%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM412+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 16.78s 3.27s
% Output : CNFRefutation 16.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 106 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 52 ~; 48 |; 10 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 3 sgn 17 !; 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_k2_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& 'transfinite$usequence'(X0)
& function(X0)
& relation(X0) )
=> 'transfinite$usequence$uof'('tseq$udom$urestriction'(X0,X1),'relation$urng'(X0)) ) ).
fof(dt_m1_ordinal1,axiom,
! [X0,X1] :
( 'transfinite$usequence$uof'(X1,X0)
=> ( 'transfinite$usequence'(X1)
& function(X1)
& relation(X1) ) ) ).
fof(redefinition_k2_ordinal1,axiom,
! [X0,X1] :
( ( ordinal(X1)
& 'transfinite$usequence'(X0)
& function(X0)
& relation(X0) )
=> 'tseq$udom$urestriction'(X0,X1) = 'relation$udom$urestriction'(X0,X1) ) ).
fof(t47_ordinal1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( 'transfinite$usequence$uof'(X2,X0)
=> 'transfinite$usequence$uof'(X2,X1) ) ) ).
fof(t48_ordinal1,conjecture,
! [X0,X1] :
( 'transfinite$usequence$uof'(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> 'transfinite$usequence$uof'('tseq$udom$urestriction'(X1,X2),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'transfinite$usequence$uof'(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> 'transfinite$usequence$uof'('tseq$udom$urestriction'(X1,X2),X0) ) ),
inference(negate_conjecture,[status(cth)],[t48_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(c14,plain,
( ~ 'transfinite$usequence'(X0)
| ~ ordinal(X1)
| 'transfinite$usequence$uof'('tseq$udom$urestriction'(X0,X1),'relation$urng'(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[dt_k2_ordinal1]) ).
cnf(c16,plain,
( relation(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c17,plain,
( function(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c18,plain,
( 'transfinite$usequence'(X0)
| ~ 'transfinite$usequence$uof'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_ordinal1]) ).
cnf(c82,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(X1)
| ~ 'transfinite$usequence'(X0)
| 'tseq$udom$urestriction'(X0,X1) = 'relation$udom$urestriction'(X0,X1) ),
inference(clausification,[status(esa)],[redefinition_k2_ordinal1]) ).
cnf(c88,plain,
( 'transfinite$usequence$uof'(X2,X1)
| ~ 'transfinite$usequence$uof'(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t47_ordinal1]) ).
cnf(c94,plain,
'transfinite$usequence$uof'(sK66,sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c95,plain,
ordinal(sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c96,plain,
~ 'transfinite$usequence$uof'('tseq$udom$urestriction'(sK66,sK67),sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'transfinite$usequence'(sK66),
inference(resolution,[status(thm)],[c18,c94]) ).
cnf(d1,plain,
( ~ relation(sK66)
| ~ ordinal(X0)
| ~ function(sK66)
| 'tseq$udom$urestriction'(sK66,X0) = 'relation$udom$urestriction'(sK66,X0) ),
inference(resolution,[status(thm)],[c82,d0]) ).
cnf(d2,plain,
relation(sK66),
inference(resolution,[status(thm)],[c16,c94]) ).
cnf(d3,plain,
( ~ ordinal(X0)
| ~ function(sK66)
| 'tseq$udom$urestriction'(sK66,X0) = 'relation$udom$urestriction'(sK66,X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
function(sK66),
inference(resolution,[status(thm)],[c17,c94]) ).
cnf(d5,plain,
( ~ ordinal(X0)
| 'tseq$udom$urestriction'(sK66,X0) = 'relation$udom$urestriction'(sK66,X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'tseq$udom$urestriction'(sK66,sK67) = 'relation$udom$urestriction'(sK66,sK67),
inference(resolution,[status(thm)],[d5,c95]) ).
cnf(d7,plain,
~ 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),sK65),
inference(demodulation,[status(thm)],[c96,d6]) ).
cnf(d8,plain,
( ~ 'transfinite$usequence'(sK66)
| ~ relation(sK66)
| ~ ordinal(sK67)
| ~ function(sK66)
| 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),'relation$urng'(sK66)) ),
inference(superposition,[status(thm)],[d6,c14]) ).
cnf(d9,plain,
( 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),'relation$urng'(sK66))
| ~ 'transfinite$usequence'(sK66)
| ~ relation(sK66)
| ~ function(sK66) ),
inference(resolution,[status(thm)],[c95,d8]) ).
cnf(d10,plain,
( 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),'relation$urng'(sK66))
| ~ 'transfinite$usequence'(sK66)
| ~ function(sK66) ),
inference(resolution,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
( 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),'relation$urng'(sK66))
| ~ 'transfinite$usequence'(sK66) ),
inference(resolution,[status(thm)],[d4,d10]) ).
cnf(d12,plain,
'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),'relation$urng'(sK66)),
inference(resolution,[status(thm)],[d0,d11]) ).
cnf(d13,plain,
( ~ 'transfinite$usequence$uof'(X2,X1)
| ~ 'transfinite$usequence'(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ 'transfinite$usequence$uof'(X0,'relation$urng'(X2))
| 'transfinite$usequence$uof'(X0,X1) ),
inference(resolution,[status(thm)],[c88,c12]) ).
cnf(d14,plain,
( 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),X0)
| ~ 'transfinite$usequence$uof'(sK66,X0)
| ~ 'transfinite$usequence'(sK66)
| ~ relation(sK66)
| ~ function(sK66) ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ 'transfinite$usequence$uof'(sK66,X0)
| 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),X0)
| ~ 'transfinite$usequence'(sK66)
| ~ function(sK66) ),
inference(resolution,[status(thm)],[d2,d14]) ).
cnf(d16,plain,
( ~ 'transfinite$usequence$uof'(sK66,X0)
| 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),X0)
| ~ 'transfinite$usequence'(sK66) ),
inference(resolution,[status(thm)],[d4,d15]) ).
cnf(d17,plain,
( ~ 'transfinite$usequence$uof'(sK66,X0)
| 'transfinite$usequence$uof'('relation$udom$urestriction'(sK66,sK67),X0) ),
inference(resolution,[status(thm)],[d0,d16]) ).
cnf(d18,plain,
~ 'transfinite$usequence$uof'(sK66,sK65),
inference(resolution,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c94,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:34:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.78/3.27 % SZS status Theorem for theBenchmark.p
% 16.78/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------