%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM411+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 : n017.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 08:12:40 AM UTC 2026
% Result : Theorem 19.42s 3.01s
% Output : CNFRefutation 19.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 88 ( 40 ~; 35 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 31 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_ordinal1,axiom,
! [X0,X1] :
( ( 'transfinite$usequence'(X1)
& function(X1)
& relation(X1) )
=> ( 'transfinite$usequence$uof'(X1,X0)
<=> subset('relation$urng'(X1),X0) ) ) ).
fof(dt_m1_ordinal1,axiom,
! [X0,X1] :
( 'transfinite$usequence$uof'(X1,X0)
=> ( 'transfinite$usequence'(X1)
& function(X1)
& relation(X1) ) ) ).
fof(t1_xboole_1,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(t47_ordinal1,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( 'transfinite$usequence$uof'(X2,X0)
=> 'transfinite$usequence$uof'(X2,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( 'transfinite$usequence$uof'(X2,X0)
=> 'transfinite$usequence$uof'(X2,X1) ) ),
inference(negate_conjecture,[status(cth)],[t47_ordinal1]) ).
cnf(c12,plain,
( ~ function(X0)
| ~ relation(X0)
| subset('relation$urng'(X0),X1)
| ~ 'transfinite$usequence$uof'(X0,X1)
| ~ 'transfinite$usequence'(X0) ),
inference(clausification,[status(esa)],[d8_ordinal1]) ).
cnf(c13,plain,
( 'transfinite$usequence$uof'(X0,X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset('relation$urng'(X0),X1)
| ~ 'transfinite$usequence'(X0) ),
inference(clausification,[status(esa)],[d8_ordinal1]) ).
cnf(c14,plain,
( relation(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c15,plain,
( function(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c16,plain,
( 'transfinite$usequence'(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c78,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c87,plain,
subset(sK55,sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
'transfinite$usequence$uof'(sK57,sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c89,plain,
~ 'transfinite$usequence$uof'(sK57,sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'transfinite$usequence$uof'(X2,X0)
| ~ 'transfinite$usequence'(X2)
| ~ relation(X2)
| ~ function(X2)
| subset('relation$urng'(X2),X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c78,c12]) ).
cnf(d1,plain,
( subset('relation$urng'(X0),sK56)
| ~ 'transfinite$usequence$uof'(X0,sK55)
| ~ 'transfinite$usequence'(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[d0,c87]) ).
cnf(d2,plain,
( 'transfinite$usequence$uof'(X0,sK56)
| ~ 'transfinite$usequence'(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ 'transfinite$usequence$uof'(X0,sK55)
| ~ 'transfinite$usequence'(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
( 'transfinite$usequence$uof'(sK57,sK56)
| ~ 'transfinite$usequence'(sK57)
| ~ relation(sK57)
| ~ function(sK57) ),
inference(resolution,[status(thm)],[d2,c88]) ).
cnf(d4,plain,
( ~ 'transfinite$usequence'(sK57)
| ~ relation(sK57)
| ~ function(sK57) ),
inference(resolution,[status(thm)],[c89,d3]) ).
cnf(d5,plain,
relation(sK57),
inference(resolution,[status(thm)],[c14,c88]) ).
cnf(d6,plain,
( ~ 'transfinite$usequence'(sK57)
| ~ function(sK57) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
function(sK57),
inference(resolution,[status(thm)],[c15,c88]) ).
cnf(d8,plain,
~ 'transfinite$usequence'(sK57),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
'transfinite$usequence'(sK57),
inference(resolution,[status(thm)],[c16,c88]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 02:34:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.42/3.01 % SZS status Theorem for theBenchmark.p
% 19.42/3.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------