%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU056+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 : n014.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 08:40:49 AM UTC 2026
% Result : Theorem 13.31s 2.91s
% Output : CNFRefutation 13.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 58 ( 25 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 15 ~; 12 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> 'set$uintersection2'(X0,X1) = 'empty$uset' ) ).
fof(idempotence_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X0) = X0 ).
fof(t121_funct_1,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( 'one$uto$uone'(X2)
=> 'relation$uimage'(X2,'set$uintersection2'(X0,X1)) = 'set$uintersection2'('relation$uimage'(X2,X0),'relation$uimage'(X2,X1)) ) ) ).
fof(t149_relat_1,axiom,
! [X0] :
( relation(X0)
=> 'relation$uimage'(X0,'empty$uset') = 'empty$uset' ) ).
fof(t2_boole,axiom,
! [X0] : 'set$uintersection2'(X0,'empty$uset') = 'empty$uset' ).
fof(t125_funct_1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( 'one$uto$uone'(X2)
& disjoint(X0,X1) )
=> disjoint('relation$uimage'(X2,X0),'relation$uimage'(X2,X1)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( 'one$uto$uone'(X2)
& disjoint(X0,X1) )
=> disjoint('relation$uimage'(X2,X0),'relation$uimage'(X2,X1)) ) ),
inference(negate_conjecture,[status(cth)],[t125_funct_1]) ).
cnf(c7,plain,
( 'set$uintersection2'(X0,X1) = 'empty$uset'
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[d7_xboole_0]) ).
cnf(c8,plain,
( 'set$uintersection2'(X0,X1) != 'empty$uset'
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[d7_xboole_0]) ).
cnf(c18,plain,
'set$uintersection2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(c41,plain,
( 'relation$uimage'(X0,'set$uintersection2'(X1,X2)) = 'set$uintersection2'('relation$uimage'(X0,X1),'relation$uimage'(X0,X2))
| ~ 'one$uto$uone'(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t121_funct_1]) ).
cnf(c42,plain,
( 'relation$uimage'(X0,'empty$uset') = 'empty$uset'
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t149_relat_1]) ).
cnf(c44,plain,
'set$uintersection2'(X0,'empty$uset') = 'empty$uset',
inference(clausification,[status(esa)],[t2_boole]) ).
cnf(c53,plain,
relation(sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
function(sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
disjoint(sK54,sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
'one$uto$uone'(sK56),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
~ disjoint('relation$uimage'(sK56,sK54),'relation$uimage'(sK56,sK55)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'relation$uimage'(sK56,'empty$uset') = 'empty$uset',
inference(resolution,[status(thm)],[c42,c53]) ).
cnf(d1,plain,
( ~ relation(sK56)
| ~ function(sK56)
| 'relation$uimage'(sK56,'set$uintersection2'(X0,X1)) = 'set$uintersection2'('relation$uimage'(sK56,X0),'relation$uimage'(sK56,X1)) ),
inference(resolution,[status(thm)],[c41,c56]) ).
cnf(d2,plain,
( ~ function(sK56)
| 'relation$uimage'(sK56,'set$uintersection2'(X0,X1)) = 'set$uintersection2'('relation$uimage'(sK56,X0),'relation$uimage'(sK56,X1)) ),
inference(resolution,[status(thm)],[c53,d1]) ).
cnf(d3,plain,
'relation$uimage'(sK56,'set$uintersection2'(X0,X1)) = 'set$uintersection2'('relation$uimage'(sK56,X0),'relation$uimage'(sK56,X1)),
inference(resolution,[status(thm)],[c54,d2]) ).
cnf(d4,plain,
( disjoint('relation$uimage'(sK56,X0),'relation$uimage'(sK56,X1))
| 'relation$uimage'(sK56,'set$uintersection2'(X0,X1)) != 'empty$uset' ),
inference(superposition,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
'set$uintersection2'(sK54,sK55) = 'empty$uset',
inference(resolution,[status(thm)],[c7,c55]) ).
cnf(d6,plain,
( disjoint('relation$uimage'(sK56,sK54),'relation$uimage'(sK56,sK55))
| 'relation$uimage'(sK56,'empty$uset') != 'empty$uset' ),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( disjoint('relation$uimage'(sK56,sK54),'relation$uimage'(sK56,sK55))
| 'empty$uset' != 'empty$uset' ),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
'empty$uset' != 'empty$uset',
inference(resolution,[status(thm)],[c57,d7]) ).
cnf(d9,plain,
'relation$uimage'(sK56,'set$uintersection2'('empty$uset',X0)) = 'set$uintersection2'('empty$uset','relation$uimage'(sK56,X0)),
inference(superposition,[status(thm)],[d0,d3]) ).
cnf(d10,plain,
'relation$uimage'(sK56,'empty$uset') = 'set$uintersection2'('empty$uset','relation$uimage'(sK56,'empty$uset')),
inference(superposition,[status(thm)],[c18,d9]) ).
cnf(d11,plain,
'empty$uset' = 'set$uintersection2'('empty$uset','relation$uimage'(sK56,'empty$uset')),
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
'empty$uset' = 'set$uintersection2'('empty$uset','empty$uset'),
inference(demodulation,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'empty$uset' = 'empty$uset',
inference(demodulation,[status(thm)],[d12,c44]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:32:46 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.31/2.91 % SZS status Theorem for theBenchmark.p
% 13.31/2.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------