%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM617+1 : 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 : n004.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 08:17:35 AM UTC 2026
% Result : Theorem 0.15s 15.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 12 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 3 !; 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(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
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,
aElementOf0(xx,szNzAzT0),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xx,szNzAzT0),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_102,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_103,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_134,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_285,plain,
aSet0(xO),
inference(clausify,[status(thm)],[m__4891]) ).
cnf(c_293,plain,
aSubsetOf0(xQ,xO),
inference(clausify,[status(thm)],[m__5093]) ).
fof(m__5106,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('theBenchmark.p',m__5106) ).
cnf(c_295,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(clausify,[status(thm)],[m__5106]) ).
fof(m__5195,axiom,
aSubsetOf0(xP,xQ),
file('theBenchmark.p',m__5195) ).
cnf(c_303,plain,
aSubsetOf0(xP,xQ),
inference(clausify,[status(thm)],[m__5195]) ).
fof(m__5348,axiom,
aElementOf0(xx,xP),
file('theBenchmark.p',m__5348) ).
cnf(c_311,plain,
aElementOf0(xx,xP),
inference(clausify,[status(thm)],[m__5348]) ).
cnf(c_312,negated_conjecture,
~ aElementOf0(xx,szNzAzT0),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_1550,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolve,[status(thm)],[c_293,c_102]) ).
cnf(c_723,plain,
aSet0(xQ),
inference(resolve,[status(thm)],[c_285,c_1550]) ).
cnf(c_1551,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_295,c_103]) ).
cnf(c_743,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xQ) ),
inference(resolve,[status(thm)],[c_134,c_1551]) ).
cnf(c_1552,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,xP)
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_303,c_103]) ).
cnf(c_818,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,xP) ),
inference(resolve,[status(thm)],[c_723,c_1552]) ).
cnf(c_1548,plain,
aElementOf0(xx,xQ),
inference(resolve,[status(thm)],[c_818,c_311]) ).
cnf(c_1553,plain,
aElementOf0(xx,szNzAzT0),
inference(resolve,[status(thm)],[c_1548,c_743]) ).
cnf(c_1549,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_312,c_1553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM617+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n004.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sat Sep 26 03:27:38 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/15.40 % Process 713184 was started by sandbox on n004,
% 0.11/15.40 % Sat Sep 26 03:27:38 2026
% 0.11/15.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/15.42
% 0.15/15.42 % From the command line: assign(max_seconds, 300).
% 0.15/15.61
% 0.15/15.61 % SZS status Theorem for theBenchmark
% 0.15/15.61
% 0.15/15.61 % Proof 1 at 0.14 (+ 0.03) seconds.
% 0.15/15.61 % Length of proof is 19.
% 0.15/15.61 % Level of proof is 5.
% 0.15/15.61 % Maximum clause weight is 16.000.
% 0.15/15.61 % Given clauses 337.
% 0.15/15.61
% 0.15/15.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------