%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU187+1 : 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 : n003.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 08:41:12 AM UTC 2026
% Result : Theorem 10.41s 2.24s
% Output : CNFRefutation 10.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 84 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 42 ~; 35 |; 6 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(d5_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$urng'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X3,X2),X0) ) ) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : element(X1,X0) ).
fof(fc1_xboole_0,axiom,
empty('empty$uset') ).
fof(fc4_relat_1,axiom,
( relation('empty$uset')
& empty('empty$uset') ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t7_boole,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ) ).
fof(t8_boole,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ) ).
fof(t60_relat_1,conjecture,
( 'relation$urng'('empty$uset') = 'empty$uset'
& 'relation$udom'('empty$uset') = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ( 'relation$urng'('empty$uset') = 'empty$uset'
& 'relation$udom'('empty$uset') = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[t60_relat_1]) ).
cnf(c3,plain,
( in('ordered$upair'(X2,sK8(X0,X2)),X0)
| ~ in(X2,X1)
| X1 != 'relation$udom'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d4_relat_1]) ).
cnf(c9,plain,
( in('ordered$upair'(sK16(X0,X2),X2),X0)
| ~ in(X2,X1)
| X1 != 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c16,plain,
element(sK24(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c17,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c22,plain,
relation('empty$uset'),
inference(clausification,[status(esa)],[fc4_relat_1]) ).
cnf(c32,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c38,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_boole]) ).
cnf(c39,plain,
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t8_boole]) ).
cnf(c40,plain,
( 'relation$urng'('empty$uset') != 'empty$uset'
| 'relation$udom'('empty$uset') != 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[c39,c17]) ).
cnf(d1,plain,
( empty(X0)
| in(sK24(X0),X0) ),
inference(resolution,[status(thm)],[c32,c16]) ).
cnf(d2,plain,
( ~ relation(X1)
| in('ordered$upair'(sK16(X1,X0),X0),X1)
| ~ in(X0,'relation$urng'(X1)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d3,plain,
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,'relation$urng'(X1)) ),
inference(resolution,[status(thm)],[d2,c38]) ).
cnf(d4,plain,
( empty('relation$urng'(X0))
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( 'empty$uset' = 'relation$urng'(X0)
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ empty('empty$uset')
| 'empty$uset' = 'relation$urng'('empty$uset') ),
inference(resolution,[status(thm)],[d5,c22]) ).
cnf(d7,plain,
'empty$uset' = 'relation$urng'('empty$uset'),
inference(resolution,[status(thm)],[c17,d6]) ).
cnf(d8,plain,
( ~ relation(X1)
| in('ordered$upair'(X0,sK8(X1,X0)),X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(d9,plain,
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(resolution,[status(thm)],[d8,c38]) ).
cnf(d10,plain,
( empty('relation$udom'(X0))
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( 'empty$uset' = 'relation$udom'(X0)
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( ~ empty('empty$uset')
| 'empty$uset' = 'relation$udom'('empty$uset') ),
inference(resolution,[status(thm)],[d11,c22]) ).
cnf(d13,plain,
'empty$uset' = 'relation$udom'('empty$uset'),
inference(resolution,[status(thm)],[c17,d12]) ).
cnf(d14,plain,
( 'relation$urng'('empty$uset') != 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(demodulation,[status(thm)],[c40,d13]) ).
cnf(d15,plain,
( 'empty$uset' != 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
$false,
inference(equality_resolution,[status(thm)],[d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n003.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 08:48:24 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.41/2.24 % SZS status Theorem for theBenchmark.p
% 10.41/2.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------