%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM587+1 : 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 : n015.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 08:17:29 AM UTC 2026
% Result : Theorem 0.70s 0.51s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 31 ( 3 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 6 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(m__3291,axiom,
( isFinite0(xT)
& aSet0(xT) ),
file('theBenchmark.p',m__3291) ).
fof(m__3453,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('theBenchmark.p',m__3453) ).
fof(m__4263,axiom,
( aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
& xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
file('theBenchmark.p',m__4263) ).
fof(m__,conjecture,
aElementOf0(xx,xT),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xx,xT),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_92,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_223,plain,
aSet0(xT),
inference(clausify,[status(thm)],[m__3291]) ).
cnf(c_231,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(clausify,[status(thm)],[m__3453]) ).
cnf(c_262,plain,
sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xx,
inference(clausify,[status(thm)],[m__4263]) ).
cnf(c_263,plain,
aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(clausify,[status(thm)],[m__4263]) ).
cnf(c_264,plain,
aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(paramod,[status(thm)],[c_262,c_263]) ).
cnf(c_265,negated_conjecture,
~ aElementOf0(xx,xT),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_758,plain,
( aElementOf0(B,xT)
| ~ aElementOf0(B,A)
| ~ aSubsetOf0(A,xT) ),
inference(resolve,[status(thm)],[c_92,c_223]) ).
cnf(c_759,plain,
( aElementOf0(A,xT)
| ~ aElementOf0(A,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(resolve,[status(thm)],[c_758,c_231]) ).
cnf(c_760,plain,
aElementOf0(xx,xT),
inference(resolve,[status(thm)],[c_759,c_264]) ).
cnf(c_757,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_265,c_760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM587+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:23:58 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 2996968 was started by sandbox on n015,
% 0.14/0.36 % Sat Sep 26 03:23:58 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 0.70/0.51
% 0.70/0.51 % SZS status Theorem for theBenchmark
% 0.70/0.51
% 0.70/0.51 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.70/0.51 % Length of proof is 13.
% 0.70/0.51 % Level of proof is 3.
% 0.70/0.51 % Maximum clause weight is 35.000.
% 0.70/0.51 % Given clauses 172.
% 0.70/0.51
% 0.70/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------