%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM541+2 : 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 08:17:20 AM UTC 2026
% Result : Theorem 0.16s 10.69s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 13 unt; 0 def)
% Number of atoms : 207 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 224 ( 81 ~; 114 |; 15 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 31 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('theBenchmark.p',mSuccNum) ).
fof(mNatNSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('theBenchmark.p',mNatNSucc) ).
fof(mSuccLess,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ),
file('theBenchmark.p',mSuccLess) ).
fof(mLessSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,szszuzczcdt0(W0)) ),
file('theBenchmark.p',mLessSucc) ).
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(mLessTrans,axiom,
! [W0,W1,W2] :
( ( aElementOf0(W2,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('theBenchmark.p',mLessTrans) ).
fof(mLessTotal,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLessTotal) ).
fof(m__1936,axiom,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
file('theBenchmark.p',m__1936) ).
fof(m__,conjecture,
( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_53,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| xn != xm ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_58,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_65,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_66,plain,
aElementOf0(xn,szNzAzT0),
inference(clausify,[status(thm)],[m__1936]) ).
cnf(c_67,plain,
aElementOf0(xm,szNzAzT0),
inference(clausify,[status(thm)],[m__1936]) ).
cnf(c_98,plain,
( sdtlseqdt0(szszuzczcdt0(B),A)
| sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessTotal]) ).
cnf(c_99,plain,
( sdtlseqdt0(A,C)
| ~ sdtlseqdt0(B,C)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(C,szNzAzT0)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessTrans]) ).
cnf(c_100,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_102,plain,
( sdtlseqdt0(A,szszuzczcdt0(A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessSucc]) ).
cnf(c_103,plain,
( ~ sdtlseqdt0(szszuzczcdt0(A),szszuzczcdt0(B))
| sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccLess]) ).
cnf(c_107,plain,
( szszuzczcdt0(A) != A
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mNatNSucc]) ).
cnf(c_112,plain,
( aElementOf0(szszuzczcdt0(A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccNum]) ).
cnf(c_205,plain,
( sdtlseqdt0(szszuzczcdt0(A),xn)
| sdtlseqdt0(xn,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_98,c_66]) ).
cnf(c_206,plain,
( sdtlseqdt0(szszuzczcdt0(xm),A)
| sdtlseqdt0(A,xm)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_98,c_67]) ).
cnf(c_1624,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),A)
| ~ sdtlseqdt0(xn,A)
| ~ aElementOf0(A,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolve,[status(thm)],[c_99,c_65]) ).
cnf(c_208,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),A)
| ~ sdtlseqdt0(xn,A)
| ~ aElementOf0(A,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolve,[status(thm)],[c_66,c_1624]) ).
cnf(c_216,plain,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sdtlseqdt0(xn,szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(factor,[status(thm)],[c_208]) ).
cnf(c_224,plain,
sdtlseqdt0(xm,szszuzczcdt0(xm)),
inference(resolve,[status(thm)],[c_102,c_67]) ).
cnf(c_225,plain,
sdtlseqdt0(xn,szszuzczcdt0(xn)),
inference(resolve,[status(thm)],[c_102,c_66]) ).
cnf(c_226,plain,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolve,[status(thm)],[c_225,c_216]) ).
cnf(c_1625,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolve,[status(thm)],[c_103,c_65]) ).
cnf(c_1626,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolve,[status(thm)],[c_67,c_1625]) ).
cnf(c_227,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_66,c_1626]) ).
cnf(c_236,plain,
szszuzczcdt0(xn) != xn,
inference(resolve,[status(thm)],[c_107,c_66]) ).
cnf(c_245,plain,
aElementOf0(szszuzczcdt0(xm),szNzAzT0),
inference(resolve,[status(thm)],[c_112,c_67]) ).
cnf(c_246,plain,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(resolve,[status(thm)],[c_112,c_66]) ).
cnf(c_1627,plain,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolve,[status(thm)],[c_245,c_226]) ).
cnf(c_251,plain,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(resolve,[status(thm)],[c_246,c_1627]) ).
cnf(c_1628,plain,
( xn = szszuzczcdt0(xn)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolve,[status(thm)],[c_225,c_100]) ).
cnf(c_1629,plain,
( szszuzczcdt0(xn) = xn
| ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(copy,[status(thm)],[c_1628]) ).
