%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:33:04 AM UTC 2026
% Result : Theorem 15.72s 3.91s
% Output : CNFRefutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 17 unt; 0 def)
% Number of atoms : 184 ( 64 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 199 ( 86 ~; 74 |; 5 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 102 ( 5 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> image(X0,'domain$uof'(X0)) = 'range$uof'(X0) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> inverse2(X0,'range$uof'(X0)) = 'domain$uof'(X0) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
& image4(X0,X1,X2,X0) = range(X0,X1,X2) ) ) ) ) ).
fof(p4,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X1))
=> 'ilf$utype'(X3,'subset$utype'('cross$uproduct'(X0,X1))) )
& ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'ilf$utype'(X2,'relation$utype'(X0,X1)) ) ) ) ) ).
fof(p12,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p23,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'relation$ulike'(X2) ) ) ) ).
fof(p27,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> domain(X0,X1,X2) = 'domain$uof'(X2) ) ) ) ).
fof(p29,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> range(X0,X1,X2) = 'range$uof'(X2) ) ) ) ).
fof(p31,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ) ).
fof(p33,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ) ).
fof(p35,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_39,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X1,X0))
=> ( inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2)
& image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X1,X0))
=> ( inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2)
& image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_39]) ).
cnf(c0,plain,
( image(X0,'domain$uof'(X0)) = 'range$uof'(X0)
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( inverse2(X0,'range$uof'(X0)) = 'domain$uof'(X0)
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c2,plain,
( image4(X0,X1,X2,X0) = range(X0,X1,X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c3,plain,
( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c5,plain,
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c17,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c44,plain,
( 'relation$ulike'(X2)
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p23]) ).
cnf(c50,plain,
( domain(X0,X1,X2) = 'domain$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p27]) ).
cnf(c52,plain,
( range(X0,X1,X2) = 'range$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p29]) ).
cnf(c54,plain,
( ~ 'ilf$utype'(X3,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X2,'set$utype')
| image4(X0,X2,X3,X1) = image(X3,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p31]) ).
cnf(c56,plain,
( inverse4(X1,X0,X2,X3) = inverse2(X2,X3)
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X1,X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p33]) ).
cnf(c58,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p35]) ).
cnf(c59,plain,
'ilf$utype'(sK88,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
'ilf$utype'(sK89,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
'ilf$utype'(sK90,'relation$utype'(sK89,sK88)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
( inverse4(sK89,sK88,sK90,image4(sK89,sK88,sK90,sK89)) != domain(sK89,sK88,sK90)
| image4(sK89,sK88,sK90,inverse4(sK89,sK88,sK90,sK88)) != range(sK89,sK88,sK90) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c58,c17]) ).
cnf(d1,plain,
( image(X0,'domain$uof'(X0)) = 'range$uof'(X0)
| ~ 'relation$ulike'(X0) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c58,c44]) ).
cnf(d3,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c58,c5]) ).
cnf(d4,plain,
( 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c58,d3]) ).
cnf(d5,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c58,d5]) ).
cnf(d7,plain,
'relation$ulike'(sK90),
inference(resolution,[status(thm)],[d6,c61]) ).
cnf(d8,plain,
image(sK90,'domain$uof'(sK90)) = 'range$uof'(sK90),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| range(X0,X1,X2) = 'range$uof'(X2) ),
inference(resolution,[status(thm)],[c58,c52]) ).
cnf(d10,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| range(sK89,sK88,sK90) = 'range$uof'(sK90) ),
inference(resolution,[status(thm)],[d9,c61]) ).
cnf(d11,plain,
range(sK89,sK88,sK90) = 'range$uof'(sK90),
inference(resolution,[status(thm)],[c58,d10]) ).
cnf(d12,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(resolution,[status(thm)],[c58,c56]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| ~ 'ilf$utype'(sK88,'set$utype')
| inverse4(sK89,sK88,sK90,X0) = inverse2(sK90,X0) ),
inference(resolution,[status(thm)],[d12,c61]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| inverse4(sK89,sK88,sK90,X0) = inverse2(sK90,X0) ),
inference(resolution,[status(thm)],[c58,d13]) ).
cnf(d15,plain,
inverse4(sK89,sK88,sK90,X0) = inverse2(sK90,X0),
inference(resolution,[status(thm)],[d14,c58]) ).
cnf(d16,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(resolution,[status(thm)],[c58,c54]) ).
cnf(d17,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| ~ 'ilf$utype'(sK88,'set$utype')
| image4(sK89,sK88,sK90,X0) = image(sK90,X0) ),
inference(resolution,[status(thm)],[d16,c61]) ).
cnf(d18,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| image4(sK89,sK88,sK90,X0) = image(sK90,X0) ),
inference(resolution,[status(thm)],[c58,d17]) ).
cnf(d19,plain,
image4(sK89,sK88,sK90,X0) = image(sK90,X0),
inference(resolution,[status(thm)],[d18,c58]) ).
cnf(d20,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c58,c50]) ).
