%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM552+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 : n019.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 08:17:23 AM UTC 2026
% Result : Theorem 0.10s 0.60s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 66 ( 8 equ)
% Maximal formula atoms : 43 ( 5 avg)
% Number of connectives : 61 ( 8 ~; 8 |; 28 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2227,axiom,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('theBenchmark.p',m__2227) ).
fof(m__2270,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('theBenchmark.p',m__2270) ).
fof(m__,conjecture,
( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_64,negated_conjecture,
~ aElementOf0(xx,xT),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_65,negated_conjecture,
aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_72,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m__2270]) ).
cnf(c_87,plain,
( aElementOf0(A,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(clausify,[status(thm)],[m__2227]) ).
cnf(c_93,plain,
( aElementOf0(B,xT)
| ~ aElementOf0(B,A)
| ~ aElementOf0(A,slbdtsldtrb0(xT,xk)) ),
inference(clausify,[status(thm)],[m__2227]) ).
cnf(c_250,plain,
aElementOf0(xQ,slbdtsldtrb0(xT,xk)),
inference(resolve,[status(thm)],[c_87,c_72]) ).
cnf(c_259,negated_conjecture,
( aElementOf0(xx,xT)
| ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
inference(resolve,[status(thm)],[c_93,c_65]) ).
cnf(c_260,negated_conjecture,
aElementOf0(xx,xT),
inference(resolve,[status(thm)],[c_250,c_259]) ).
cnf(c_258,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_64,c_260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM552+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n019.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Sat Sep 26 03:12:34 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.56 % Process 270101 was started by sandbox on n019,
% 0.10/0.56 % Sat Sep 26 03:12:34 2026
% 0.10/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.58
% 0.10/0.58 % From the command line: assign(max_seconds, 300).
% 0.10/0.60
% 0.10/0.60 % SZS status Theorem for theBenchmark
% 0.10/0.60
% 0.10/0.60 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.60 % Length of proof is 10.
% 0.10/0.60 % Level of proof is 3.
% 0.10/0.60 % Maximum clause weight is 21.000.
% 0.10/0.60 % Given clauses 28.
% 0.10/0.60
% 0.10/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------