%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU009+1 : 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 : n013.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 08:40:45 AM UTC 2026
% Result : Theorem 16.29s 2.86s
% Output : CNFRefutation 16.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 136 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 169 ( 74 ~; 75 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k6_relat_1,axiom,
! [X0] : relation('identity$urelation'(X0)) ).
fof(fc2_funct_1,axiom,
! [X0] :
( function('identity$urelation'(X0))
& relation('identity$urelation'(X0)) ) ).
fof(t21_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,'relation$udom'('relation$ucomposition'(X2,X1)))
<=> ( in(apply(X2,X0),'relation$udom'(X1))
& in(X0,'relation$udom'(X2)) ) ) ) ) ).
fof(t34_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = 'identity$urelation'(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& 'relation$udom'(X1) = X0 ) ) ) ).
fof(t40_funct_1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,'relation$udom'('relation$ucomposition'(X2,'identity$urelation'(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,'relation$udom'(X2)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,'relation$udom'('relation$ucomposition'(X2,'identity$urelation'(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,'relation$udom'(X2)) ) ) ),
inference(negate_conjecture,[status(cth)],[t40_funct_1]) ).
cnf(c4,plain,
relation('identity$urelation'(X0)),
inference(clausification,[status(esa)],[dt_k6_relat_1]) ).
cnf(c16,plain,
function('identity$urelation'(X0)),
inference(clausification,[status(esa)],[fc2_funct_1]) ).
cnf(c40,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,'relation$udom'('relation$ucomposition'(X2,X0)))
| ~ function(X0)
| in(X1,'relation$udom'(X2))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t21_funct_1]) ).
cnf(c41,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,'relation$udom'('relation$ucomposition'(X1,X0)))
| ~ function(X0)
| in(apply(X1,X2),'relation$udom'(X0))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t21_funct_1]) ).
cnf(c42,plain,
( ~ in(apply(X2,X1),'relation$udom'(X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X0)
| ~ in(X1,'relation$udom'(X2))
| in(X1,'relation$udom'('relation$ucomposition'(X2,X0)))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t21_funct_1]) ).
cnf(c44,plain,
( 'relation$udom'(X0) = X1
| X0 != 'identity$urelation'(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t34_funct_1]) ).
cnf(c55,plain,
relation(sK57),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
function(sK57),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
( in(sK56,'relation$udom'(sK57))
| in(sK56,'relation$udom'('relation$ucomposition'(sK57,'identity$urelation'(sK55)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
( in(apply(sK57,sK56),sK55)
| in(sK56,'relation$udom'('relation$ucomposition'(sK57,'identity$urelation'(sK55)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
( ~ in(sK56,'relation$udom'('relation$ucomposition'(sK57,'identity$urelation'(sK55))))
| ~ in(apply(sK57,sK56),sK55)
| ~ in(sK56,'relation$udom'(sK57)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(sK56,'relation$udom'(sK57))
| ~ relation(sK57)
| ~ relation('identity$urelation'(sK55))
| ~ function(sK57)
| ~ function('identity$urelation'(sK55))
| in(sK56,'relation$udom'(sK57)) ),
inference(resolution,[status(thm)],[c40,c58]) ).
cnf(d1,plain,
( ~ relation('identity$urelation'(sK55))
| ~ function(sK57)
| ~ function('identity$urelation'(sK55))
| in(sK56,'relation$udom'(sK57)) ),
inference(resolution,[status(thm)],[c55,d0]) ).
cnf(d2,plain,
( ~ relation('identity$urelation'(sK55))
| ~ function('identity$urelation'(sK55))
| in(sK56,'relation$udom'(sK57)) ),
inference(resolution,[status(thm)],[c56,d1]) ).
cnf(d3,plain,
( ~ function('identity$urelation'(sK55))
| in(sK56,'relation$udom'(sK57)) ),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
in(sK56,'relation$udom'(sK57)),
inference(resolution,[status(thm)],[c16,d3]) ).
cnf(d5,plain,
( ~ in(sK56,'relation$udom'('relation$ucomposition'(sK57,'identity$urelation'(sK55))))
| ~ in(apply(sK57,sK56),sK55) ),
inference(resolution,[status(thm)],[d4,c60]) ).
