%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM582+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 : n010.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 1.17s 0.66s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 39 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 31 ( 11 ~; 9 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('theBenchmark.p',mZeroLess) ).
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__3754,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('theBenchmark.p',m__3754) ).
fof(m__,conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_121,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_128,plain,
( sdtlseqdt0(sz00,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mZeroLess]) ).
cnf(c_238,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausify,[status(thm)],[m__3623]) ).
cnf(c_243,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),sdtlpdtrp0(xN,B))
| ~ sdtlseqdt0(B,A)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3754]) ).
fof(m__3989,axiom,
aElementOf0(xi,szNzAzT0),
file('theBenchmark.p',m__3989) ).
cnf(c_245,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3989]) ).
cnf(c_248,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_593,plain,
sdtlseqdt0(sz00,xi),
inference(resolve,[status(thm)],[c_245,c_128]) ).
cnf(c_827,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_593,c_243]) ).
cnf(c_828,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(paramod,[status(thm)],[c_238,c_827]) ).
cnf(c_829,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolve,[status(thm)],[c_245,c_828]) ).
cnf(c_830,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(resolve,[status(thm)],[c_121,c_829]) ).
cnf(c_826,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_248,c_830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM582+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n010.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 03:19:44 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2371209 was started by sandbox2 on n010,
% 0.18/0.44 % Sat Sep 26 03:19:44 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 1.17/0.66
% 1.17/0.66 % SZS status Theorem for theBenchmark
% 1.17/0.66
% 1.17/0.66 % Proof 1 at 0.11 (+ 0.03) seconds.
% 1.17/0.66 % Length of proof is 12.
% 1.17/0.66 % Level of proof is 3.
% 1.17/0.66 % Maximum clause weight is 16.000.
% 1.17/0.66 % Given clauses 241.
% 1.17/0.66
% 1.17/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------