%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:33:04 AM UTC 2026
% Result : Theorem 28.20s 4.51s
% Output : CNFRefutation 28.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 103 ( 16 unt; 0 def)
% Number of atoms : 314 ( 33 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 362 ( 151 ~; 154 |; 6 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 149 ( 8 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( subset('domain$uof'(X1),X0)
=> compose('identity$urelation$uof'(X0),X1) = X1 ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( subset('range$uof'(X1),X0)
=> compose(X1,'identity$urelation$uof'(X0)) = X1 ) ) ) ).
fof(p7,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
<=> 'ilf$utype'(X1,'relation$utype'(X0,X0)) ) ) ) ).
fof(p13,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p15,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(p19,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( subset(X0,X1)
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p22,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$uset'(X0))) ) ) ) ).
fof(p25,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'relation$ulike'(X2) ) ) ) ).
fof(p26,axiom,
! [X0] :
( 'ilf$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(p27,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p28,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(p32,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$uof'(X2) ) ) ) ).
fof(p33,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> 'ilf$utype'(domain(X0,X1,X2),'subset$utype'(X0)) ) ) ) ).
fof(p34,axiom,
! [X0] :
( 'ilf$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(p35,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(p38,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_45,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
=> ( compose('identity$urelation$uof'(X0),X1) = X1
& compose(X1,'identity$urelation$uof'(X0)) = X1 ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
=> ( compose('identity$urelation$uof'(X0),X1) = X1
& compose(X1,'identity$urelation$uof'(X0)) = X1 ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_45]) ).
cnf(c0,plain,
( compose('identity$urelation$uof'(X0),X1) = X1
| ~ subset('domain$uof'(X1),X0)
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( compose(X1,'identity$urelation$uof'(X0)) = X1
| ~ subset('range$uof'(X1),X0)
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c11,plain,
( 'ilf$utype'(X1,'relation$utype'(X0,X0))
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c29,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c32,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$utype') ),
inference(clausification,[status(esa)],[p15]) ).
cnf(c38,plain,
( member(sK46(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p19]) ).
cnf(c39,plain,
( ~ member(sK46(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p19]) ).
cnf(c42,plain,
( 'ilf$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)],[p22]) ).
cnf(c53,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)],[p25]) ).
cnf(c54,plain,
( member(X2,X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X2,X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ member(X0,'power$uset'(X1)) ),
inference(clausification,[status(esa)],[p26]) ).
cnf(c58,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p27]) ).
cnf(c60,plain,
( ~ 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| member(X0,X1)
| empty(X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p28]) ).
cnf(c67,plain,
( domain(X0,X1,X2) = 'domain$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p32]) ).
cnf(c68,plain,
( 'ilf$utype'(domain(X0,X1,X2),'subset$utype'(X0))
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p33]) ).
cnf(c69,plain,
( range(X0,X1,X2) = 'range$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p34]) ).
cnf(c70,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)],[p35]) ).
cnf(c73,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p38]) ).
cnf(c75,plain,
'ilf$utype'(sK102,'identity$urelation$uof$utype'(sK101)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
( compose('identity$urelation$uof'(sK101),sK102) != sK102
| compose(sK102,'identity$urelation$uof'(sK101)) != sK102 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c73,c29]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X0,'binary$urelation$utype')
| ~ subset('range$uof'(X0),X1)
| compose(X0,'identity$urelation$uof'(X1)) = X0 ),
inference(resolution,[status(thm)],[c73,c1]) ).
cnf(d2,plain,
( ~ member(sK46(X0,X1),X1)
| ~ 'ilf$utype'(X1,'set$utype')
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c73,c39]) ).
cnf(d3,plain,
( member(sK46(X0,X1),X0)
| ~ 'ilf$utype'(X1,'set$utype')
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c73,c38]) ).
cnf(d4,plain,
( ~ member(X1,X0)
| member(X1,X2)
| ~ member(X0,'power$uset'(X2))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c73,c54]) ).
cnf(d5,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c73,c42]) ).
cnf(d6,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c73,c60]) ).
cnf(d7,plain,
( ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| empty('power$uset'(X1))
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( empty('power$uset'(X1))
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c73,d7]) ).
cnf(d9,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c73,c58]) ).
cnf(d10,plain,
( member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X1))
| ~ 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c73,c11]) ).
cnf(d12,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)],[c73,c70]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| range(X0,X1,X2) = 'range$uof'(X2) ),
inference(resolution,[status(thm)],[c73,c69]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| range(X0,X0,X1) = 'range$uof'(X1) ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| range(X0,X0,X1) = 'range$uof'(X1) ),
inference(resolution,[status(thm)],[c73,d14]) ).
