%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM560+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:24:49 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 81 ( 13 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 95 ( 28 ~; 16 |; 40 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f68,conjecture,
( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f77,plain,
~ ( ( aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xF,xy))
=> aElementOf0(X1,szDzozmdt0(xF)) )
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ) ),
inference(rectify,[],[f69]) ).
fof(f168,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) ),
inference(ennf_transformation,[],[f77]) ).
fof(f169,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy ) ) ),
inference(flattening,[],[f168]) ).
fof(f226,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X0,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X0) )
& ( ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) ) ),
inference(nnf_transformation,[],[f169]) ).
fof(f227,plain,
( ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X0,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X0) )
& ( ( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = xy )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) ) ),
inference(flattening,[],[f226]) ).
fof(f228,plain,
( ? [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
& aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X1,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X1) )
& ( ( aElementOf0(X1,szDzozmdt0(xF))
& xy = sdtlpdtrp0(xF,X1) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ) ),
inference(rectify,[],[f227]) ).
fof(f229,plain,
( ~ aElementOf0(sK17,szDzozmdt0(xF))
& aElementOf0(sK17,sdtlbdtrb0(xF,xy))
& ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& aSet0(sdtlbdtrb0(xF,xy))
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| ~ aElementOf0(X1,szDzozmdt0(xF))
| xy != sdtlpdtrp0(xF,X1) )
& ( ( aElementOf0(X1,szDzozmdt0(xF))
& xy = sdtlpdtrp0(xF,X1) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f228]) ).
fof(f355,plain,
! [X1] :
( ~ aElementOf0(X1,sdtlbdtrb0(xF,xy))
| aElementOf0(X1,szDzozmdt0(xF)) ),
inference(cnf_transformation,[],[f229]) ).
fof(f359,plain,
aElementOf0(sK17,sdtlbdtrb0(xF,xy)),
inference(cnf_transformation,[],[f229]) ).
fof(f360,plain,
~ aElementOf0(sK17,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f229]) ).
fof(f404,plain,
aElementOf0(sK17,szDzozmdt0(xF)),
inference(resolution,[],[f355,f359]) ).
fof(f405,plain,
$false,
inference(forward_subsumption_resolution,[],[f404,f360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM560+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:30:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % (527328)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (527336)dis+10_1_sil=32000:sp=arity:random_seed=1882877103:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (527336) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-527328-527336"...
% 0.12/0.45 % (527336)...printing done.
% 0.12/0.45 % (527336)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (527336)------------------------------
% 0.12/0.45 % (527336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (527336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (527336)CaDiCaL version: 2.1.3
% 0.12/0.45 % (527336)Termination reason: Refutation
% 0.12/0.45 % (527336)Time elapsed: 0.003 s
% 0.12/0.45 % (527336)Peak memory usage: 11 MB
% 0.12/0.45 % (527336)Instructions burned: 6 (million)
% 0.12/0.45 % (527328)Success in time 0.028 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------