%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET865-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:33:28 AM UTC 2026
% Result : Unsatisfiable 83.38s 15.04s
% Output : CNFRefutation 83.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 9 unt; 0 nHn; 26 RR)
% Number of literals : 67 ( 19 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Zorn_OHausdorff_0,axiom,
'c$uin'('c$uZorn$uOHausdorff$u$u1'(X0,X1),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'(X1))) ).
cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
( 'c$uUnion'(X3,X2) = X0
| ~ 'c$ulessequals'('c$uUnion'(X3,X2),X0,'tc$uset'(X2))
| ~ 'c$uin'(X3,'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
'c$ulessequals'('c$uZorn$uOmaxchain'(X0,X1),'c$uZorn$uOchain'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1)))) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ 'c$uin'(X0,'c$uZorn$uOchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uUnion'(X0,'t$ua'),'v$uS','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$uin'('v$ux'(X0),'v$uS','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$ux'(X0),'tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ) ).
cnf(cls_List_Oappend__same__eq__iff1_0,axiom,
( X0 = X3
| 'c$uappend'(X0,X1,X2) != 'c$uappend'(X3,X1,X2) ) ).
cnf(cls_List_Oappend__self__conv__iff2_0,axiom,
'c$uappend'(X0,'c$uList$uOlist$uONil',X1) = X0 ).
cnf(cls_Set_OsubsetD_0,axiom,
( 'c$uin'(X0,X3,X2)
| ~ 'c$ulessequals'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(c0,plain,
'c$uin'('c$uZorn$uOHausdorff$u$u1'(X0,X1),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'(X1))),
inference(clausification,[status(esa)],[cls_Zorn_OHausdorff_0]) ).
cnf(c1,plain,
( 'c$uUnion'(X3,X2) = X0
| ~ 'c$ulessequals'('c$uUnion'(X3,X2),X0,'tc$uset'(X2))
| ~ 'c$uin'(X3,'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Zorn_Omaxchain__Zorn_0]) ).
cnf(c2,plain,
'c$ulessequals'('c$uZorn$uOmaxchain'(X0,X1),'c$uZorn$uOchain'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1)))),
inference(clausification,[status(esa)],[cls_Zorn_Omaxchain__subset__chain_0]) ).
cnf(c3,plain,
( ~ 'c$uin'(X0,'c$uZorn$uOchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uUnion'(X0,'t$ua'),'v$uS','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c4,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$uin'('v$ux'(X0),'v$uS','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c5,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$ux'(X0),'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c72,plain,
( X0 = X3
| 'c$uappend'(X0,X1,X2) != 'c$uappend'(X3,X1,X2) ),
inference(clausification,[status(esa)],[cls_List_Oappend__same__eq__iff1_0]) ).
cnf(c76,plain,
'c$uappend'(X0,'c$uList$uOlist$uONil',X1) = X0,
inference(clausification,[status(esa)],[cls_List_Oappend__self__conv__iff2_0]) ).
cnf(c312,plain,
( 'c$uin'(X0,X3,X2)
| ~ 'c$ulessequals'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetD_0]) ).
cnf(d0,plain,
( ~ 'c$ulessequals'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,X1),X1),X2,'tc$uset'(X1))
| ~ 'c$uin'(X2,X0,'tc$uset'(X1))
| 'c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,X1),X1) = X2 ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'('v$ux'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua')),X0,'tc$uset'('t$ua'))
| 'c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua') = 'v$ux'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua')) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( X2 = X0
| 'c$uappend'(X2,'c$uList$uOlist$uONil',X1) != X0 ),
inference(superposition,[status(thm)],[c76,c72]) ).
cnf(d3,plain,
( X0 != X2
| X0 = X2 ),
inference(demodulation,[status(thm)],[d2,c76]) ).
cnf(d4,plain,
( ~ 'c$uin'('v$ux'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua')),X0,'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua'))
| 'c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua') = 'v$ux'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua')) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d6,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ),
inference(resolution,[status(thm)],[d3,d5]) ).
cnf(d7,plain,
( ~ 'c$uin'('v$ux'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua')),X0,'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'(X0,'t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'('v$uS','t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'('v$uS','t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( ~ 'c$uin'(X0,'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| 'c$uin'(X0,'c$uZorn$uOchain'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(resolution,[status(thm)],[c312,c2]) ).
cnf(d10,plain,
'c$uin'('c$uZorn$uOHausdorff$u$u1'(X0,X1),'c$uZorn$uOchain'(X0,X1),'tc$uset'('tc$uset'(X1))),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
'c$uin'('c$uUnion'('c$uZorn$uOHausdorff$u$u1'('v$uS','t$ua'),'t$ua'),'v$uS','tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET865-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % Computer : n008.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8046.5625MB
% 0.12/0.45 % OS : Linux 6.8.0-71-generic
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Sat Sep 26 08:24:24 UTC 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.38/15.04 % SZS status Unsatisfiable for theBenchmark.p
% 83.38/15.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------