cnf(d16,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| range(sK101,sK101,sK102) = 'range$uof'(sK102) ),
inference(resolution,[status(thm)],[d15,c75]) ).
cnf(d17,plain,
range(sK101,sK101,sK102) = 'range$uof'(sK102),
inference(resolution,[status(thm)],[c73,d16]) ).
cnf(d18,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| ~ 'ilf$utype'(sK102,'relation$utype'(sK101,sK101))
| 'ilf$utype'('range$uof'(sK102),'subset$utype'(sK101)) ),
inference(superposition,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
( ~ 'ilf$utype'(sK102,'relation$utype'(sK101,sK101))
| 'ilf$utype'('range$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[c73,d18]) ).
cnf(d20,plain,
( ~ 'ilf$utype'(sK102,'identity$urelation$uof$utype'(sK101))
| ~ 'ilf$utype'(sK102,'set$utype')
| 'ilf$utype'('range$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
( ~ 'ilf$utype'(sK102,'set$utype')
| 'ilf$utype'('range$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[c75,d20]) ).
cnf(d22,plain,
'ilf$utype'('range$uof'(sK102),'subset$utype'(sK101)),
inference(resolution,[status(thm)],[c73,d21]) ).
cnf(d23,plain,
member('range$uof'(sK102),'power$uset'(sK101)),
inference(resolution,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
( ~ member(X0,'range$uof'(sK102))
| member(X0,sK101)
| ~ 'ilf$utype'('range$uof'(sK102),'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d23,d4]) ).
cnf(d25,plain,
( member(X0,sK101)
| ~ member(X0,'range$uof'(sK102))
| ~ 'ilf$utype'('range$uof'(sK102),'set$utype') ),
inference(resolution,[status(thm)],[c73,d24]) ).
cnf(d26,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| subset('range$uof'(sK102),X0)
| member(sK46('range$uof'(sK102),X0),sK101)
| ~ 'ilf$utype'('range$uof'(sK102),'set$utype') ),
inference(resolution,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
( member(sK46('range$uof'(sK102),X0),sK101)
| ~ 'ilf$utype'('range$uof'(sK102),'set$utype')
| subset('range$uof'(sK102),X0) ),
inference(resolution,[status(thm)],[c73,d26]) ).
cnf(d28,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| subset('range$uof'(sK102),sK101)
| ~ 'ilf$utype'('range$uof'(sK102),'set$utype')
| subset('range$uof'(sK102),sK101) ),
inference(resolution,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| subset('range$uof'(sK102),sK101) ),
inference(resolution,[status(thm)],[c73,d28]) ).
cnf(d30,plain,
( ~ 'ilf$utype'(sK102,'binary$urelation$utype')
| compose(sK102,'identity$urelation$uof'(sK101)) = sK102
| ~ 'ilf$utype'(sK101,'set$utype') ),
inference(resolution,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
( ~ 'ilf$utype'(sK102,'binary$urelation$utype')
| compose(sK102,'identity$urelation$uof'(sK101)) = sK102 ),
inference(resolution,[status(thm)],[c73,d30]) ).
cnf(d32,plain,
( ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ subset('domain$uof'(X1),X0)
| compose('identity$urelation$uof'(X0),X1) = X1 ),
inference(resolution,[status(thm)],[c73,c0]) ).
cnf(d33,plain,
( 'ilf$utype'(domain(X1,X2,X0),'subset$utype'(X1))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c73,c68]) ).
cnf(d34,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c73,c67]) ).
cnf(d35,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| domain(X0,X0,X1) = 'domain$uof'(X1) ),
inference(resolution,[status(thm)],[d34,d11]) ).
cnf(d36,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| domain(X0,X0,X1) = 'domain$uof'(X1) ),
inference(resolution,[status(thm)],[c73,d35]) ).
cnf(d37,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| domain(sK101,sK101,sK102) = 'domain$uof'(sK102) ),
inference(resolution,[status(thm)],[d36,c75]) ).
cnf(d38,plain,
domain(sK101,sK101,sK102) = 'domain$uof'(sK102),
inference(resolution,[status(thm)],[c73,d37]) ).
cnf(d39,plain,
( ~ 'ilf$utype'(sK102,'relation$utype'(sK101,sK101))
| ~ 'ilf$utype'(sK101,'set$utype')
| 'ilf$utype'('domain$uof'(sK102),'subset$utype'(sK101)) ),
inference(superposition,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
( ~ 'ilf$utype'(sK102,'relation$utype'(sK101,sK101))
| 'ilf$utype'('domain$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[c73,d39]) ).
