%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU215+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 : n007.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 35.42s 5.19s
% Output : CNFRefutation 35.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 209 ( 20 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 291 ( 133 ~; 123 |; 16 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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 : 37 ( 0 sgn 19 !; 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_k5_relat_1,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation('relation$ucomposition'(X0,X1)) ) ).
fof(fc1_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function('relation$ucomposition'(X0,X1))
& relation('relation$ucomposition'(X0,X1)) ) ) ).
fof(t21_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,'relation$udom'('relation$ucomposition'(X2,X1)))
<=> ( in(apply(X2,X0),'relation$udom'(X1))
& in(X0,'relation$udom'(X2)) ) ) ) ) ).
fof(t22_funct_1,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,'relation$udom'('relation$ucomposition'(X2,X1)))
=> apply('relation$ucomposition'(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ) ).
fof(t23_funct_1,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,'relation$udom'(X1))
=> apply('relation$ucomposition'(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,'relation$udom'(X1))
=> apply('relation$ucomposition'(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
inference(negate_conjecture,[status(cth)],[t23_funct_1]) ).
cnf(c6,plain,
( ~ relation(X1)
| ~ function(X1)
| X2 != apply(X1,X0)
| X2 = 'empty$uset'
| in(X0,'relation$udom'(X1)) ),
inference(clausification,[status(esa)],[d4_funct_1]) ).
cnf(c9,plain,
( relation('relation$ucomposition'(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[dt_k5_relat_1]) ).
cnf(c17,plain,
( ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| function('relation$ucomposition'(X1,X0))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[fc1_funct_1]) ).
cnf(c47,plain,
( ~ in(X2,'relation$udom'('relation$ucomposition'(X1,X0)))
| in(apply(X1,X2),'relation$udom'(X0))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(clausification,[status(esa)],[t21_funct_1]) ).
cnf(c48,plain,
( in(X1,'relation$udom'('relation$ucomposition'(X0,X2)))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X2)
| ~ in(X1,'relation$udom'(X0))
| ~ function(X2)
| ~ in(apply(X0,X1),'relation$udom'(X2)) ),
inference(clausification,[status(esa)],[t21_funct_1]) ).
cnf(c49,plain,
( ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ~ in(X2,'relation$udom'('relation$ucomposition'(X0,X1)))
| apply('relation$ucomposition'(X0,X1),X2) = apply(X1,apply(X0,X2)) ),
inference(clausification,[status(esa)],[t22_funct_1]) ).
cnf(c58,plain,
relation(sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
function(sK65),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
relation(sK66),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
function(sK66),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
in(sK64,'relation$udom'(sK65)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c63,plain,
apply('relation$ucomposition'(sK65,sK66),sK64) != apply(sK66,apply(sK65,sK64)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation(X0)
| ~ function(X0)
| in(X1,'relation$udom'(X0))
| apply(X0,X1) = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d1,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| 'empty$uset' != apply(sK66,apply(sK65,sK64)) ),
inference(superposition,[status(thm)],[d0,c63]) ).
cnf(d2,plain,
( ~ relation(sK66)
| ~ function(sK66)
| in(apply(sK65,sK64),'relation$udom'(sK66))
| ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| in(apply(sK65,sK64),'relation$udom'(sK66))
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c60,d2]) ).
cnf(d4,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| in(apply(sK65,sK64),'relation$udom'(sK66))
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c61,d3]) ).
cnf(d5,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(apply(sK65,sK64),'relation$udom'(sK66))
| ~ relation(sK66)
| ~ relation(sK65)
| ~ function(sK66)
| ~ function(sK65)
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(resolution,[status(thm)],[c47,d5]) ).
cnf(d7,plain,
( ~ relation(sK66)
| ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function(sK65)
| ~ function('relation$ucomposition'(sK65,sK66))
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(resolution,[status(thm)],[c58,d6]) ).
cnf(d8,plain,
( ~ relation(sK66)
| ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function('relation$ucomposition'(sK65,sK66))
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(resolution,[status(thm)],[c59,d7]) ).
cnf(d9,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function('relation$ucomposition'(sK65,sK66))
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(resolution,[status(thm)],[c60,d8]) ).
cnf(d10,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(apply(sK65,sK64),'relation$udom'(sK66)) ),
inference(resolution,[status(thm)],[c61,d9]) ).
