%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:41:17 AM UTC 2026
% Result : Theorem 23.95s 8.00s
% Output : CNFRefutation 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 82 ( 17 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 97 ( 41 ~; 38 |; 7 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 12 !; 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(t20_relat_1,lemma,
! [X0,X1,X2] :
( relation(X2)
=> ( in('ordered$upair'(X0,X1),X2)
=> ( in(X1,'relation$urng'(X2))
& in(X0,'relation$udom'(X2)) ) ) ) ).
fof(t8_funct_1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in('ordered$upair'(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,'relation$udom'(X2)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in('ordered$upair'(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,'relation$udom'(X2)) ) ) ),
inference(negate_conjecture,[status(cth)],[t8_funct_1]) ).
cnf(c158,plain,
( ~ function(X1)
| in('ordered$upair'(X2,X0),X1)
| ~ relation(X1)
| ~ in(X2,'relation$udom'(X1))
| X0 != apply(X1,X2) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c159,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,'relation$udom'(X2))
| X1 = apply(X2,X0)
| ~ in('ordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c353,plain,
( in(X1,'relation$udom'(X0))
| ~ in('ordered$upair'(X1,X2),X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t20_relat_1]) ).
cnf(c454,plain,
relation(sK534),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c455,plain,
function(sK534),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c457,plain,
( in(sK532,'relation$udom'(sK534))
| in('ordered$upair'(sK532,sK533),sK534) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c458,plain,
( sK533 = apply(sK534,sK532)
| in('ordered$upair'(sK532,sK533),sK534) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c459,plain,
( ~ in('ordered$upair'(sK532,sK533),sK534)
| sK533 != apply(sK534,sK532)
| ~ in(sK532,'relation$udom'(sK534)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK533 = apply(sK534,sK532)
| ~ relation(sK534)
| ~ function(sK534)
| ~ in(sK532,'relation$udom'(sK534))
| sK533 = apply(sK534,sK532) ),
inference(resolution,[status(thm)],[c159,c458]) ).
cnf(d1,plain,
( ~ function(sK534)
| ~ in(sK532,'relation$udom'(sK534))
| sK533 = apply(sK534,sK532) ),
inference(resolution,[status(thm)],[c454,d0]) ).
cnf(d2,plain,
( ~ in(sK532,'relation$udom'(sK534))
| sK533 = apply(sK534,sK532) ),
inference(resolution,[status(thm)],[c455,d1]) ).
cnf(d3,plain,
( ~ in(sK532,'relation$udom'(sK534))
| ~ in(sK532,'relation$udom'(sK534))
| ~ in('ordered$upair'(sK532,sK533),sK534)
| sK533 != sK533 ),
inference(superposition,[status(thm)],[d2,c459]) ).
cnf(d4,plain,
( ~ in(sK532,'relation$udom'(sK534))
| ~ in('ordered$upair'(sK532,sK533),sK534) ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ in(sK532,'relation$udom'(sK534))
| ~ relation(sK534)
| ~ function(sK534)
| in('ordered$upair'(sK532,X0),sK534)
| ~ in(sK532,'relation$udom'(sK534))
| X0 != sK533 ),
inference(superposition,[status(thm)],[d2,c158]) ).
cnf(d6,plain,
( ~ function(sK534)
| ~ in(sK532,'relation$udom'(sK534))
| in('ordered$upair'(sK532,X0),sK534)
| X0 != sK533 ),
inference(resolution,[status(thm)],[c454,d5]) ).
cnf(d7,plain,
( ~ in(sK532,'relation$udom'(sK534))
| in('ordered$upair'(sK532,X0),sK534)
| X0 != sK533 ),
inference(resolution,[status(thm)],[c455,d6]) ).
cnf(d8,plain,
( ~ in(sK532,'relation$udom'(sK534))
| in('ordered$upair'(sK532,sK533),sK534) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ in(sK532,'relation$udom'(sK534))
| ~ in(sK532,'relation$udom'(sK534)) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
in('ordered$upair'(sK532,sK533),sK534),
inference(resolution,[status(thm)],[d9,c457]) ).
cnf(d11,plain,
( ~ relation(sK534)
| in(sK532,'relation$udom'(sK534)) ),
inference(resolution,[status(thm)],[c353,d10]) ).
cnf(d12,plain,
in(sK532,'relation$udom'(sK534)),
inference(resolution,[status(thm)],[c454,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d9,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n004.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 08:50:51 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.95/8.00 % SZS status Theorem for theBenchmark.p
% 23.95/8.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------