%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM561+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 : n008.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 08:17:24 AM UTC 2026
% Result : Theorem 1.71s 0.64s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 44 ( 19 ~; 17 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('theBenchmark.p',mSubRefl) ).
fof(mDomSet,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('theBenchmark.p',mDomSet) ).
fof(mDefSImg,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtlcdtrc0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) ) )
& aSet0(W2) ) ) ) ),
file('theBenchmark.p',mDefSImg) ).
fof(m__,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__2911,axiom,
aFunction0(xF),
file('theBenchmark.p',m__2911) ).
cnf(c_68,plain,
aFunction0(xF),
inference(clausify,[status(thm)],[m__2911]) ).
cnf(c_71,plain,
( sdtlpdtrp0(A,E) != D
| ~ aElementOf0(E,B)
| aElementOf0(D,C)
| sdtlcdtrc0(A,B) != C
| ~ aSubsetOf0(B,szDzozmdt0(A))
| ~ aFunction0(A) ),
inference(clausify,[status(thm)],[mDefSImg]) ).
cnf(c_84,plain,
( aSet0(szDzozmdt0(A))
| ~ aFunction0(A) ),
inference(clausify,[status(thm)],[mDomSet]) ).
cnf(c_85,plain,
aSet0(szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_84,c_68]) ).
cnf(c_98,plain,
( sdtlpdtrp0(xF,D) != C
| ~ aElementOf0(D,A)
| aElementOf0(C,B)
| sdtlcdtrc0(xF,A) != B
| ~ aSubsetOf0(A,szDzozmdt0(xF)) ),
inference(resolve,[status(thm)],[c_71,c_68]) ).
cnf(c_115,plain,
( aSubsetOf0(A,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mSubRefl]) ).
fof(m__2911_02,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('theBenchmark.p',m__2911_02) ).
cnf(c_214,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(clausify,[status(thm)],[m__2911_02]) ).
cnf(c_215,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_261,plain,
aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_115,c_85]) ).
cnf(c_1210,plain,
( sdtlpdtrp0(xF,C) != B
| ~ aElementOf0(C,szDzozmdt0(xF))
| aElementOf0(B,A)
| sdtlcdtrc0(xF,szDzozmdt0(xF)) != A ),
inference(resolve,[status(thm)],[c_98,c_261]) ).
cnf(c_1211,plain,
( sdtlpdtrp0(xF,B) != A
| ~ aElementOf0(B,szDzozmdt0(xF))
| aElementOf0(A,sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
inference(xxres,[status(thm)],[c_1210]) ).
cnf(c_1212,plain,
( sdtlpdtrp0(xF,xx) != A
| aElementOf0(A,sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
inference(resolve,[status(thm)],[c_1211,c_214]) ).
cnf(c_1213,plain,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(xxres,[status(thm)],[c_1212]) ).
cnf(c_1209,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_215,c_1213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:14:55 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 2659876 was started by sandbox on n008,
% 0.10/0.37 % Sat Sep 26 03:14:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 1.71/0.64
% 1.71/0.64 % SZS status Theorem for theBenchmark
% 1.71/0.64
% 1.71/0.64 % Proof 1 at 0.15 (+ 0.03) seconds.
% 1.71/0.64 % Length of proof is 14.
% 1.71/0.64 % Level of proof is 4.
% 1.71/0.64 % Maximum clause weight is 30.000.
% 1.71/0.64 % Given clauses 172.
% 1.71/0.64
% 1.71/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------