cnf(d41,plain,
( ~ 'ilf$utype'(sK102,'identity$urelation$uof$utype'(sK101))
| ~ 'ilf$utype'(sK102,'set$utype')
| 'ilf$utype'('domain$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[d40,d11]) ).
cnf(d42,plain,
( ~ 'ilf$utype'(sK102,'set$utype')
| 'ilf$utype'('domain$uof'(sK102),'subset$utype'(sK101)) ),
inference(resolution,[status(thm)],[c75,d41]) ).
cnf(d43,plain,
'ilf$utype'('domain$uof'(sK102),'subset$utype'(sK101)),
inference(resolution,[status(thm)],[c73,d42]) ).
cnf(d44,plain,
member('domain$uof'(sK102),'power$uset'(sK101)),
inference(resolution,[status(thm)],[d43,d10]) ).
cnf(d45,plain,
( ~ member(X0,'domain$uof'(sK102))
| member(X0,sK101)
| ~ 'ilf$utype'('domain$uof'(sK102),'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d44,d4]) ).
cnf(d46,plain,
( member(X0,sK101)
| ~ member(X0,'domain$uof'(sK102))
| ~ 'ilf$utype'('domain$uof'(sK102),'set$utype') ),
inference(resolution,[status(thm)],[c73,d45]) ).
cnf(d47,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| subset('domain$uof'(sK102),X0)
| member(sK46('domain$uof'(sK102),X0),sK101)
| ~ 'ilf$utype'('domain$uof'(sK102),'set$utype') ),
inference(resolution,[status(thm)],[d46,d3]) ).
cnf(d48,plain,
( member(sK46('domain$uof'(sK102),X0),sK101)
| ~ 'ilf$utype'('domain$uof'(sK102),'set$utype')
| subset('domain$uof'(sK102),X0) ),
inference(resolution,[status(thm)],[c73,d47]) ).
cnf(d49,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| subset('domain$uof'(sK102),sK101)
| ~ 'ilf$utype'('domain$uof'(sK102),'set$utype')
| subset('domain$uof'(sK102),sK101) ),
inference(resolution,[status(thm)],[d48,d2]) ).
cnf(d50,plain,
( ~ 'ilf$utype'(sK101,'set$utype')
| subset('domain$uof'(sK102),sK101) ),
inference(resolution,[status(thm)],[c73,d49]) ).
cnf(d51,plain,
( ~ 'ilf$utype'(sK102,'binary$urelation$utype')
| compose('identity$urelation$uof'(sK101),sK102) = sK102
| ~ 'ilf$utype'(sK101,'set$utype') ),
inference(resolution,[status(thm)],[d50,d32]) ).
cnf(d52,plain,
( ~ 'ilf$utype'(sK102,'binary$urelation$utype')
| compose('identity$urelation$uof'(sK101),sK102) = sK102 ),
inference(resolution,[status(thm)],[c73,d51]) ).
cnf(d53,plain,
( ~ 'relation$ulike'(sK102)
| compose('identity$urelation$uof'(sK101),sK102) = sK102 ),
inference(resolution,[status(thm)],[d52,d0]) ).
cnf(d54,plain,
( 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c73,c32]) ).
cnf(d55,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c73,c53]) ).
cnf(d56,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| 'relation$ulike'(X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c73,d56]) ).
cnf(d58,plain,
( ~ 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| 'relation$ulike'(X0) ),
inference(resolution,[status(thm)],[d57,d11]) ).
cnf(d59,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1)) ),
inference(resolution,[status(thm)],[c73,d58]) ).
cnf(d60,plain,
'relation$ulike'(sK102),
inference(resolution,[status(thm)],[d59,c75]) ).
cnf(d61,plain,
compose('identity$urelation$uof'(sK101),sK102) = sK102,
inference(resolution,[status(thm)],[d60,d53]) ).
cnf(d62,plain,
compose(sK102,'identity$urelation$uof'(sK101)) != sK102,
inference(resolution,[status(thm)],[d61,c76]) ).
cnf(d63,plain,
~ 'ilf$utype'(sK102,'binary$urelation$utype'),
inference(resolution,[status(thm)],[d62,d31]) ).
cnf(d64,plain,
~ 'relation$ulike'(sK102),
inference(resolution,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
$false,
inference(resolution,[status(thm)],[d60,d64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:07:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.20/4.51 % SZS status Theorem for theBenchmark.p
% 28.20/4.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------