%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM565+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 08:17:25 AM UTC 2026
% Result : Theorem 41.27s 5.78s
% Output : CNFRefutation 41.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 51 ( 19 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 51 ( 14 ~; 5 |; 24 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('theBenchmark.p',mCardEmpty) ).
fof(m__,conjecture,
! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) )
=> ( ( ~ ? [W1] : aElementOf0(W1,slcrc0)
& aSet0(slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) )
=> ( ( ~ ? [W1] : aElementOf0(W1,slcrc0)
& aSet0(slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_75,plain,
? [W0] :
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,W0)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& aSet0(slcrc0)
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(W0) = sz00
& aSubsetOf0(W0,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,W0) )
& aSet0(W0) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK0)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& aSet0(slcrc0)
& aElementOf0(sK0,slbdtsldtrb0(xS,sz00))
& sbrdtbr0(sK0) = sz00
& aSubsetOf0(sK0,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sK0) )
& aSet0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_75]) ).
cnf(c_1198,negated_conjecture,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_1202,negated_conjecture,
sbrdtbr0(sK0) = sz00,
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_1203,negated_conjecture,
sz00 = sbrdtbr0(sK0),
inference(copy,[status(thm)],[c_1202]) ).
cnf(c_1206,negated_conjecture,
aSet0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_1515,plain,
( slcrc0 = A
| sbrdtbr0(A) != sz00
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardEmpty]) ).
cnf(c_8006,negated_conjecture,
( slcrc0 = sK0
| sbrdtbr0(sK0) != sz00 ),
inference(resolve,[status(thm)],[c_1515,c_1206]) ).
cnf(c_7737,negated_conjecture,
slcrc0 = sK0,
inference(resolve,[status(thm)],[c_1203,c_8006]) ).
cnf(c_8007,plain,
sdtlpdtrp0(xc,sK0) != sdtlpdtrp0(xc,sK0),
inference(paramod,[status(thm)],[c_7737,c_1198]) ).
cnf(c_8005,plain,
$false,
inference(copy,[status(thm)],[c_8007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM565+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n015.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 03:18:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2989605 was started by sandbox on n015,
% 0.08/0.35 % Sat Sep 26 03:18:28 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.47
% 0.11/0.47 % From the command line: assign(max_seconds, 300).
% 41.27/5.78
% 41.27/5.78 % given #500 (I,wt=45): 1189 szDzozmdt0(A) != slbdtsldtrb0(B,C) | -aElementOf0(C,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(A) | -aSubsetOf0(sdtlcdtrc0(A,szDzozmdt0(A)),xT) | -iLess0(C,xK) | isCountable0(f28(C,B,A)). [resolve(76,a,81,e)].
% 41.27/5.78
% 41.27/5.78 % given #1000 (I,wt=68): 1807 -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),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | aSubsetOf0(f28(A,B,C),B). [resolve(269,a,199,f)].
% 41.27/5.78
% 41.27/5.78 % given #1500 (I,wt=79): 2529 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | 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) | -aSubsetOf0(D,f28(A,B,C)) | sbrdtbr0(D) != A | f27(A,B,C) = sdtlpdtrp0(C,D). [copy(2528),flip(m)].
% 41.27/5.78
% 41.27/5.78 % given #2000 (I,wt=85): 3251 -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),B) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,E),szDzozmdt0(C)) | -iLess0(A,xK) | -aElementOf0(F,f28(A,B,C)) | aElementOf0(F,B). [resolve(274,a,254,f)].
% 41.27/5.78
% 41.27/5.78 % given #2500 (I,wt=86): 3974 aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -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) | -aSet0(F) | -aElementOf0(f29(A,B,C,F),f28(A,B,C)) | sbrdtbr0(F) != A | f27(A,B,C) = sdtlpdtrp0(C,F). [copy(3973),flip(o)].
% 41.27/5.78
% 41.27/5.78 % given #3000 (I,wt=83): 4591 -aSubsetOf0(f23(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) | -aElementOf0(f26(A,B,C),xT) | -iLess0(A,xK) | -aSet0(f23(A,B,C)) | -aElementOf0(f29(A,B,C,f23(A,B,C)),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(907,b,l)].
% 41.27/5.78
% 41.27/5.78 % given #3500 (I,wt=85): 5093 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | aSubsetOf0(f23(A,B,C),B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSubsetOf0(f23(A,B,C),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(2113,c,m)].
% 41.27/5.78
% 41.27/5.78 % given #4000 (I,wt=76): 5593 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f23(A,B,C)) != D | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [factor(2499,d,j)].
% 41.27/5.78
% 41.27/5.78 % given #4500 (I,wt=82): 6093 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f22(A,B),f23(A,B,C)) | aElementOf0(f22(A,B),B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(E,szDzozmdt0(C)) | sdtlpdtrp0(C,E) != D | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [factor(3227,e,h)].
% 41.27/5.78
% 41.27/5.78 % given #5000 (I,wt=67): 6593 aElementOf0(f23(A,szDzozmdt0(B),B),szDzozmdt0(B)) | -aElementOf0(f23(A,szDzozmdt0(B),B),f23(A,szDzozmdt0(B),B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | aElementOf0(f22(A,szDzozmdt0(B)),szDzozmdt0(B)) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | -aSubsetOf0(sdtlcdtrc0(B,szDzozmdt0(B)),xT) | -iLess0(A,xK) | aSet0(f28(A,szDzozmdt0(B),B)). [factor(4006,a,c)].
% 41.27/5.78
% 41.27/5.78 % given #5500 (I,wt=123): 7093 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | -aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(A,szNzAzT0) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),szNzAzT0) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | -iLess0(A,xK) | -aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(5291,e,m)].
% 41.27/5.78
% 41.27/5.78 % given #6000 (I,wt=134): 7593 -aSubsetOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(B,szDzozmdt0(B))) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | sdtlpdtrp0(B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != f22(A,sdtlcdtrc0(B,szDzozmdt0(B))) | -iLess0(A,xK) | -aSubsetOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(6897,f,i)].
% 41.27/5.78
% 41.27/5.78 % SZS status Theorem for theBenchmark
% 41.27/5.78
% 41.27/5.78 % Proof 1 at 4.99 (+ 0.25) seconds.
% 41.27/5.78 % Length of proof is 9.
% 41.27/5.78 % Level of proof is 4.
% 41.27/5.78 % Maximum clause weight is 19.000.
% 41.27/5.78 % Given clauses 6064.
% 41.27/5.78
% 41.27/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------