%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12.55s 2.26s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 83 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 39 ~; 37 |; 6 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 12 !; 1 ?)
% 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(d4_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$udom'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X2,X3),X0) ) ) ) ).
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(c4,plain,
( ~ relation(X1)
| ~ function(X1)
| X2 != apply(X1,X0)
| in('ordered$upair'(X0,X2),X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c5,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in('ordered$upair'(X0,X2),X1)
| X2 = apply(X1,X0)
| ~ in(X0,'relation$udom'(X1)) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c9,plain,
( ~ in('ordered$upair'(X2,X3),X0)
| in(X2,X1)
| X1 != 'relation$udom'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d4_relat_1]) ).
cnf(c53,plain,
relation(sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
function(sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
( in(sK58,'relation$udom'(sK60))
| in('ordered$upair'(sK58,sK59),sK60) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
( sK59 = apply(sK60,sK58)
| in('ordered$upair'(sK58,sK59),sK60) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
( ~ in('ordered$upair'(sK58,sK59),sK60)
| sK59 != apply(sK60,sK58)
| ~ in(sK58,'relation$udom'(sK60)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation(X1)
| ~ function(X1)
| in('ordered$upair'(X0,apply(X1,X0)),X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(d1,plain,
( sK59 = apply(sK60,sK58)
| ~ relation(sK60)
| ~ function(sK60)
| ~ in(sK58,'relation$udom'(sK60))
| sK59 = apply(sK60,sK58) ),
inference(resolution,[status(thm)],[c5,c57]) ).
cnf(d2,plain,
( ~ function(sK60)
| ~ in(sK58,'relation$udom'(sK60))
| sK59 = apply(sK60,sK58) ),
inference(resolution,[status(thm)],[c53,d1]) ).
cnf(d3,plain,
( ~ in(sK58,'relation$udom'(sK60))
| sK59 = apply(sK60,sK58) ),
inference(resolution,[status(thm)],[c54,d2]) ).
cnf(d4,plain,
( ~ relation(X1)
| ~ in('ordered$upair'(X0,X2),X1)
| in(X0,'relation$udom'(X1)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d5,plain,
( in(sK58,'relation$udom'(sK60))
| ~ relation(sK60)
| in(sK58,'relation$udom'(sK60)) ),
inference(resolution,[status(thm)],[d4,c56]) ).
cnf(d6,plain,
in(sK58,'relation$udom'(sK60)),
inference(resolution,[status(thm)],[c53,d5]) ).
cnf(d7,plain,
sK59 = apply(sK60,sK58),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( ~ relation(sK60)
| ~ function(sK60)
| ~ in(sK58,'relation$udom'(sK60))
| in('ordered$upair'(sK58,sK59),sK60) ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ function(sK60)
| ~ in(sK58,'relation$udom'(sK60))
| in('ordered$upair'(sK58,sK59),sK60) ),
inference(resolution,[status(thm)],[c53,d8]) ).
cnf(d10,plain,
( ~ in(sK58,'relation$udom'(sK60))
| in('ordered$upair'(sK58,sK59),sK60) ),
inference(resolution,[status(thm)],[c54,d9]) ).
cnf(d11,plain,
in('ordered$upair'(sK58,sK59),sK60),
inference(resolution,[status(thm)],[d6,d10]) ).
cnf(d12,plain,
( ~ in('ordered$upair'(sK58,sK59),sK60)
| sK59 != apply(sK60,sK58) ),
inference(resolution,[status(thm)],[d6,c58]) ).
cnf(d13,plain,
( ~ in('ordered$upair'(sK58,sK59),sK60)
| sK59 != sK59 ),
inference(demodulation,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
~ in('ordered$upair'(sK58,sK59),sK60),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:56:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.55/2.26 % SZS status Theorem for theBenchmark.p
% 12.55/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------