%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ062-2 : 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 : n010.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 08:22:13 AM UTC 2026
% Result : Unsatisfiable 10.51s 7.16s
% Output : CNFRefutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 29 unt; 5 nHn; 33 RR)
% Number of literals : 66 ( 20 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 54 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
( 'c$uFinite$u$uSet$uOcard'('c$uinsert'(X2,X0,X1),X1) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'(X0,X1))
| 'c$uin'(X2,X0,X1)
| ~ 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'(X1)) ) ).
cnf(cls_Finite__Set_Ofinite__Int_1,axiom,
( 'c$uin'('c$uinter'(X2,X0,X1),'c$uFinite$u$uSet$uOFinites','tc$uset'(X1))
| ~ 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'(X1)) ) ).
cnf(cls_Mutil_Otiling__domino__finite_0,axiom,
( 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'('tc$uprod'('tc$unat','tc$unat')))
| ~ 'c$uin'(X0,'c$uMutil$uOtiling'('c$uMutil$uOdomino','tc$uprod'('tc$unat','tc$unat')),'tc$uset'('tc$uprod'('tc$unat','tc$unat'))) ) ).
cnf(cls_Set_OInt__iff_1,axiom,
( 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ) ).
cnf(cls_Set_OInt__iff_2,axiom,
( 'c$uin'(X0,'c$uinter'(X3,X1,X2),X2)
| ~ 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_Oinsert__iff_1,axiom,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ 'c$uin'(X0,'c$uemptyset',X1) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('v$ut','c$uMutil$uOtiling'('c$uMutil$uOdomino','tc$uprod'('tc$unat','tc$unat')),'tc$uset'('tc$uprod'('tc$unat','tc$unat'))) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) = 'c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uinter'('v$ua','v$ut','tc$uprod'('tc$unat','tc$unat')) = 'c$uemptyset' ).
cnf(cls_conjecture_3,negated_conjecture,
'c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ua','tc$uprod'('tc$unat','tc$unat')) = 'c$uinsert'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uemptyset','tc$uprod'('tc$unat','tc$unat')) ).
cnf(cls_conjecture_4,negated_conjecture,
'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ua','tc$uprod'('tc$unat','tc$unat')) = 'c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uemptyset','tc$uprod'('tc$unat','tc$unat')) ).
cnf(cls_conjecture_5,negated_conjecture,
'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) != 'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) ).
cnf(c0,plain,
( 'c$uFinite$u$uSet$uOcard'('c$uinsert'(X2,X0,X1),X1) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'(X0,X1))
| 'c$uin'(X2,X0,X1)
| ~ 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'(X1)) ),
inference(clausification,[status(esa)],[cls_Finite__Set_Ocard__insert__disjoint_0]) ).
cnf(c1,plain,
( 'c$uin'('c$uinter'(X2,X0,X1),'c$uFinite$u$uSet$uOFinites','tc$uset'(X1))
| ~ 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'(X1)) ),
inference(clausification,[status(esa)],[cls_Finite__Set_Ofinite__Int_1]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'('tc$uprod'('tc$unat','tc$unat')))
| ~ 'c$uin'(X0,'c$uMutil$uOtiling'('c$uMutil$uOdomino','tc$uprod'('tc$unat','tc$unat')),'tc$uset'('tc$uprod'('tc$unat','tc$unat'))) ),
inference(clausification,[status(esa)],[cls_Mutil_Otiling__domino__finite_0]) ).
cnf(c3,plain,
( 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_Set_OInt__iff_1]) ).
cnf(c4,plain,
( 'c$uin'(X0,'c$uinter'(X3,X1,X2),X2)
| ~ 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OInt__iff_2]) ).
cnf(c5,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_Oinsert__iff_1]) ).
cnf(c6,plain,
~ 'c$uin'(X0,'c$uemptyset',X1),
inference(clausification,[status(esa)],[cls_Set_Oempty__iff_0]) ).
