%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM582+3 : 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 : n015.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 56.70s 7.78s
% Output : CNFRefutation 56.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 57 ( 4 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 48 ( 10 ~; 10 |; 16 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('theBenchmark.p',mZeroLess) ).
fof(m__3623,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('theBenchmark.p',m__3623) ).
fof(m__3754,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) ),
file('theBenchmark.p',m__3754) ).
fof(m__,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_597,plain,
( sdtlseqdt0(sz00,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mZeroLess]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_604,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_653,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausify,[status(thm)],[m__3623]) ).
cnf(c_692,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),sdtlpdtrp0(xN,B))
| ~ sdtlseqdt0(B,A)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3754]) ).
fof(m__3989,axiom,
aElementOf0(xi,szNzAzT0),
file('theBenchmark.p',m__3989) ).
cnf(c_698,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3989]) ).
cnf(c_719,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_6718,plain,
sdtlseqdt0(sz00,xi),
inference(resolve,[status(thm)],[c_698,c_597]) ).
cnf(c_16342,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_6718,c_692]) ).
cnf(c_16343,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolve,[status(thm)],[c_698,c_16342]) ).
cnf(c_7035,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)),
inference(resolve,[status(thm)],[c_604,c_16343]) ).
cnf(c_16344,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(paramod,[status(thm)],[c_653,c_7035]) ).
cnf(c_16341,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_719,c_16344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM582+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % 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 2995744 was started by sandbox on n015,
% 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".
% 0.23/0.47
% 0.23/0.47 % From the command line: assign(max_seconds, 300).
% 56.70/7.78
% 56.70/7.78 % given #500 (I,wt=68): 816 szDzozmdt0(A) != slbdtsldtrb0(B,C) | -aElementOf0(C,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(C,B),szNzAzT0) | -isCountable0(B) | -aFunction0(A) | -aSubsetOf0(sdtlcdtrc0(A,szDzozmdt0(A)),xT) | -iLess0(C,xK) | -aSet0(D) | -aElementOf0(f29(C,B,A,D),f28(C,B,A)) | sbrdtbr0(D) != C | f27(C,B,A) = sdtlpdtrp0(A,D). [copy(815),flip(l)].
% 56.70/7.78
% 56.70/7.78 % given #1000 (I,wt=63): 1649 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | aSet0(f28(A,B,C)). [resolve(275,a,144,e)].
% 56.70/7.78
% 56.70/7.78 % given #1500 (I,wt=85): 2373 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSet0(E) | aElementOf0(f29(A,B,C,E),E) | sbrdtbr0(E) != A | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(2372),flip(p)].
% 56.70/7.78
% 56.70/7.78 % given #2000 (I,wt=82): 3093 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,E),szDzozmdt0(C)) | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [resolve(280,a,199,f)].
% 56.70/7.78
% 56.70/7.78 % given #2500 (I,wt=73): 3793 -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | defn_00(A,B,C,D) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,E),szDzozmdt0(C)) | -iLess0(A,xK) | -aElementOf0(f29(A,B,C,B),f28(A,B,C)) | sbrdtbr0(B) != A | f27(A,B,C) = sdtlpdtrp0(C,B). [factor(468,b,j)].
% 56.70/7.78
% 56.70/7.78 % given #3000 (I,wt=96): 4302 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,D)) = D | -iLess0(A,xK) | -aElementOf0(f29(A,B,C,f23(A,B,C)),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(1799,a,m),merge(n)].
% 56.70/7.78
% 56.70/7.78 % given #3500 (I,wt=94): 4819 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(F,szDzozmdt0(C)) | sdtlpdtrp0(C,F) != E | -iLess0(A,xK) | -aSubsetOf0(f23(A,B,C),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(2330,c,p)].
% 56.70/7.78
% 56.70/7.78 % given #4000 (I,wt=97): 5334 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,E)) = E | -iLess0(A,xK) | -aSubsetOf0(f23(A,B,C),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(3071,c,o)].
% 56.70/7.78
% 56.70/7.78 % given #4500 (I,wt=125): 5844 -aSet0(f23(A,szDzozmdt0(B),B)) | -aElementOf0(f24(A,szDzozmdt0(B),B),szDzozmdt0(B)) | sbrdtbr0(f23(A,szDzozmdt0(B),B)) != A | aSubsetOf0(f23(A,szDzozmdt0(B),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | -aElementOf0(f22(A,szDzozmdt0(B)),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | aElementOf0(f29(A,szDzozmdt0(B),B,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(B,szDzozmdt0(B))) | f29(A,szDzozmdt0(B),B,sdtlcdtrc0(B,szDzozmdt0(B))) != sdtlpdtrp0(B,f24(A,szDzozmdt0(B),B)) | -iLess0(A,xK) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(sdtlcdtrc0(B,szDzozmdt0(B))) != A | f27(A,szDzozmdt0(B),B) = sdtlpdtrp0(B,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(4411,j,n),flip(k)].
% 56.70/7.78
% 56.70/7.78 % given #5000 (T,wt=8): 6394 sdtlseqdt0(sz00,sz00). [resolve(604,a,597,a)].
% 56.70/7.78
% 56.70/7.78 % given #5500 (A,wt=23): 6517 xk = sz00 | szszuzczcdt0(f5(xk)) = xk. [resolve(649,a,599,a),flip(a)].
% 56.70/7.78
% 56.70/7.78 % SZS status Theorem for theBenchmark
% 56.70/7.78
% 56.70/7.78 % Proof 1 at 6.78 (+ 0.44) seconds.
% 56.70/7.78 % Length of proof is 13.
% 56.70/7.78 % Level of proof is 4.
% 56.70/7.78 % Maximum clause weight is 26.000.
% 56.70/7.78 % Given clauses 5572.
% 56.70/7.78
% 56.70/7.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------