cnf(d6,plain,
( ~ relation('identity$urelation'(X0))
| ~ function('identity$urelation'(X0))
| 'relation$udom'('identity$urelation'(X0)) = X0 ),
inference(equality_resolution,[status(thm)],[c44]) ).
cnf(d7,plain,
( ~ function('identity$urelation'(X0))
| 'relation$udom'('identity$urelation'(X0)) = X0 ),
inference(resolution,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
'relation$udom'('identity$urelation'(X0)) = X0,
inference(resolution,[status(thm)],[c16,d7]) ).
cnf(d9,plain,
( in(apply(sK57,sK56),sK55)
| ~ relation(sK57)
| ~ relation('identity$urelation'(sK55))
| ~ function(sK57)
| ~ function('identity$urelation'(sK55))
| in(apply(sK57,sK56),'relation$udom'('identity$urelation'(sK55))) ),
inference(resolution,[status(thm)],[c41,c59]) ).
cnf(d10,plain,
( ~ relation('identity$urelation'(sK55))
| ~ function(sK57)
| ~ function('identity$urelation'(sK55))
| in(apply(sK57,sK56),sK55)
| in(apply(sK57,sK56),'relation$udom'('identity$urelation'(sK55))) ),
inference(resolution,[status(thm)],[c55,d9]) ).
cnf(d11,plain,
( ~ relation('identity$urelation'(sK55))
| ~ function('identity$urelation'(sK55))
| in(apply(sK57,sK56),sK55)
| in(apply(sK57,sK56),'relation$udom'('identity$urelation'(sK55))) ),
inference(resolution,[status(thm)],[c56,d10]) ).
cnf(d12,plain,
( ~ function('identity$urelation'(sK55))
| in(apply(sK57,sK56),sK55)
| in(apply(sK57,sK56),'relation$udom'('identity$urelation'(sK55))) ),
inference(resolution,[status(thm)],[c4,d11]) ).
cnf(d13,plain,
( in(apply(sK57,sK56),sK55)
| in(apply(sK57,sK56),'relation$udom'('identity$urelation'(sK55))) ),
inference(resolution,[status(thm)],[c16,d12]) ).
cnf(d14,plain,
( in(apply(sK57,sK56),sK55)
| in(apply(sK57,sK56),sK55) ),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
~ in(sK56,'relation$udom'('relation$ucomposition'(sK57,'identity$urelation'(sK55)))),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( ~ relation(X1)
| ~ relation('identity$urelation'(X0))
| ~ function(X1)
| ~ function('identity$urelation'(X0))
| in(X2,'relation$udom'('relation$ucomposition'(X1,'identity$urelation'(X0))))
| ~ in(X2,'relation$udom'(X1))
| ~ in(apply(X1,X2),X0) ),
inference(superposition,[status(thm)],[d8,c42]) ).
cnf(d17,plain,
( ~ relation(X1)
| ~ function('identity$urelation'(X2))
| ~ function(X1)
| ~ in(apply(X1,X0),X2)
| in(X0,'relation$udom'('relation$ucomposition'(X1,'identity$urelation'(X2))))
| ~ in(X0,'relation$udom'(X1)) ),
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(apply(X1,X0),X2)
| in(X0,'relation$udom'('relation$ucomposition'(X1,'identity$urelation'(X2))))
| ~ in(X0,'relation$udom'(X1)) ),
inference(resolution,[status(thm)],[c16,d17]) ).
cnf(d19,plain,
( ~ relation(sK57)
| ~ function(sK57)
| ~ in(apply(sK57,sK56),sK55)
| ~ in(sK56,'relation$udom'(sK57)) ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( ~ function(sK57)
| ~ in(sK56,'relation$udom'(sK57))
| ~ in(apply(sK57,sK56),sK55) ),
inference(resolution,[status(thm)],[c55,d19]) ).
cnf(d21,plain,
( ~ in(sK56,'relation$udom'(sK57))
| ~ in(apply(sK57,sK56),sK55) ),
inference(resolution,[status(thm)],[c56,d20]) ).
cnf(d22,plain,
~ in(sK56,'relation$udom'(sK57)),
inference(resolution,[status(thm)],[d14,d21]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d4,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n013.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 08:29:52 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.29/2.86 % SZS status Theorem for theBenchmark.p
% 16.29/2.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------