%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET682+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 : n018.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 08:33:05 AM UTC 2026
% Result : Theorem 12.58s 2.53s
% Output : CNFRefutation 12.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 14 unt; 0 def)
% Number of atoms : 224 ( 10 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 256 ( 105 ~; 97 |; 11 &)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 7 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( member(X0,'domain$uof'(X1))
=> ? [X2] :
( member(X2,'range$uof'(X1))
& 'ilf$utype'(X2,'set$utype') ) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$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$utype'(X0,X1)) ) ) ) ) ).
fof(p4,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ( 'ilf$utype'(X0,'member$utype'(X1))
<=> member(X0,X1) ) ) ) ).
fof(p10,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p12,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'subset$utype'(X0))
<=> 'ilf$utype'(X1,'member$utype'('power$uset'(X0))) ) ) ) ).
fof(p14,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X0,'power$uset'(X1))
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p15,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p18,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'relation$ulike'(X2) ) ) ) ).
fof(p20,axiom,
! [X0] :
( 'ilf$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(p22,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$uof'(X2) ) ) ) ).
fof(p23,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> 'ilf$utype'(range(X0,X1,X2),'subset$utype'(X1)) ) ) ) ).
fof(p24,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_49,conjecture,
! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'member$utype'(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( member(X4,range(X0,X1,X2))
& 'ilf$utype'(X4,'member$utype'(X1)) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'member$utype'(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( member(X4,range(X0,X1,X2))
& 'ilf$utype'(X4,'member$utype'(X1)) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_49]) ).
cnf(c1,plain,
( member(sK2(X1),'range$uof'(X1))
| ~ member(X0,'domain$uof'(X1))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c3,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$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c5,plain,
( empty(X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| member(X0,X1)
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c6,plain,
( empty(X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c16,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p10]) ).
cnf(c18,plain,
( 'ilf$utype'(X1,'member$utype'('power$uset'(X0)))
| ~ 'ilf$utype'(X1,'subset$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c21,plain,
( ~ member(X1,X2)
| ~ member(X2,'power$uset'(X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| member(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p14]) ).
cnf(c25,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p15]) ).
cnf(c36,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)],[p18]) ).
cnf(c38,plain,
( domain(X0,X1,X2) = 'domain$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p20]) ).
cnf(c40,plain,
( range(X0,X1,X2) = 'range$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p22]) ).
cnf(c41,plain,
( 'ilf$utype'(range(X0,X1,X2),'subset$utype'(X1))
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p23]) ).
cnf(c42,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p24]) ).
cnf(c45,plain,
~ empty(sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'ilf$utype'(sK61,'relation$utype'(sK59,sK60)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
member(sK62,domain(sK59,sK60,sK61)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c50,plain,
( ~ member(X0,range(sK59,sK60,sK61))
| ~ 'ilf$utype'(X0,'member$utype'(sK60)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c42,c16]) ).
cnf(d1,plain,
( empty(X1)
| ~ member(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,c6]) ).
cnf(d2,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,d1]) ).
cnf(d3,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| range(X0,X1,X2) = 'range$uof'(X2) ),
inference(resolution,[status(thm)],[c42,c40]) ).
cnf(d4,plain,
( ~ 'ilf$utype'(sK59,'set$utype')
| range(sK59,sK60,sK61) = 'range$uof'(sK61) ),
inference(resolution,[status(thm)],[d3,c47]) ).
cnf(d5,plain,
range(sK59,sK60,sK61) = 'range$uof'(sK61),
inference(resolution,[status(thm)],[c42,d4]) ).
cnf(d6,plain,
( ~ member(X0,'range$uof'(sK61))
| ~ 'ilf$utype'(X0,'member$utype'(sK60)) ),
inference(demodulation,[status(thm)],[c50,d5]) ).
cnf(d7,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c42,c38]) ).
