%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:17:26 AM UTC 2026
% Result : Theorem 0.13s 5.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 43 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 37 ( 14 ~; 9 |; 11 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 1 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3623,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('theBenchmark.p',m__3623) ).
fof(m__3702_02,axiom,
( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) ) ) ),
file('theBenchmark.p',m__3702_02) ).
fof(m__,conjecture,
( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_221,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_222,plain,
isCountable0(xS),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_237,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausify,[status(thm)],[m__3623]) ).
cnf(c_245,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| xi = sz00 ),
inference(clausify,[status(thm)],[m__3702_02]) ).
cnf(c_246,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| xi = sz00 ),
inference(clausify,[status(thm)],[m__3702_02]) ).
cnf(c_247,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_757,negated_conjecture,
( xi = sz00
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(resolve,[status(thm)],[c_247,c_245]) ).
cnf(c_758,negated_conjecture,
( xi = sz00
| xi = sz00 ),
inference(resolve,[status(thm)],[c_757,c_246]) ).
cnf(c_755,negated_conjecture,
xi = sz00,
inference(copy,[status(thm)],[c_758]) ).
cnf(c_759,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0) ),
inference(paramod,[status(thm)],[c_755,c_247]) ).
cnf(c_760,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(paramod,[status(thm)],[c_237,c_759]) ).
cnf(c_761,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(paramod,[status(thm)],[c_755,c_760]) ).
cnf(c_762,negated_conjecture,
( ~ isCountable0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(paramod,[status(thm)],[c_237,c_761]) ).
cnf(c_763,negated_conjecture,
~ isCountable0(xS),
inference(resolve,[status(thm)],[c_221,c_762]) ).
cnf(c_756,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_222,c_763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 03:19:15 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 4163624 was started by sandbox2 on n026,
% 0.09/5.38 % Sat Sep 26 03:19:15 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.41
% 0.13/5.41 % From the command line: assign(max_seconds, 300).
% 0.13/5.53
% 0.13/5.53 % SZS status Theorem for theBenchmark
% 0.13/5.53
% 0.13/5.53 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.13/5.53 % Length of proof is 12.
% 0.13/5.53 % Level of proof is 3.
% 0.13/5.53 % Maximum clause weight is 19.000.
% 0.13/5.53 % Given clauses 165.
% 0.13/5.53
% 0.13/5.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------