cnf(d21,plain,
( ~ 'ilf$utype'(sK88,'set$utype')
| domain(sK89,sK88,sK90) = 'domain$uof'(sK90) ),
inference(resolution,[status(thm)],[d20,c61]) ).
cnf(d22,plain,
domain(sK89,sK88,sK90) = 'domain$uof'(sK90),
inference(resolution,[status(thm)],[c58,d21]) ).
cnf(d23,plain,
( ~ 'ilf$utype'(sK88,'set$utype')
| ~ 'ilf$utype'(sK89,'set$utype')
| image4(sK89,sK88,sK90,sK89) = range(sK89,sK88,sK90) ),
inference(resolution,[status(thm)],[c2,c61]) ).
cnf(d24,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| image4(sK89,sK88,sK90,sK89) = range(sK89,sK88,sK90) ),
inference(resolution,[status(thm)],[c59,d23]) ).
cnf(d25,plain,
image4(sK89,sK88,sK90,sK89) = range(sK89,sK88,sK90),
inference(resolution,[status(thm)],[c60,d24]) ).
cnf(d26,plain,
( ~ 'ilf$utype'(sK88,'set$utype')
| ~ 'ilf$utype'(sK89,'set$utype')
| inverse4(sK89,sK88,sK90,sK88) = domain(sK89,sK88,sK90) ),
inference(resolution,[status(thm)],[c3,c61]) ).
cnf(d27,plain,
( ~ 'ilf$utype'(sK89,'set$utype')
| inverse4(sK89,sK88,sK90,sK88) = domain(sK89,sK88,sK90) ),
inference(resolution,[status(thm)],[c59,d26]) ).
cnf(d28,plain,
inverse4(sK89,sK88,sK90,sK88) = domain(sK89,sK88,sK90),
inference(resolution,[status(thm)],[c60,d27]) ).
cnf(d29,plain,
( inverse4(sK89,sK88,sK90,image4(sK89,sK88,sK90,sK89)) != domain(sK89,sK88,sK90)
| image4(sK89,sK88,sK90,domain(sK89,sK88,sK90)) != range(sK89,sK88,sK90) ),
inference(demodulation,[status(thm)],[c62,d28]) ).
cnf(d30,plain,
( inverse4(sK89,sK88,sK90,range(sK89,sK88,sK90)) != domain(sK89,sK88,sK90)
| image4(sK89,sK88,sK90,domain(sK89,sK88,sK90)) != range(sK89,sK88,sK90) ),
inference(demodulation,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( inverse4(sK89,sK88,sK90,range(sK89,sK88,sK90)) != domain(sK89,sK88,sK90)
| image4(sK89,sK88,sK90,'domain$uof'(sK90)) != range(sK89,sK88,sK90) ),
inference(demodulation,[status(thm)],[d30,d22]) ).
cnf(d32,plain,
( inverse4(sK89,sK88,sK90,range(sK89,sK88,sK90)) != 'domain$uof'(sK90)
| image4(sK89,sK88,sK90,'domain$uof'(sK90)) != range(sK89,sK88,sK90) ),
inference(demodulation,[status(thm)],[d31,d22]) ).
cnf(d33,plain,
( inverse4(sK89,sK88,sK90,range(sK89,sK88,sK90)) != 'domain$uof'(sK90)
| image(sK90,'domain$uof'(sK90)) != range(sK89,sK88,sK90) ),
inference(demodulation,[status(thm)],[d32,d19]) ).
cnf(d34,plain,
( inverse4(sK89,sK88,sK90,range(sK89,sK88,sK90)) != 'domain$uof'(sK90)
| image(sK90,'domain$uof'(sK90)) != 'range$uof'(sK90) ),
inference(demodulation,[status(thm)],[d33,d11]) ).
cnf(d35,plain,
( inverse2(sK90,range(sK89,sK88,sK90)) != 'domain$uof'(sK90)
| image(sK90,'domain$uof'(sK90)) != 'range$uof'(sK90) ),
inference(demodulation,[status(thm)],[d34,d15]) ).
cnf(d36,plain,
( inverse2(sK90,'range$uof'(sK90)) != 'domain$uof'(sK90)
| image(sK90,'domain$uof'(sK90)) != 'range$uof'(sK90) ),
inference(demodulation,[status(thm)],[d35,d11]) ).
cnf(d37,plain,
( inverse2(X0,'range$uof'(X0)) = 'domain$uof'(X0)
| ~ 'relation$ulike'(X0) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d38,plain,
inverse2(sK90,'range$uof'(sK90)) = 'domain$uof'(sK90),
inference(resolution,[status(thm)],[d7,d37]) ).
cnf(d39,plain,
image(sK90,'domain$uof'(sK90)) != 'range$uof'(sK90),
inference(resolution,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
'range$uof'(sK90) != 'range$uof'(sK90),
inference(demodulation,[status(thm)],[d39,d8]) ).
cnf(d41,plain,
$false,
inference(equality_resolution,[status(thm)],[d40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n016.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 08:09:16 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.72/3.91 % SZS status Theorem for theBenchmark.p
% 15.72/3.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------