%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU225+3 : 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 : n009.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 08:41:20 AM UTC 2026
% Result : Theorem 34.12s 4.96s
% Output : CNFRefutation 34.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 170 ( 22 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 229 ( 105 ~; 96 |; 11 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,'relation$udom'(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = 'empty$uset' ) )
& ( in(X1,'relation$udom'(X0))
=> ( X2 = apply(X0,X1)
<=> in('ordered$upair'(X1,X2),X0) ) ) ) ) ).
fof(dt_k7_relat_1,axiom,
! [X0,X1] :
( relation(X0)
=> relation('relation$udom$urestriction'(X0,X1)) ) ).
fof(fc4_funct_1,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function('relation$udom$urestriction'(X0,X1))
& relation('relation$udom$urestriction'(X0,X1)) ) ) ).
fof(l82_funct_1,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,'relation$udom'('relation$udom$urestriction'(X2,X0)))
<=> ( in(X1,X0)
& in(X1,'relation$udom'(X2)) ) ) ) ).
fof(t68_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = 'relation$udom$urestriction'(X2,X0)
<=> ( ! [X3] :
( in(X3,'relation$udom'(X1))
=> apply(X1,X3) = apply(X2,X3) )
& 'relation$udom'(X1) = 'set$uintersection2'('relation$udom'(X2),X0) ) ) ) ) ).
fof(t72_funct_1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply('relation$udom$urestriction'(X2,X0),X1) = apply(X2,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply('relation$udom$urestriction'(X2,X0),X1) = apply(X2,X1) ) ),
inference(negate_conjecture,[status(cth)],[t72_funct_1]) ).
cnf(c10,plain,
( ~ function(X1)
| in(X2,'relation$udom'(X1))
| ~ relation(X1)
| X0 != apply(X1,X2)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c13,plain,
( relation('relation$udom$urestriction'(X0,X1))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[dt_k7_relat_1]) ).
cnf(c27,plain,
( function('relation$udom$urestriction'(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[fc4_funct_1]) ).
cnf(c34,plain,
( in(X1,'relation$udom'(X0))
| ~ in(X1,'relation$udom'('relation$udom$urestriction'(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[l82_funct_1]) ).
cnf(c36,plain,
( in(X0,'relation$udom'('relation$udom$urestriction'(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ function(X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(clausification,[status(esa)],[l82_funct_1]) ).
cnf(c66,plain,
( ~ in(X1,'relation$udom'(X0))
| ~ function(X2)
| X0 != 'relation$udom$urestriction'(X2,X3)
| ~ function(X0)
| ~ relation(X2)
| apply(X0,X1) = apply(X2,X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t68_funct_1]) ).
cnf(c72,plain,
relation(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
function(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
in(sK75,sK74),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
apply('relation$udom$urestriction'(sK76,sK74),sK75) != apply(sK76,sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation('relation$udom$urestriction'(X0,X1))
| ~ relation(X0)
| ~ function('relation$udom$urestriction'(X0,X1))
| ~ function(X0)
| ~ in(X2,'relation$udom'('relation$udom$urestriction'(X0,X1)))
| apply('relation$udom$urestriction'(X0,X1),X2) = apply(X0,X2) ),
inference(equality_resolution,[status(thm)],[c66]) ).
cnf(d1,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ relation(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ function(sK76)
| ~ in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| apply(sK76,sK75) != apply(sK76,sK75) ),
inference(superposition,[status(thm)],[d0,c75]) ).
cnf(d2,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| apply(sK76,sK75) != apply(sK76,sK75) ),
inference(resolution,[status(thm)],[c72,d1]) ).
cnf(d3,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| apply(sK76,sK75) != apply(sK76,sK75) ),
inference(resolution,[status(thm)],[c73,d2]) ).
cnf(d4,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74))) ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ relation(sK76)
| ~ function(sK76)
| ~ in(sK75,'relation$udom'(sK76))
| ~ in(sK75,sK74)
| ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74)) ),
inference(resolution,[status(thm)],[d4,c36]) ).
cnf(d6,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,sK74)
| ~ in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c72,d5]) ).
cnf(d7,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,sK74)
| ~ in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c73,d6]) ).
cnf(d8,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| ~ in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c74,d7]) ).
cnf(d9,plain,
( ~ relation(X0)
| ~ function(X0)
| in(X1,'relation$udom'(X0))
| apply(X0,X1) = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(d10,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| 'empty$uset' != apply(sK76,sK75) ),
inference(superposition,[status(thm)],[d9,c75]) ).
cnf(d11,plain,
( ~ relation(sK76)
| ~ function(sK76)
| in(sK75,'relation$udom'(sK76))
| ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d9,d10]) ).
cnf(d12,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76))
| in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c72,d11]) ).
cnf(d13,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76))
| in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74)))
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c73,d12]) ).
cnf(d14,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76))
| in(sK75,'relation$udom'('relation$udom$urestriction'(sK76,sK74))) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ relation(sK76)
| ~ function(sK76)
| in(sK75,'relation$udom'(sK76))
| ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[d14,c34]) ).
cnf(d16,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c72,d15]) ).
cnf(d17,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c73,d16]) ).
cnf(d18,plain,
( ~ relation(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[d17,c13]) ).
cnf(d19,plain,
( ~ function('relation$udom$urestriction'(sK76,sK74))
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c72,d18]) ).
cnf(d20,plain,
( ~ relation(sK76)
| ~ function(sK76)
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[d19,c27]) ).
cnf(d21,plain,
( ~ function(sK76)
| in(sK75,'relation$udom'(sK76)) ),
inference(resolution,[status(thm)],[c72,d20]) ).
cnf(d22,plain,
in(sK75,'relation$udom'(sK76)),
inference(resolution,[status(thm)],[c73,d21]) ).
cnf(d23,plain,
( ~ relation('relation$udom$urestriction'(sK76,sK74))
| ~ function('relation$udom$urestriction'(sK76,sK74)) ),
inference(resolution,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
( ~ relation(sK76)
| ~ function('relation$udom$urestriction'(sK76,sK74)) ),
inference(resolution,[status(thm)],[d23,c13]) ).
cnf(d25,plain,
~ function('relation$udom$urestriction'(sK76,sK74)),
inference(resolution,[status(thm)],[c72,d24]) ).
cnf(d26,plain,
( ~ relation(sK76)
| ~ function(sK76) ),
inference(resolution,[status(thm)],[d25,c27]) ).
cnf(d27,plain,
~ function(sK76),
inference(resolution,[status(thm)],[c72,d26]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c73,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:53:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.12/4.96 % SZS status Theorem for theBenchmark.p
% 34.12/4.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------