%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM615+1 : 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 : n016.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 08:17:34 AM UTC 2026
% Result : Theorem 11.30s 7.01s
% Output : CNFRefutation 11.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 30 ( 11 ~; 8 |; 10 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4982,axiom,
! [W0] :
( aElementOf0(W0,xO)
=> ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
file('theBenchmark.p',m__4982) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_90,plain,
! [W0] :
( ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) )
| ~ aElementOf0(W0,xO) ),
inference(fof_nnf,[status(thm)],[m__4982]) ).
fof(sk_m__4982_sk,plain,
! [W0] :
( ( sdtlpdtrp0(xe,sK0(W0)) = W0
& aElementOf0(sK0(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(sK0(W0),szNzAzT0) )
| ~ aElementOf0(W0,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_90]) ).
fof(sk_m__4982,plain,
( ! [VAR_0] :
( sdtlpdtrp0(xe,sK0(VAR_0)) = VAR_0
| ~ aElementOf0(VAR_0,xO) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(VAR_0,xO) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),szNzAzT0)
| ~ aElementOf0(VAR_0,xO) ) ),
inference(cnf_transformation,[status(thm)],[sk_m__4982_sk]) ).
cnf(c_288,plain,
( aElementOf0(sK0(A),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(A,xO) ),
inference(split_conjunct,[status(thm)],[sk_m__4982]) ).
cnf(c_289,plain,
( sdtlpdtrp0(xe,sK0(A)) = A
| ~ aElementOf0(A,xO) ),
inference(split_conjunct,[status(thm)],[sk_m__4982]) ).
fof(m__5182,axiom,
aElementOf0(xp,xO),
file('theBenchmark.p',m__5182) ).
cnf(c_301,plain,
aElementOf0(xp,xO),
inference(clausify,[status(thm)],[m__5182]) ).
cnf(c_306,negated_conjecture,
( sdtlpdtrp0(xe,A) != xp
| ~ aElementOf0(A,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_909,plain,
sdtlpdtrp0(xe,sK0(xp)) = xp,
inference(resolve,[status(thm)],[c_301,c_289]) ).
cnf(c_910,plain,
aElementOf0(sK0(xp),sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(resolve,[status(thm)],[c_301,c_288]) ).
cnf(c_21362,negated_conjecture,
sdtlpdtrp0(xe,sK0(xp)) != xp,
inference(resolve,[status(thm)],[c_910,c_306]) ).
cnf(c_21361,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_909,c_21362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM615+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n016.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 03:32:21 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 4100567 was started by sandbox on n016,
% 0.09/5.36 % Sat Sep 26 03:32:21 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 11.30/7.01
% 11.30/7.01 % given #500 (F,wt=19): 2383 -aSet0(sdtlpdtrp0(xN,sz00)) | sdtlpdtrp0(xN,sz00) != slcrc0. [resolve(613,a,100,b),flip(b)].
% 11.30/7.01
% 11.30/7.01 % given #1000 (A,wt=37): 524 -aSet0(A) | slbdtsldtrb0(A,xk) = B | -aSet0(B) | aElementOf0(f11(A,xk,B),B) | sbrdtbr0(f11(A,xk,B)) = xk. [resolve(248,a,194,b)].
% 11.30/7.01
% 11.30/7.01 % given #1500 (T,wt=16): 12901 -isFinite0(szNzAzT0) | isFinite0(sdtlbdtrb0(xC,sz00)). [resolve(12857,a,105,c),unit_del(a,133)].
% 11.30/7.01
% 11.30/7.01 % given #2000 (F,wt=15): 17012 sdtmndt0(xO,xp) != szNzAzT0. [resolve(16932,a,284,a)].
% 11.30/7.01
% 11.30/7.01 % given #2500 (A,wt=20): 886 -aSet0(A) | aSubsetOf0(xP,A) | aElementOf0(f2(A,xP),xP). [resolve(298,a,103,c)].
% 11.30/7.01
% 11.30/7.01 % SZS status Theorem for theBenchmark
% 11.30/7.01
% 11.30/7.01 % Proof 1 at 1.22 (+ 0.34) seconds.
% 11.30/7.01 % Length of proof is 9.
% 11.30/7.01 % Level of proof is 3.
% 11.30/7.01 % Maximum clause weight is 26.000.
% 11.30/7.01 % Given clauses 2585.
% 11.30/7.01
% 11.30/7.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------