cnf(c_1630,plain,
( szszuzczcdt0(xn) = xn
| ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolve,[status(thm)],[c_246,c_1629]) ).
cnf(c_1631,plain,
( szszuzczcdt0(xn) = xn
| ~ sdtlseqdt0(szszuzczcdt0(xn),xn) ),
inference(resolve,[status(thm)],[c_66,c_1630]) ).
cnf(c_558,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xn),
inference(resolve,[status(thm)],[c_236,c_1631]) ).
cnf(c_1101,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xn,xm) ),
inference(resolve,[status(thm)],[c_205,c_67]) ).
cnf(c_1107,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sdtlseqdt0(szszuzczcdt0(xn),xm) ),
inference(resolve,[status(thm)],[c_206,c_246]) ).
cnf(c_1632,plain,
( sdtlseqdt0(A,xn)
| ~ sdtlseqdt0(A,szszuzczcdt0(xm))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0)
| xn = xm
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_227,c_99]) ).
cnf(c_1633,plain,
( sdtlseqdt0(A,xn)
| ~ sdtlseqdt0(A,szszuzczcdt0(xm))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0)
| xn = xm
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_245,c_1632]) ).
cnf(c_1141,plain,
( sdtlseqdt0(A,xn)
| ~ sdtlseqdt0(A,szszuzczcdt0(xm))
| ~ aElementOf0(A,szNzAzT0)
| xn = xm
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_66,c_1633]) ).
cnf(c_1634,plain,
( ~ sdtlseqdt0(xm,szszuzczcdt0(xm))
| ~ aElementOf0(xm,szNzAzT0)
| xn = xm
| sdtlseqdt0(xm,xn) ),
inference(factor,[status(thm)],[c_1141]) ).
cnf(c_1635,plain,
( ~ sdtlseqdt0(xm,szszuzczcdt0(xm))
| xn = xm
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_67,c_1634]) ).
cnf(c_1145,plain,
( xn = xm
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_224,c_1635]) ).
cnf(c_1636,plain,
( xm = xn
| ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| xn = xm ),
inference(resolve,[status(thm)],[c_1145,c_100]) ).
cnf(c_1637,plain,
( xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| xn = xm ),
inference(copy,[status(thm)],[c_1636]) ).
cnf(c_1638,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| xn = xm ),
inference(copy,[status(thm)],[c_1637]) ).
cnf(c_1639,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| xn = xm ),
inference(resolve,[status(thm)],[c_66,c_1638]) ).
cnf(c_1146,plain,
( ~ sdtlseqdt0(xn,xm)
| xn = xm ),
inference(resolve,[status(thm)],[c_67,c_1639]) ).
cnf(c_1513,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| xn = xm ),
inference(resolve,[status(thm)],[c_251,c_58]) ).
cnf(c_1608,plain,
( sdtlseqdt0(xn,xm)
| xn = xm ),
inference(resolve,[status(thm)],[c_1513,c_1101]) ).
cnf(c_1640,plain,
( xn = xm
| xn = xm ),
inference(resolve,[status(thm)],[c_1608,c_1146]) ).
cnf(c_1609,plain,
xn = xm,
inference(copy,[status(thm)],[c_1640]) ).
cnf(c_1610,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
inference(resolve,[status(thm)],[c_1609,c_53]) ).
cnf(c_1612,negated_conjecture,
sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(resolve,[status(thm)],[c_1610,c_1107]) ).
cnf(c_1641,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(paramod,[status(thm)],[c_1609,c_558]) ).
cnf(c_1623,plain,
$false,
inference(resolve,[status(thm)],[c_1612,c_1641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n026.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 03:12:52 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 4158866 was started by sandbox2 on n026,
% 0.11/10.39 % Sat Sep 26 03:12:52 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.42
% 0.16/10.42 % From the command line: assign(max_seconds, 300).
% 0.16/10.69
% 0.16/10.69 % SZS status Theorem for theBenchmark
% 0.16/10.69
% 0.16/10.69 % Proof 1 at 0.19 (+ 0.07) seconds.
% 0.16/10.69 % Length of proof is 45.
% 0.16/10.69 % Level of proof is 11.
% 0.16/10.69 % Maximum clause weight is 32.000.
% 0.16/10.69 % Given clauses 351.
% 0.16/10.69
% 0.16/10.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------