cnf(d8,plain,
( ~ 'ilf$utype'(sK59,'set$utype')
| domain(sK59,sK60,sK61) = 'domain$uof'(sK61) ),
inference(resolution,[status(thm)],[d7,c47]) ).
cnf(d9,plain,
domain(sK59,sK60,sK61) = 'domain$uof'(sK61),
inference(resolution,[status(thm)],[c42,d8]) ).
cnf(d10,plain,
member(sK62,'domain$uof'(sK61)),
inference(demodulation,[status(thm)],[c49,d9]) ).
cnf(d11,plain,
( member(sK2(X0),'range$uof'(X0))
| ~ member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c42,c1]) ).
cnf(d12,plain,
( member(sK2(sK61),'range$uof'(sK61))
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(sK2(sK61),'member$utype'(sK60))
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( empty(sK60)
| ~ member(sK2(sK61),sK60)
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( ~ member(sK2(sK61),sK60)
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c45,d14]) ).
cnf(d16,plain,
( ~ member(X1,'power$uset'(X2))
| ~ member(X0,X1)
| member(X0,X2)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c21]) ).
cnf(d17,plain,
( 'ilf$utype'(range(X0,X2,X1),'subset$utype'(X2))
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c41]) ).
cnf(d18,plain,
( ~ 'ilf$utype'(sK59,'set$utype')
| ~ 'ilf$utype'(sK61,'relation$utype'(sK59,sK60))
| 'ilf$utype'('range$uof'(sK61),'subset$utype'(sK60)) ),
inference(superposition,[status(thm)],[d5,d17]) ).
cnf(d19,plain,
( ~ 'ilf$utype'(sK59,'set$utype')
| 'ilf$utype'('range$uof'(sK61),'subset$utype'(sK60)) ),
inference(resolution,[status(thm)],[c47,d18]) ).
cnf(d20,plain,
'ilf$utype'('range$uof'(sK61),'subset$utype'(sK60)),
inference(resolution,[status(thm)],[c42,d19]) ).
cnf(d21,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c18]) ).
cnf(d22,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,c5]) ).
cnf(d23,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,d22]) ).
cnf(d24,plain,
( ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| empty('power$uset'(X1))
| member(X0,'power$uset'(X1)) ),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( empty('power$uset'(X1))
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,d24]) ).
cnf(d26,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c42,c25]) ).
cnf(d27,plain,
( member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
member('range$uof'(sK61),'power$uset'(sK60)),
inference(resolution,[status(thm)],[d27,d20]) ).
cnf(d29,plain,
( ~ member(X0,'range$uof'(sK61))
| member(X0,sK60)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'('range$uof'(sK61),'set$utype') ),
inference(resolution,[status(thm)],[d28,d16]) ).
cnf(d30,plain,
( member(X0,sK60)
| ~ member(X0,'range$uof'(sK61))
| ~ 'ilf$utype'('range$uof'(sK61),'set$utype') ),
inference(resolution,[status(thm)],[c42,d29]) ).
cnf(d31,plain,
( ~ 'ilf$utype'(sK61,'binary$urelation$utype')
| member(sK2(sK61),sK60)
| ~ 'ilf$utype'('range$uof'(sK61),'set$utype') ),
inference(resolution,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
( member(sK2(sK61),sK60)
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c42,d31]) ).
cnf(d33,plain,
( ~ 'ilf$utype'(sK61,'binary$urelation$utype')
| ~ 'ilf$utype'(sK61,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
~ 'relation$ulike'(sK61),
inference(resolution,[status(thm)],[d33,d0]) ).
cnf(d35,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c42,c36]) ).
cnf(d36,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c42,c3]) ).
cnf(d37,plain,
( ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c42,d36]) ).
cnf(d38,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c42,d38]) ).
cnf(d40,plain,
'relation$ulike'(sK61),
inference(resolution,[status(thm)],[d39,c47]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[d40,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:07:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.58/2.53 % SZS status Theorem for theBenchmark.p
% 12.58/2.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------