%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM618+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:17:35 AM UTC 2026
% Result : Theorem 2.89s 0.86s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 36 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 8 |; 11 &)
% ( 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__5365,axiom,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ),
file('theBenchmark.p',m__5365) ).
fof(m__,conjecture,
? [W0] :
( xx = sdtlpdtrp0(xe,W0)
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( xx = sdtlpdtrp0(xe,W0)
& aElementOf0(W0,szNzAzT0) ),
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_291,plain,
( aElementOf0(sK0(A),szNzAzT0)
| ~ aElementOf0(A,xO) ),
inference(split_conjunct,[status(thm)],[sk_m__4982]) ).
cnf(c_293,plain,
( sdtlpdtrp0(xe,sK0(A)) = A
| ~ aElementOf0(A,xO) ),
inference(split_conjunct,[status(thm)],[sk_m__4982]) ).
cnf(c_317,plain,
aElementOf0(xx,xO),
inference(clausify,[status(thm)],[m__5365]) ).
cnf(c_318,negated_conjecture,
( sdtlpdtrp0(xe,A) != xx
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_1118,plain,
sdtlpdtrp0(xe,sK0(xx)) = xx,
inference(resolve,[status(thm)],[c_317,c_293]) ).
cnf(c_1120,plain,
aElementOf0(sK0(xx),szNzAzT0),
inference(resolve,[status(thm)],[c_317,c_291]) ).
cnf(c_3302,negated_conjecture,
sdtlpdtrp0(xe,sK0(xx)) != xx,
inference(resolve,[status(thm)],[c_1120,c_318]) ).
cnf(c_3303,negated_conjecture,
xx != xx,
inference(paramod,[status(thm)],[c_1118,c_3302]) ).
cnf(c_3301,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_3303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM618+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 03:30:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 4182305 was started by sandbox2 on n026,
% 0.12/0.38 % Sat Sep 26 03:30:54 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.40
% 0.16/0.40 % From the command line: assign(max_seconds, 300).
% 2.89/0.86
% 2.89/0.86 % SZS status Theorem for theBenchmark
% 2.89/0.86
% 2.89/0.86 % Proof 1 at 0.35 (+ 0.09) seconds.
% 2.89/0.86 % Length of proof is 10.
% 2.89/0.86 % Level of proof is 3.
% 2.89/0.86 % Maximum clause weight is 9.000.
% 2.89/0.86 % Given clauses 490.
% 2.89/0.86
% 2.89/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------