%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM607+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 : n004.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 35.13s 5.75s
% Output : CNFRefutation 35.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 44 ( 1 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 47 ( 16 ~; 11 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn 6 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4998,axiom,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__4998) ).
fof(m__5093,axiom,
( ~ ( xQ = slcrc0
| ~ ? [W0] : aElementOf0(W0,xQ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
file('theBenchmark.p',m__5093) ).
fof(m__,conjecture,
( aElementOf0(xQ,szDzozmdt0(xc))
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(xQ,szDzozmdt0(xc))
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
| aSubsetOf0(xQ,xS)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_96,plain,
( ~ aElementOf0(xQ,szDzozmdt0(xc))
& ~ aSubsetOf0(xQ,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xQ) )
& ~ aSubsetOf0(xQ,xS)
& ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xQ) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ aElementOf0(xQ,szDzozmdt0(xc))
& ~ aSubsetOf0(xQ,xS)
& ~ aElementOf0(sK1,xS)
& aElementOf0(sK1,xQ)
& ~ aSubsetOf0(xQ,xS)
& ~ aElementOf0(sK0,xS)
& aElementOf0(sK0,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(W0,sK1)],[nnf_96]) ).
cnf(c_1107,negated_conjecture,
~ aElementOf0(sK0,xS),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_1108,negated_conjecture,
aElementOf0(sK0,xQ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_1113,plain,
( aElementOf0(A,xO)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5093]) ).
cnf(c_1119,plain,
( aElementOf0(A,xS)
| ~ aElementOf0(A,xO) ),
inference(clausify,[status(thm)],[m__4998]) ).
cnf(c_7931,plain,
aElementOf0(sK0,xO),
inference(resolve,[status(thm)],[c_1113,c_1108]) ).
cnf(c_9582,plain,
aElementOf0(sK0,xS),
inference(resolve,[status(thm)],[c_7931,c_1119]) ).
cnf(c_9581,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1107,c_9582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM607+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:26:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 711092 was started by sandbox on n004,
% 0.09/0.38 % Sat Sep 26 03:26:06 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.36/0.63
% 0.36/0.63 % From the command line: assign(max_seconds, 300).
% 35.13/5.75
% 35.13/5.75 % given #500 (I,wt=34): 1167 -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(B,slbdtsldtrb0(f39(A),xk)) | sdtlpdtrp0(sdtlpdtrp0(xC,A),B) = f38(A) # tptp_name(m__4411). [clausify(83)].
% 35.13/5.75
% 35.13/5.75 % given #1000 (I,wt=11): 1680 -aSet0(A) | -isCountable0(A) | -isFinite0(A) # tptp_name(mCountNFin). [clausify(7)].
% 35.13/5.75
% 35.13/5.75 % given #1500 (I,wt=75): 2460 -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) | -aSubsetOf0(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(292,a,151,e)].
% 35.13/5.75
% 35.13/5.75 % given #2000 (I,wt=78): 3184 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | 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(D,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,D),szDzozmdt0(C)) | -iLess0(A,xK) | isCountable0(f28(A,B,C)). [resolve(294,a,273,f)].
% 35.13/5.75
% 35.13/5.75 % given #2500 (I,wt=75): 3905 aElementOf0(f23(A,B,C),szDzozmdt0(C)) | aSubsetOf0(f23(A,B,C),B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,D),szDzozmdt0(C)) | -iLess0(A,xK) | -aElementOf0(E,slbdtsldtrb0(f28(A,B,C),A)) | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(3904),flip(l)].
% 35.13/5.75
% 35.13/5.75 % given #3000 (I,wt=71): 4608 -aSubsetOf0(f23(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(F,szDzozmdt0(C)) | sdtlpdtrp0(C,F) != E | -iLess0(A,xK) | -aElementOf0(D,f28(A,B,C)). [factor(507,d,n)].
% 35.13/5.75
% 35.13/5.75 % given #3500 (I,wt=144): 5110 -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(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),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) | sdtlpdtrp0(B,f25(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B))) = f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) | -iLess0(A,xK) | -aSubsetOf0(C,f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | sbrdtbr0(C) != A | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,C). [factor(1983,b,j)].
% 35.13/5.75
% 35.13/5.75 % given #4000 (I,wt=133): 5610 -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(C,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(C,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) | sdtlpdtrp0(B,f25(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B))) = f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) | -iLess0(A,xK) | aSet0(f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(2537,b,k)].
% 35.13/5.75
% 35.13/5.75 % given #4500 (I,wt=70): 6110 -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) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(C)),xT) | -iLess0(A,xK) | -aElementOf0(D,f28(A,B,C)). [factor(3212,e,m)].
% 35.13/5.75
% 35.13/5.75 % given #5000 (I,wt=63): 6610 aElementOf0(f23(A,szDzozmdt0(B),B),szDzozmdt0(B)) | -aElementOf0(f23(A,szDzozmdt0(B),B),f23(A,szDzozmdt0(B),B)) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(szDzozmdt0(B),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | -aElementOf0(f26(A,szDzozmdt0(B),B),xT) | -iLess0(A,xK) | aElementOf0(f27(A,szDzozmdt0(B),B),xT). [factor(4046,a,c)].
% 35.13/5.75
% 35.13/5.75 % given #5500 (I,wt=81): 7110 aElementOf0(f23(A,B,C),szDzozmdt0(C)) | aSet0(f23(A,B,C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(E,szDzozmdt0(C)) | sdtlpdtrp0(C,E) != D | -iLess0(A,xK) | -aElementOf0(f29(A,B,C,B),f28(A,B,C)) | sbrdtbr0(B) != A | f27(A,B,C) = sdtlpdtrp0(C,B). [factor(4520,d,l)].
% 35.13/5.75
% 35.13/5.75 % given #6000 (I,wt=147): 7612 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(C,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(C,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) | -aElementOf0(D,szDzozmdt0(B)) | sdtlpdtrp0(B,D) != C | -iLess0(A,xK) | -aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,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(6216,e,k)].
% 35.13/5.75
% 35.13/5.75 % SZS status Theorem for theBenchmark
% 35.13/5.75
% 35.13/5.75 % Proof 1 at 4.82 (+ 0.20) seconds.
% 35.13/5.75 % Length of proof is 9.
% 35.13/5.75 % Level of proof is 3.
% 35.13/5.75 % Maximum clause weight is 11.000.
% 35.13/5.75 % Given clauses 6329.
% 35.13/5.75
% 35.13/5.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------