%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM602+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 : n013.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 18.47s 6.20s
% Output : CNFRefutation 18.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 40 ( 12 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 30 ( 6 ~; 5 |; 15 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 11 ( 0 sgn 4 !; 4 ?)
% 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__5009,axiom,
( aElementOf0(xx,xO)
& ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('theBenchmark.p',m__5009) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,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_92,plain,
( aElementOf0(xx,xO)
& ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(fof_nnf,[status(thm)],[m__5009]) ).
fof(sk_m__5009,plain,
( aElementOf0(xx,xO)
& sdtlpdtrp0(xe,sK0) = xx
& aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_92]) ).
cnf(c_961,plain,
aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(split_conjunct,[status(thm)],[sk_m__5009]) ).
cnf(c_962,plain,
sdtlpdtrp0(xe,sK0) = xx,
inference(split_conjunct,[status(thm)],[sk_m__5009]) ).
cnf(c_964,negated_conjecture,
( sdtlpdtrp0(xe,A) != xx
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_4969,plain,
aElementOf0(sK0,szNzAzT0),
inference(resolve,[status(thm)],[c_961,c_937]) ).
cnf(c_5032,negated_conjecture,
~ aElementOf0(sK0,szNzAzT0),
inference(resolve,[status(thm)],[c_964,c_962]) ).
cnf(c_5031,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4969,c_5032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM602+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n013.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sat Sep 26 03:24:36 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.43 % Process 1830080 was started by sandbox on n013,
% 0.10/0.43 % Sat Sep 26 03:24:36 2026
% 0.10/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.34/0.74
% 0.34/0.74 % From the command line: assign(max_seconds, 300).
% 18.47/6.20
% 18.47/6.20 % given #500 (I,wt=25): 899 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 18.47/6.20
% 18.47/6.20 % SZS status Theorem for theBenchmark
% 18.47/6.20
% 18.47/6.20 % Proof 1 at 2.36 (+ 0.17) seconds.
% 18.47/6.20 % Length of proof is 12.
% 18.47/6.20 % Level of proof is 4.
% 18.47/6.20 % Maximum clause weight is 15.000.
% 18.47/6.20 % Given clauses 551.
% 18.47/6.20
% 18.47/6.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------