%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM582+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 : 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 12:15:51 PM UTC 2026
% Result : Theorem 2.40s 0.94s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 20 |; 14 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(f88,conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(flattening,[],[f89]) ).
fof(f99,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f100,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f99]) ).
fof(f102,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f103,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f102]) ).
fof(f136,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f243,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f100]) ).
fof(f248,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f250,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f253,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(cnf_transformation,[],[f90]) ).
fof(f295,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f300,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f504,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)),
inference(superposition,[],[f253,f243]) ).
fof(f821,plain,
( ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolution,[],[f248,f504]) ).
fof(f852,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f821,f295]) ).
fof(f871,plain,
~ aElementOf0(sz00,szNzAzT0),
inference(forward_subsumption_resolution,[],[f852,f250]) ).
fof(f872,plain,
$false,
inference(forward_subsumption_resolution,[],[f871,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM582+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:35:50 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 2.40/0.94 % (2714236)Detected formulas, will run a generic FOF schedule.
% 2.40/0.94 % (2714242)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=1014477083:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.40/0.94 % (2714244)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1181260352:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.40/0.94 % (2714245)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3278720605:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.40/0.94 % (2714247)dis-21_1_sil=8000:lcm=predicate:random_seed=4241011903: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)
% 2.40/0.94 % (2714241)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=676578745:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.40/0.94 % (2714246)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2895375001:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.40/0.94 % (2714243)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=3434286676:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.40/0.94 % (2714244)First to succeed.
% 2.40/0.94 % (2714244)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2714236"
% 2.40/0.94 % (2714245)Also succeeded, but the first one will report.
% 2.40/0.94 % (2714247)Instruction limit reached!
% 2.40/0.94 % (2714247)------------------------------
% 2.40/0.94 % (2714247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.94 % (2714247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.94 % (2714247)CaDiCaL version: 2.1.3
% 2.40/0.94 % (2714247)Termination reason: Instruction limit
% 2.40/0.94 % (2714247)Termination phase: Saturation
% 2.40/0.94 % (2714247)Time elapsed: 0.034 s
% 2.40/0.94 % (2714247)Peak memory usage: 88 MB
% 2.40/0.94 % (2714247)Instructions burned: 132 (million)
% 2.40/0.94 % (2714246)Also succeeded, but the first one will report.
% 2.40/0.94 % (2714255)lrs+10_1_sil=8000:sp=occurrence:random_seed=1539583573:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.40/0.94 % (2714244)Refutation found. Thanks to Tanya!
% 2.40/0.94 % SZS status Theorem for theBenchmark
% 2.40/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/0.94 % (2714244)------------------------------
% 2.40/0.94 % (2714244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.94 % (2714244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.94 % (2714244)CaDiCaL version: 2.1.3
% 2.40/0.94 % (2714244)Termination reason: Refutation
% 2.40/0.94 % (2714244)Time elapsed: 0.010 s
% 2.40/0.94 % (2714244)Peak memory usage: 89 MB
% 2.40/0.94 % (2714244)Instructions burned: 25 (million)
% 2.40/0.94 % (2714244)------------------------------
% 2.40/0.94 % (2714244)------------------------------
% 2.40/0.94 % (2714236)Success in time 0.311 s
% 2.40/0.94 % Vampire exiting
%------------------------------------------------------------------------------