%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM606+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 08:17:32 AM UTC 2026
% Result : Theorem 0.17s 5.88s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 74 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 74 ( 32 ~; 29 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mSubTrans,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('theBenchmark.p',mSubTrans) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__4891,axiom,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('theBenchmark.p',m__4891) ).
fof(m__5093,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('theBenchmark.p',m__5093) ).
fof(m__,conjecture,
aSubsetOf0(xQ,szNzAzT0),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aSubsetOf0(xQ,szNzAzT0),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_100,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_107,plain,
( aSubsetOf0(A,C)
| ~ aSubsetOf0(B,C)
| ~ aSubsetOf0(A,B)
| ~ aSet0(C)
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mSubTrans]) ).
cnf(c_132,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_235,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_283,plain,
aSet0(xO),
inference(clausify,[status(thm)],[m__4891]) ).
fof(m__4998,axiom,
aSubsetOf0(xO,xS),
file('theBenchmark.p',m__4998) ).
cnf(c_289,plain,
aSubsetOf0(xO,xS),
inference(clausify,[status(thm)],[m__4998]) ).
cnf(c_291,plain,
aSubsetOf0(xQ,xO),
inference(clausify,[status(thm)],[m__5093]) ).
cnf(c_293,negated_conjecture,
~ aSubsetOf0(xQ,szNzAzT0),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_1287,plain,
( aSubsetOf0(A,szNzAzT0)
| ~ aSubsetOf0(A,xS)
| ~ aSet0(szNzAzT0)
| ~ aSet0(xS)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_235,c_107]) ).
cnf(c_461,plain,
( aSubsetOf0(A,szNzAzT0)
| ~ aSubsetOf0(A,xS)
| ~ aSet0(xS)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_132,c_1287]) ).
cnf(c_1288,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_235,c_100]) ).
cnf(c_466,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_132,c_1288]) ).
cnf(c_470,plain,
( aSubsetOf0(A,szNzAzT0)
| ~ aSubsetOf0(A,xS)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_466,c_461]) ).
cnf(c_1289,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(xS)
| ~ aSet0(xO)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_289,c_107]) ).
cnf(c_1290,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(xS)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_283,c_1289]) ).
cnf(c_675,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_466,c_1290]) ).
cnf(c_1291,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolve,[status(thm)],[c_291,c_100]) ).
cnf(c_704,plain,
aSet0(xQ),
inference(resolve,[status(thm)],[c_283,c_1291]) ).
cnf(c_1292,plain,
( aSubsetOf0(xQ,xS)
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_675,c_291]) ).
cnf(c_1285,plain,
aSubsetOf0(xQ,xS),
inference(resolve,[status(thm)],[c_704,c_1292]) ).
cnf(c_1293,plain,
( aSubsetOf0(xQ,szNzAzT0)
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_1285,c_470]) ).
cnf(c_1294,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(resolve,[status(thm)],[c_704,c_1293]) ).
cnf(c_1286,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_293,c_1294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.60 % Computer : n006.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Sat Sep 26 03:25:34 UTC 2026
% 0.10/5.60 % CPUTime :
% 0.10/5.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.61 % Process 273333 was started by sandbox2 on n006,
% 0.10/5.61 % Sat Sep 26 03:25:34 2026
% 0.10/5.61 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.65
% 0.10/5.65 % From the command line: assign(max_seconds, 300).
% 0.17/5.88
% 0.17/5.88 % SZS status Theorem for theBenchmark
% 0.17/5.88
% 0.17/5.88 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.17/5.88 % Length of proof is 22.
% 0.17/5.88 % Level of proof is 5.
% 0.17/5.88 % Maximum clause weight is 20.000.
% 0.17/5.88 % Given clauses 333.
% 0.17/5.88
% 0.17/5.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------