,
aElementOf0(sK53,xS),
inference(resolution,[],[f2075,f657]) ).
fof(f2606,plain,
~ aElementOf0(sK53,xS),
inference(resolution,[],[f988,f1123]) ).
fof(f2613,plain,
$false,
inference(forward_subsumption_resolution,[],[f2606,f2122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.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 20:43:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.69/1.35 % (145646)Detected formulas, will run a generic FOF schedule.
% 2.69/1.35 % (145654)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=85410956:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.35 % (145654)First to succeed.
% 2.69/1.35 % (145654)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-145646"
% 2.69/1.35 % (145653)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=1476717764:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.35 % (145651)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=3081123414:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.35 % (145652)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=1787840361:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.35 % (145655)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2443983612:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.35 % (145657)dis-21_1_sil=8000:lcm=predicate:random_seed=745119146: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)
% 2.69/1.35 % (145656)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2765160622:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.35 % (145655)Also succeeded, but the first one will report.
% 2.69/1.35 % (145657)Also succeeded, but the first one will report.
% 2.69/1.35 % (145656)Also succeeded, but the first one will report.
% 2.69/1.35 % (145654)Refutation found. Thanks to Tanya!
% 2.69/1.35 % SZS status Theorem for theBenchmark
% 2.69/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.35 % (145654)------------------------------
% 2.69/1.35 % (145654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.35 % (145654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.35 % (145654)CaDiCaL version: 2.1.3
% 2.69/1.35 % (145654)Termination reason: Refutation
% 2.69/1.35 % (145654)Time elapsed: 0.026 s
% 2.69/1.35 % (145654)Peak memory usage: 90 MB
% 2.69/1.35 % (145654)Instructions burned: 73 (million)
% 2.69/1.35 % (145654)------------------------------
% 2.69/1.35 % (145654)------------------------------
% 2.69/1.35 % (145646)Success in time 0.3 s
% 2.69/1.35 % Vampire exiting
%------------------------------------------------------------------------------