cnf(d11,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| ~ relation(sK66)
| ~ relation(sK65)
| ~ function(sK66)
| ~ function(sK65)
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| ~ in(sK64,'relation$udom'(sK65)) ),
inference(resolution,[status(thm)],[c48,d10]) ).
cnf(d12,plain,
( ~ relation(sK66)
| ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function(sK65)
| ~ function('relation$ucomposition'(sK65,sK66))
| ~ in(sK64,'relation$udom'(sK65))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))) ),
inference(resolution,[status(thm)],[c58,d11]) ).
cnf(d13,plain,
( ~ relation(sK66)
| ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function('relation$ucomposition'(sK65,sK66))
| ~ in(sK64,'relation$udom'(sK65))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))) ),
inference(resolution,[status(thm)],[c59,d12]) ).
cnf(d14,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function(sK66)
| ~ function('relation$ucomposition'(sK65,sK66))
| ~ in(sK64,'relation$udom'(sK65))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))) ),
inference(resolution,[status(thm)],[c60,d13]) ).
cnf(d15,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| ~ in(sK64,'relation$udom'(sK65))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))) ),
inference(resolution,[status(thm)],[c61,d14]) ).
cnf(d16,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66))
| in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))) ),
inference(resolution,[status(thm)],[c62,d15]) ).
cnf(d17,plain,
( ~ relation(sK66)
| ~ relation(sK65)
| ~ function(sK66)
| ~ function(sK65)
| ~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| apply(sK66,apply(sK65,sK64)) != apply(sK66,apply(sK65,sK64)) ),
inference(superposition,[status(thm)],[c49,c63]) ).
cnf(d18,plain,
( ~ relation(sK66)
| ~ function(sK66)
| ~ function(sK65)
| ~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| apply(sK66,apply(sK65,sK64)) != apply(sK66,apply(sK65,sK64)) ),
inference(resolution,[status(thm)],[c58,d17]) ).
cnf(d19,plain,
( ~ relation(sK66)
| ~ function(sK66)
| ~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| apply(sK66,apply(sK65,sK64)) != apply(sK66,apply(sK65,sK64)) ),
inference(resolution,[status(thm)],[c59,d18]) ).
cnf(d20,plain,
( ~ function(sK66)
| ~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| apply(sK66,apply(sK65,sK64)) != apply(sK66,apply(sK65,sK64)) ),
inference(resolution,[status(thm)],[c60,d19]) ).
cnf(d21,plain,
( ~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66)))
| apply(sK66,apply(sK65,sK64)) != apply(sK66,apply(sK65,sK64)) ),
inference(resolution,[status(thm)],[c61,d20]) ).
cnf(d22,plain,
~ in(sK64,'relation$udom'('relation$ucomposition'(sK65,sK66))),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
( ~ relation('relation$ucomposition'(sK65,sK66))
| ~ function('relation$ucomposition'(sK65,sK66)) ),
inference(resolution,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
( ~ relation(sK66)
| ~ relation(sK65)
| ~ function('relation$ucomposition'(sK65,sK66)) ),
inference(resolution,[status(thm)],[d23,c9]) ).
cnf(d25,plain,
( ~ relation(sK66)
| ~ function('relation$ucomposition'(sK65,sK66)) ),
inference(resolution,[status(thm)],[c58,d24]) ).
cnf(d26,plain,
~ function('relation$ucomposition'(sK65,sK66)),
inference(resolution,[status(thm)],[c60,d25]) ).
cnf(d27,plain,
( ~ relation(sK66)
| ~ relation(sK65)
| ~ function(sK66)
| ~ function(sK65) ),
inference(resolution,[status(thm)],[d26,c17]) ).
cnf(d28,plain,
( ~ relation(sK66)
| ~ function(sK66)
| ~ function(sK65) ),
inference(resolution,[status(thm)],[c58,d27]) ).
cnf(d29,plain,
( ~ relation(sK66)
| ~ function(sK66) ),
inference(resolution,[status(thm)],[c59,d28]) ).
cnf(d30,plain,
~ function(sK66),
inference(resolution,[status(thm)],[c60,d29]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[c61,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:49:55 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.42/5.19 % SZS status Theorem for theBenchmark.p
% 35.42/5.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------