%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM547+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 : n014.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 08:17:21 AM UTC 2026
% Result : Theorem 0.68s 0.53s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 60 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 23 ~; 20 |; 13 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mDefSel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2227,axiom,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('theBenchmark.p',m__2227) ).
fof(m__,conjecture,
? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_61,negated_conjecture,
~ aElementOf0(A,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_63,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(clausify,[status(thm)],[m__2227]) ).
cnf(c_67,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__2202_02]) ).
fof(m__2202,axiom,
aElementOf0(xk,szNzAzT0),
file('theBenchmark.p',m__2202) ).
cnf(c_68,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[m__2202]) ).
cnf(c_78,plain,
( aSet0(C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
fof(nnf_5,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X0] : ~ aElementOf0(X0,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(fof_nnf,[status(thm)],[mDefEmp]) ).
fof(sk_mDefEmp_sk,plain,
! [W0] :
( ( aElementOf0(sK0(W0),W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X0] : ~ aElementOf0(X0,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_5]) ).
fof(sk_mDefEmp,plain,
( ! [VAR_0] :
( aElementOf0(sK0(VAR_0),VAR_0)
| ~ aSet0(VAR_0)
| slcrc0 = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ aElementOf0(VAR_1,VAR_0)
| slcrc0 != VAR_0 )
& ! [VAR_0] :
( aSet0(VAR_0)
| slcrc0 != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefEmp_sk]) ).
cnf(c_170,plain,
( aElementOf0(sK0(A),A)
| ~ aSet0(A)
| slcrc0 = A ),
inference(split_conjunct,[status(thm)],[sk_mDefEmp]) ).
cnf(c_210,plain,
( aSet0(B)
| slbdtsldtrb0(A,xk) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_78,c_68]) ).
cnf(c_756,plain,
( aSet0(A)
| slbdtsldtrb0(xS,xk) != A ),
inference(resolve,[status(thm)],[c_210,c_67]) ).
cnf(c_1700,plain,
aSet0(slbdtsldtrb0(xS,xk)),
inference(xxres,[status(thm)],[c_756]) ).
cnf(c_1721,plain,
( aElementOf0(sK0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk))
| slcrc0 = slbdtsldtrb0(xS,xk) ),
inference(resolve,[status(thm)],[c_1700,c_170]) ).
cnf(c_1722,plain,
( aElementOf0(sK0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ),
inference(copy,[status(thm)],[c_1721]) ).
cnf(c_1723,plain,
aElementOf0(sK0(slbdtsldtrb0(xS,xk)),slbdtsldtrb0(xS,xk)),
inference(resolve,[status(thm)],[c_63,c_1722]) ).
cnf(c_1720,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_61,c_1723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:11:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2017807 was started by sandbox2 on n014,
% 0.10/0.37 % Sat Sep 26 03:11:02 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.68/0.53
% 0.68/0.53 % SZS status Theorem for theBenchmark
% 0.68/0.53
% 0.68/0.53 % Proof 1 at 0.09 (+ 0.04) seconds.
% 0.68/0.53 % Length of proof is 15.
% 0.68/0.53 % Level of proof is 5.
% 0.68/0.53 % Maximum clause weight is 22.000.
% 0.68/0.53 % Given clauses 352.
% 0.68/0.53
% 0.68/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------