%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM576+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 : n006.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 08:17:27 AM UTC 2026
% Result : Theorem 0.13s 5.87s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 58 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 23 ~; 25 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(mLessTotal,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLessTotal) ).
fof(m__3856,axiom,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('theBenchmark.p',m__3856) ).
fof(m__,conjecture,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_134,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_136,plain,
( sdtlseqdt0(szszuzczcdt0(B),A)
| sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessTotal]) ).
cnf(c_244,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_245,plain,
aElementOf0(xj,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_246,negated_conjecture,
xj != xi,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_247,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_248,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_1625,plain,
( sdtlseqdt0(szszuzczcdt0(A),xi)
| sdtlseqdt0(xi,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_136,c_244]) ).
cnf(c_1626,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(xi,xj) ),
inference(resolve,[status(thm)],[c_1625,c_245]) ).
cnf(c_724,negated_conjecture,
sdtlseqdt0(xi,xj),
inference(resolve,[status(thm)],[c_247,c_1626]) ).
cnf(c_1627,plain,
( sdtlseqdt0(szszuzczcdt0(A),xj)
| sdtlseqdt0(xj,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_136,c_245]) ).
cnf(c_1628,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(xj,xi) ),
inference(resolve,[status(thm)],[c_1627,c_244]) ).
cnf(c_727,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(resolve,[status(thm)],[c_248,c_1628]) ).
cnf(c_1629,plain,
( xi = xj
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_724,c_134]) ).
cnf(c_1630,plain,
( xj = xi
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(copy,[status(thm)],[c_1629]) ).
cnf(c_1631,plain,
( xj = xi
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_245,c_1630]) ).
cnf(c_1632,plain,
( xj = xi
| ~ sdtlseqdt0(xj,xi) ),
inference(resolve,[status(thm)],[c_244,c_1631]) ).
cnf(c_1633,plain,
xj = xi,
inference(resolve,[status(thm)],[c_727,c_1632]) ).
cnf(c_1624,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_246,c_1633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM576+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.58 % Computer : n006.cluster.edu
% 0.08/5.58 % Model : x86_64 x86_64
% 0.08/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.58 % Memory : 8046.5625MB
% 0.08/5.58 % OS : Linux 6.8.0-71-generic
% 0.08/5.58 % CPULimit : 300
% 0.08/5.58 % WCLimit : 300
% 0.08/5.58 % DateTime : Sat Sep 26 03:17:48 UTC 2026
% 0.08/5.58 % CPUTime :
% 0.08/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.58 % Process 264378 was started by sandbox2 on n006,
% 0.08/5.58 % Sat Sep 26 03:17:48 2026
% 0.08/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.61
% 0.13/5.61 % From the command line: assign(max_seconds, 300).
% 0.13/5.87
% 0.13/5.87 % SZS status Theorem for theBenchmark
% 0.13/5.87
% 0.13/5.87 % Proof 1 at 0.19 (+ 0.06) seconds.
% 0.13/5.87 % Length of proof is 14.
% 0.13/5.87 % Level of proof is 3.
% 0.13/5.87 % Maximum clause weight is 23.000.
% 0.13/5.87 % Given clauses 230.
% 0.13/5.87
% 0.13/5.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------