%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:12:39 AM UTC 2026
% Result : Theorem 12.83s 3.64s
% Output : CNFRefutation 12.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 16 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_ordinal1,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'transfinite$usequence'(X0)
<=> ordinal('relation$udom'(X0)) ) ) ).
fof(d8_ordinal1,axiom,
! [X0,X1] :
( ( 'transfinite$usequence'(X1)
& function(X1)
& relation(X1) )
=> ( 'transfinite$usequence$uof'(X1,X0)
<=> subset('relation$urng'(X1),X0) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t46_ordinal1,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal('relation$udom'(X0))
=> 'transfinite$usequence$uof'(X0,'relation$urng'(X0)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal('relation$udom'(X0))
=> 'transfinite$usequence$uof'(X0,'relation$urng'(X0)) ) ),
inference(negate_conjecture,[status(cth)],[t46_ordinal1]) ).
cnf(c13,plain,
( ~ ordinal('relation$udom'(X0))
| 'transfinite$usequence'(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d7_ordinal1]) ).
cnf(c15,plain,
( 'transfinite$usequence$uof'(X0,X1)
| ~ 'transfinite$usequence'(X0)
| ~ function(X0)
| ~ subset('relation$urng'(X0),X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d8_ordinal1]) ).
cnf(c81,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c91,plain,
relation(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c92,plain,
function(sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c93,plain,
ordinal('relation$udom'(sK55)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c94,plain,
~ 'transfinite$usequence$uof'(sK55,'relation$urng'(sK55)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'transfinite$usequence$uof'(X0,'relation$urng'(X0))
| ~ 'transfinite$usequence'(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[c81,c15]) ).
cnf(d1,plain,
( ~ 'transfinite$usequence'(sK55)
| ~ relation(sK55)
| ~ function(sK55) ),
inference(resolution,[status(thm)],[d0,c94]) ).
cnf(d2,plain,
( ~ 'transfinite$usequence'(sK55)
| ~ function(sK55) ),
inference(resolution,[status(thm)],[c91,d1]) ).
cnf(d3,plain,
~ 'transfinite$usequence'(sK55),
inference(resolution,[status(thm)],[c92,d2]) ).
cnf(d4,plain,
( 'transfinite$usequence'(sK55)
| ~ relation(sK55)
| ~ function(sK55) ),
inference(resolution,[status(thm)],[c13,c93]) ).
cnf(d5,plain,
( 'transfinite$usequence'(sK55)
| ~ function(sK55) ),
inference(resolution,[status(thm)],[c91,d4]) ).
cnf(d6,plain,
'transfinite$usequence'(sK55),
inference(resolution,[status(thm)],[c92,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n015.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Sat Sep 26 02:42:42 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.83/3.64 % SZS status Theorem for theBenchmark.p
% 12.83/3.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------