%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM600+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 : n003.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 08:17:31 AM UTC 2026
% Result : Theorem 27.89s 4.62s
% Output : CNFRefutation 27.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 69 ( 25 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 76 ( 25 ~; 18 |; 27 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4730,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('theBenchmark.p',m__4730) ).
fof(m__4854,axiom,
( ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) ) )
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(szDzizrdt0(xd),xT) ),
file('theBenchmark.p',m__4854) ).
fof(m__,conjecture,
! [W0] :
( ( aElementOf0(W0,xO)
& ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& ( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xd,W1) = szDzizrdt0(xd) )
& aElementOf0(W1,szNzAzT0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( ( aElementOf0(W0,xO)
& ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& ( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xd,W1) = szDzizrdt0(xd) )
& aElementOf0(W1,szNzAzT0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_917,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(clausify,[status(thm)],[m__4730]) ).
cnf(c_936,plain,
( aElementOf0(A,szDzozmdt0(xd))
| ~ aElementOf0(A,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(clausify,[status(thm)],[m__4854]) ).
cnf(c_937,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(paramod,[status(thm)],[c_917,c_936]) ).
fof(nnf_91,plain,
? [W0] :
( ! [W1] :
( sdtlpdtrp0(xe,W1) != W0
| ( ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) != sdtlpdtrp0(xd,W1) )
| ~ aElementOf0(W1,szNzAzT0) )
& aElementOf0(W0,xO)
& ? [X0] :
( sdtlpdtrp0(xe,X0) = W0
& aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
( ! [W1] :
( sdtlpdtrp0(xe,W1) != sK1
| ( ~ aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) != sdtlpdtrp0(xd,W1) )
| ~ aElementOf0(W1,szNzAzT0) )
& aElementOf0(sK1,xO)
& sdtlpdtrp0(xe,sK0) = sK1
& aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(W0,sK1),skolemize(X0,sK0)],[nnf_91]) ).
fof(sk_m___neg,plain,
( ! [VAR_0] :
( sdtlpdtrp0(xe,VAR_0) != sK1
| ~ aElementOf0(VAR_0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( sdtlpdtrp0(xe,VAR_0) != sK1
| szDzizrdt0(xd) != sdtlpdtrp0(xd,VAR_0)
| ~ aElementOf0(VAR_0,szNzAzT0) )
& aElementOf0(sK1,xO)
& sdtlpdtrp0(xe,sK0) = sK1
& aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_951,negated_conjecture,
aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_952,negated_conjecture,
sdtlpdtrp0(xe,sK0) = sK1,
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_956,negated_conjecture,
( sdtlpdtrp0(xe,A) != sK1
| ~ aElementOf0(A,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_5622,plain,
aElementOf0(sK0,szNzAzT0),
inference(resolve,[status(thm)],[c_951,c_937]) ).
cnf(c_5695,negated_conjecture,
( sdtlpdtrp0(xe,sK0) != sK1
| ~ aElementOf0(sK0,szNzAzT0) ),
inference(resolve,[status(thm)],[c_956,c_951]) ).
cnf(c_5696,negated_conjecture,
( sK1 != sK1
| ~ aElementOf0(sK0,szNzAzT0) ),
inference(paramod,[status(thm)],[c_952,c_5695]) ).
cnf(c_5697,negated_conjecture,
~ aElementOf0(sK0,szNzAzT0),
inference(copy,[status(thm)],[c_5696]) ).
cnf(c_5694,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5622,c_5697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM600+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:25:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1918621 was started by sandbox on n003,
% 0.09/0.37 % Sat Sep 26 03:25:53 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.32/0.62
% 0.32/0.62 % From the command line: assign(max_seconds, 300).
% 27.89/4.62
% 27.89/4.62 % given #500 (I,wt=17): 899 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 27.89/4.62
% 27.89/4.62 % SZS status Theorem for theBenchmark
% 27.89/4.62
% 27.89/4.62 % Proof 1 at 3.78 (+ 0.17) seconds.
% 27.89/4.62 % Length of proof is 11.
% 27.89/4.62 % Level of proof is 4.
% 27.89/4.62 % Maximum clause weight is 14.000.
% 27.89/4.62 % Given clauses 544.
% 27.89/4.62
% 27.89/4.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------