%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM607+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 : n007.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 08:17:33 AM UTC 2026
% Result : Theorem 35.45s 10.02s
% Output : CNFRefutation 35.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 21 unt; 0 def)
% Number of atoms : 113 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 114 ( 48 ~; 45 |; 13 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 10 !; 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(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__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(xQ,szDzozmdt0(xc)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xQ,szDzozmdt0(xc)),
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_190,plain,
( sbrdtbr0(D) = B
| ~ aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
cnf(c_191,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_234,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[m__3418]) ).
cnf(c_235,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_238,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(clausify,[status(thm)],[m__3453]) ).
cnf(c_239,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_285,plain,
aSet0(xO),
inference(clausify,[status(thm)],[m__4891]) ).
fof(m__4998,axiom,
aSubsetOf0(xO,xS),
file('theBenchmark.p',m__4998) ).
cnf(c_291,plain,
aSubsetOf0(xO,xS),
inference(clausify,[status(thm)],[m__4998]) ).
fof(m__5078,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('theBenchmark.p',m__5078) ).
cnf(c_292,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(clausify,[status(thm)],[m__5078]) ).
cnf(c_293,plain,
aSubsetOf0(xQ,xO),
inference(clausify,[status(thm)],[m__5093]) ).
cnf(c_296,negated_conjecture,
~ aElementOf0(xQ,szDzozmdt0(xc)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_475,plain,
( sbrdtbr0(C) = B
| ~ aElementOf0(C,slbdtsldtrb0(A,B))
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(xxres,[status(thm)],[c_190]) ).
cnf(c_23053,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_235,c_100]) ).
cnf(c_751,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_132,c_23053]) ).
cnf(c_23054,plain,
( sbrdtbr0(A) != xK
| ~ aSubsetOf0(A,xS)
| aElementOf0(A,szDzozmdt0(xc))
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_239,c_191]) ).
cnf(c_23055,plain,
( sbrdtbr0(A) != xK
| ~ aSubsetOf0(A,xS)
| aElementOf0(A,szDzozmdt0(xc))
| ~ aElementOf0(xK,szNzAzT0) ),
inference(resolve,[status(thm)],[c_751,c_23054]) ).
cnf(c_804,plain,
( sbrdtbr0(A) != xK
| ~ aSubsetOf0(A,xS)
| aElementOf0(A,szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_234,c_23055]) ).
cnf(c_23056,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(xS)
| ~ aSet0(xO)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_291,c_107]) ).
cnf(c_23057,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(xS)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_285,c_23056]) ).
cnf(c_1389,plain,
( aSubsetOf0(A,xS)
| ~ aSubsetOf0(A,xO)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_751,c_23057]) ).
cnf(c_23058,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolve,[status(thm)],[c_293,c_100]) ).
cnf(c_1433,plain,
aSet0(xQ),
inference(resolve,[status(thm)],[c_285,c_23058]) ).
cnf(c_23059,plain,
( aSubsetOf0(xQ,xS)
| ~ aSubsetOf0(xQ,xO) ),
inference(resolve,[status(thm)],[c_1389,c_1433]) ).
cnf(c_2874,plain,
aSubsetOf0(xQ,xS),
inference(resolve,[status(thm)],[c_293,c_23059]) ).
cnf(c_23060,plain,
( sbrdtbr0(xQ) = xK
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolve,[status(thm)],[c_475,c_292]) ).
cnf(c_23061,plain,
( sbrdtbr0(xQ) = xK
| ~ aElementOf0(xK,szNzAzT0) ),
inference(resolve,[status(thm)],[c_285,c_23060]) ).
cnf(c_9966,plain,
sbrdtbr0(xQ) = xK,
inference(resolve,[status(thm)],[c_234,c_23061]) ).
cnf(c_23062,plain,
( sbrdtbr0(xQ) != xK
| aElementOf0(xQ,szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_804,c_2874]) ).
cnf(c_23063,plain,
( xK != xK
| aElementOf0(xQ,szDzozmdt0(xc)) ),
inference(paramod,[status(thm)],[c_9966,c_23062]) ).
cnf(c_23064,plain,
aElementOf0(xQ,szDzozmdt0(xc)),
inference(copy,[status(thm)],[c_23063]) ).
cnf(c_23052,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_296,c_23064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM607+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n007.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 03:23:44 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.38 % Process 2683692 was started by sandbox on n007,
% 0.08/5.38 % Sat Sep 26 03:23:44 2026
% 0.08/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 35.45/10.02
% 35.45/10.02 % given #500 (F,wt=15): 3687 slbdtsldtrb0(xS,xk) != slcrc0. [resolve(1686,a,247,a)].
% 35.45/10.02
% 35.45/10.02 % given #1000 (W,wt=14): 13145 isCountable0(sdtmndt0(xO,xK)). [resolve(1313,a,726,a)].
% 35.45/10.02
% 35.45/10.02 % given #1500 (F,wt=14): 20066 -isCountable0(sdtmndt0(xT,xQ)). [resolve(19477,a,98,a),unit_del(b,19509)].
% 35.45/10.02
% 35.45/10.02 % SZS status Theorem for theBenchmark
% 35.45/10.02
% 35.45/10.02 % Proof 1 at 3.29 (+ 1.23) seconds.
% 35.45/10.02 % Length of proof is 31.
% 35.45/10.02 % Level of proof is 5.
% 35.45/10.02 % Maximum clause weight is 30.000.
% 35.45/10.02 % Given clauses 1849.
% 35.45/10.02
% 35.45/10.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------