%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 08:17:28 AM UTC 2026
% Result : Theorem 10.95s 3.54s
% Output : CNFRefutation 10.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 54 ( 10 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 50 ( 6 ~; 10 |; 19 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 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 : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4007,axiom,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('theBenchmark.p',m__4007) ).
fof(m__4024,axiom,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('theBenchmark.p',m__4024) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) ) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_714,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(clausify,[status(thm)],[m__4007]) ).
cnf(c_716,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(clausify,[status(thm)],[m__4024]) ).
cnf(c_721,negated_conjecture,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_723,negated_conjecture,
( xK != xK
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(paramod,[status(thm)],[c_714,c_721]) ).
cnf(c_724,negated_conjecture,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(copy,[status(thm)],[c_723]) ).
cnf(c_722,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_716,c_724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.33 % Computer : n026.cluster.edu
% 0.05/0.33 % Model : x86_64 x86_64
% 0.05/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.33 % Memory : 8046.5625MB
% 0.05/0.33 % OS : Linux 6.8.0-71-generic
% 0.05/0.33 % CPULimit : 300
% 0.05/0.33 % WCLimit : 300
% 0.05/0.33 % DateTime : Sat Sep 26 03:22:54 UTC 2026
% 0.05/0.34 % CPUTime :
% 0.05/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.35 % Process 4169858 was started by sandbox on n026,
% 0.05/0.35 % Sat Sep 26 03:22:54 2026
% 0.05/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.50
% 0.18/0.50 % From the command line: assign(max_seconds, 300).
% 10.95/3.54
% 10.95/3.54 % SZS status Theorem for theBenchmark
% 10.95/3.54
% 10.95/3.54 % Proof 1 at 1.34 (+ 0.01) seconds.
% 10.95/3.54 % Length of proof is 7.
% 10.95/3.54 % Level of proof is 2.
% 10.95/3.54 % Maximum clause weight is 19.000.
% 10.95/3.54 % Given clauses 0.
% 10.95/3.54
% 10.95/3.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------