cnf(c7,plain,
'c$uin'('v$ut','c$uMutil$uOtiling'('c$uMutil$uOdomino','tc$uprod'('tc$unat','tc$unat')),'tc$uset'('tc$uprod'('tc$unat','tc$unat'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c8,plain,
'c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) = 'c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c9,plain,
'c$uinter'('v$ua','v$ut','tc$uprod'('tc$unat','tc$unat')) = 'c$uemptyset',
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c10,plain,
'c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ua','tc$uprod'('tc$unat','tc$unat')) = 'c$uinsert'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uemptyset','tc$uprod'('tc$unat','tc$unat')),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c11,plain,
'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ua','tc$uprod'('tc$unat','tc$unat')) = 'c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uemptyset','tc$uprod'('tc$unat','tc$unat')),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c12,plain,
'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) != 'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(d0,plain,
'c$uin'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ua','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),
inference(superposition,[status(thm)],[c11,c5]) ).
cnf(d1,plain,
'c$uin'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'v$ua','tc$uprod'('tc$unat','tc$unat')),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ 'c$uin'(X0,'v$ua','tc$uprod'('tc$unat','tc$unat'))
| ~ 'c$uin'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'(X0,'c$uemptyset','tc$uprod'('tc$unat','tc$unat')) ),
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(d3,plain,
( ~ 'c$uin'(X0,'v$ua','tc$uprod'('tc$unat','tc$unat'))
| ~ 'c$uin'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat')) ),
inference(resolution,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
~ 'c$uin'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'v$ut','tc$uprod'('tc$unat','tc$unat')),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'c$uin'('v$ut','c$uFinite$u$uSet$uOFinites','tc$uset'('tc$uprod'('tc$unat','tc$unat'))),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d6,plain,
( 'c$uin'(X2,'c$uinter'(X3,X0,X1),X1)
| 'c$uFinite$u$uSet$uOcard'('c$uinsert'(X2,'c$uinter'(X3,X0,X1),X1),X1) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'(X3,X0,X1),X1))
| ~ 'c$uin'(X0,'c$uFinite$u$uSet$uOFinites','tc$uset'(X1)) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d7,plain,
( 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X2,'c$uFinite$u$uSet$uOFinites','tc$uset'(X3))
| 'c$uFinite$u$uSet$uOcard'('c$uinsert'(X0,'c$uinter'(X1,X2,X3),X3),X3) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'(X1,X2,X3),X3)) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( 'c$uin'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat'))
| 'c$uFinite$u$uSet$uOcard'('c$uinsert'(X0,'c$uinter'(X1,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'(X1,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uinter'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
'c$uin'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ua','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),
inference(superposition,[status(thm)],[c10,c5]) ).
cnf(d11,plain,
'c$uin'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'v$ua','tc$uprod'('tc$unat','tc$unat')),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
~ 'c$uin'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'v$ut','tc$uprod'('tc$unat','tc$unat')),
inference(resolution,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$ui','v$uj','tc$unat','tc$unat'),'c$uinter'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')) = 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'(X0,'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))),
inference(resolution,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))) != 'c$uFinite$u$uSet$uOcard'('c$uinsert'('c$uPair'('v$um','v$un','tc$unat','tc$unat'),'c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat')),
inference(demodulation,[status(thm)],[c12,d13]) ).
cnf(d15,plain,
'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))) != 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$uSuc'('c$u0')),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))),
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))) != 'c$uSuc'('c$uFinite$u$uSet$uOcard'('c$uinter'('c$uMutil$uOcoloured'('c$u0'),'v$ut','tc$uprod'('tc$unat','tc$unat')),'tc$uprod'('tc$unat','tc$unat'))),
inference(demodulation,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
$false,
inference(equality_resolution,[status(thm)],[d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n010.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Sat Sep 26 05:11:13 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.51/7.16 % SZS status Unsatisfiable for theBenchmark.p
% 10.51/7.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------