%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM584+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 : 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 08:17:28 AM UTC 2026
% Result : Theorem 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 61 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 18 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 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(mDefSel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3453,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('theBenchmark.p',m__3453) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_87,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_119,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_178,plain,
( sbrdtbr0(D) != B
| ~ aSubsetOf0(D,A)
| aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
fof(m__3418,axiom,
aElementOf0(xK,szNzAzT0),
file('theBenchmark.p',m__3418) ).
cnf(c_221,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[m__3418]) ).
cnf(c_222,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_225,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(clausify,[status(thm)],[m__3453]) ).
cnf(c_226,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(copy,[status(thm)],[c_225]) ).
fof(m__4007,axiom,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('theBenchmark.p',m__4007) ).
cnf(c_247,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(clausify,[status(thm)],[m__4007]) ).
fof(m__4024,axiom,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('theBenchmark.p',m__4024) ).
cnf(c_248,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(clausify,[status(thm)],[m__4024]) ).
cnf(c_249,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_250,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(paramod,[status(thm)],[c_226,c_249]) ).
cnf(c_1026,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_222,c_87]) ).
cnf(c_446,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_119,c_1026]) ).
cnf(c_1027,plain,
( sbrdtbr0(C) != A
| ~ aSubsetOf0(C,xS)
| aElementOf0(C,B)
| slbdtsldtrb0(xS,A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_178,c_446]) ).
cnf(c_1028,plain,
( sbrdtbr0(B) != xK
| ~ aSubsetOf0(B,xS)
| aElementOf0(B,A)
| slbdtsldtrb0(xS,xK) != A ),
inference(resolve,[status(thm)],[c_1027,c_221]) ).
cnf(c_1029,plain,
( sbrdtbr0(A) != xK
| ~ aSubsetOf0(A,xS)
| aElementOf0(A,szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_1028,c_226]) ).
cnf(c_1030,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_1029,c_248]) ).
cnf(c_1031,plain,
aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(resolve,[status(thm)],[c_1030,c_247]) ).
cnf(c_1025,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_250,c_1031]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM584+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 03:22:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 4168836 was started by sandbox on n026,
% 0.08/0.36 % Sat Sep 26 03:22:42 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.12/0.47 % Length of proof is 19.
% 0.12/0.47 % Level of proof is 4.
% 0.12/0.47 % Maximum clause weight is 34.000.
% 0.12/0.47 % Given clauses 199.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------