%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM550+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 : n008.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 12:15:42 PM UTC 2026
% Result : Theorem 3.79s 1.51s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 69 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 30 ~; 23 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 22 ( 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f68,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f69,plain,
slcrc0 = xQ,
inference(flattening,[],[f68]) ).
fof(f77,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f122,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f124,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK1(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f126]) ).
fof(f140,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f147,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f150,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f69]) ).
fof(f152,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f162,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f127]) ).
fof(f201,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| xQ != X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f152,f150]) ).
fof(f205,plain,
! [X0] :
( aSet0(X0)
| xQ != X0 ),
inference(definition_unfolding,[],[f162,f150]) ).
fof(f209,plain,
( sz00 = sbrdtbr0(xQ)
| ~ aSet0(xQ) ),
inference(equality_resolution,[],[f201]) ).
fof(f210,plain,
aSet0(xQ),
inference(equality_resolution,[],[f205]) ).
fof(f219,plain,
sz00 = sbrdtbr0(xQ),
inference(forward_subsumption_resolution,[],[f209,f210]) ).
fof(f222,plain,
sz00 = xk,
inference(superposition,[],[f219,f147]) ).
fof(f223,plain,
$false,
inference(forward_subsumption_resolution,[],[f222,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM550+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n008.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 20:28:09 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.79/1.51 % (1576571)Detected formulas, will run a generic FOF schedule.
% 3.79/1.51 % (1576582)dis-21_1_sil=8000:lcm=predicate:random_seed=1250755530: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)
% 3.79/1.51 % (1576580)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=240057175:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.79/1.51 % (1576581)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3971865875:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.79/1.51 % (1576578)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=4274233450:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.79/1.51 % (1576577)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=3336003352:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.79/1.51 % (1576579)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3746682252:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.79/1.51 % (1576576)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=2348601675:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.79/1.51 % (1576582)Instruction limit reached!
% 3.79/1.51 % (1576582)------------------------------
% 3.79/1.51 % (1576582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (1576582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (1576582)CaDiCaL version: 2.1.3
% 3.79/1.51 % (1576582)Termination reason: Instruction limit
% 3.79/1.51 % (1576582)Termination phase: Saturation
% 3.79/1.51 % (1576582)Time elapsed: 0.034 s
% 3.79/1.51 % (1576582)Peak memory usage: 88 MB
% 3.79/1.51 % (1576582)Instructions burned: 132 (million)
% 3.79/1.51 % (1576580)First to succeed.
% 3.79/1.51 % (1576580)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1576571"
% 3.79/1.51 % (1576581)Also succeeded, but the first one will report.
% 3.79/1.51 % (1576579)Also succeeded, but the first one will report.
% 3.79/1.51 % (1576590)lrs+10_1_sil=8000:sp=occurrence:random_seed=1009539877:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.79/1.51 % (1576590)Also succeeded, but the first one will report.
% 3.79/1.51 % (1576580)Refutation found. Thanks to Tanya!
% 3.79/1.51 % SZS status Theorem for theBenchmark
% 3.79/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.52 % (1576580)------------------------------
% 3.79/1.52 % (1576580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.52 % (1576580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.52 % (1576580)CaDiCaL version: 2.1.3
% 3.79/1.52 % (1576580)Termination reason: Refutation
% 3.79/1.52 % (1576580)Time elapsed: 0.003 s
% 3.79/1.52 % (1576580)Peak memory usage: 88 MB
% 3.79/1.52 % (1576580)Instructions burned: 3 (million)
% 3.79/1.52 % (1576580)------------------------------
% 3.79/1.52 % (1576580)------------------------------
% 3.79/1.52 % (1576571)Success in time 0.446 s
% 3.79/1.52 % Vampire exiting
%------------------------------------------------------------------------------