%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV879-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 09:04:52 AM UTC 2026
% Result : Unsatisfiable 205.26s 44.80s
% Output : CNFRefutation 205.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 41 ( 24 unt; 0 nHn; 21 RR)
% Number of literals : 66 ( 8 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-4 aty)
% Number of variables : 102 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Suc__n__not__le__n_0,axiom,
~ 'c$ulessequals'('c$uSuc'(X0),X0,'tc$unat') ).
cnf(cls_Max__ge_0,axiom,
( ~ 'c$uFinite$u$uSet$uOfinite'(X2,X0)
| ~ hBOOL('c$uin'(X1,X2,X0))
| 'c$ulessequals'(X1,hAPP('c$uFinite$u$uSet$uOlinorder$u$uclass$uOMax'(X0),X2),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Collect__def_0,axiom,
'c$uCollect'(X0,X1) = X0 ).
cnf(cls_inj__on__inv__into_0,axiom,
( ~ 'c$ulessequals'(X4,'c$uSet$uOimage'(X1,X0,X2,X3),'tc$ufun'(X3,'tc$ubool'))
| 'c$uFun$uOinj$u$uon'('c$uHilbert$u$uChoice$uOinv$u$uinto'(X0,X1,X2,X3),X4,X3,X2) ) ).
cnf(cls_equalityE_0,axiom,
'c$ulessequals'(X0,X0,'tc$ufun'(X1,'tc$ubool')) ).
cnf(cls_rangeI_0,axiom,
hBOOL('c$uin'(hAPP(X0,X1),'c$uSet$uOimage'(X0,'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'(X2,'tc$ubool')),X2,X3),X3)) ).
cnf(cls_singleton__conv2_0,axiom,
'c$uCollect'('c$ufequal'(X0,X1),X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1) ).
cnf(cls_fold1__singleton_0,axiom,
hAPP('c$uFinite$u$uSet$uOfold1'(X0,X1),'c$uSet$uOinsert'(X2,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1)) = X2 ).
cnf(cls_finite__imageD_0,axiom,
( ~ 'c$uFinite$u$uSet$uOfinite'('c$uSet$uOimage'(X2,X0,X1,X3),X3)
| ~ 'c$uFun$uOinj$u$uon'(X2,X0,X1,X3)
| 'c$uFinite$u$uSet$uOfinite'(X0,X1) ) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X1,X0))
| hBOOL('c$uin'(X0,X1,X2)) ) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_finite_0,axiom,
( 'c$uFinite$u$uSet$uOfinite'(X1,X0)
| ~ 'class$uFinite$u$uSet$uOfinite$uOfinite'(X0) ) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
'class$uOrderings$uOlinorder'('tc$unat') ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
'class$uFinite$u$uSet$uOfinite$uOfinite'('tc$ubool') ).
cnf(c119,plain,
~ 'c$ulessequals'('c$uSuc'(X0),X0,'tc$unat'),
inference(clausification,[status(esa)],[cls_Suc__n__not__le__n_0]) ).
cnf(c579,plain,
( ~ 'c$uFinite$u$uSet$uOfinite'(X2,X0)
| ~ hBOOL('c$uin'(X1,X2,X0))
| 'c$ulessequals'(X1,hAPP('c$uFinite$u$uSet$uOlinorder$u$uclass$uOMax'(X0),X2),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Max__ge_0]) ).
cnf(c664,plain,
'c$uCollect'(X0,X1) = X0,
inference(clausification,[status(esa)],[cls_Collect__def_0]) ).
cnf(c691,plain,
( ~ 'c$ulessequals'(X4,'c$uSet$uOimage'(X1,X0,X2,X3),'tc$ufun'(X3,'tc$ubool'))
| 'c$uFun$uOinj$u$uon'('c$uHilbert$u$uChoice$uOinv$u$uinto'(X0,X1,X2,X3),X4,X3,X2) ),
inference(clausification,[status(esa)],[cls_inj__on__inv__into_0]) ).
cnf(c734,plain,
'c$ulessequals'(X0,X0,'tc$ufun'(X1,'tc$ubool')),
inference(clausification,[status(esa)],[cls_equalityE_0]) ).
cnf(c767,plain,
hBOOL('c$uin'(hAPP(X0,X1),'c$uSet$uOimage'(X0,'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'(X2,'tc$ubool')),X2,X3),X3)),
inference(clausification,[status(esa)],[cls_rangeI_0]) ).
cnf(c773,plain,
'c$uCollect'('c$ufequal'(X0,X1),X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),
inference(clausification,[status(esa)],[cls_singleton__conv2_0]) ).
cnf(c790,plain,
hAPP('c$uFinite$u$uSet$uOfold1'(X0,X1),'c$uSet$uOinsert'(X2,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1)) = X2,
inference(clausification,[status(esa)],[cls_fold1__singleton_0]) ).
cnf(c796,plain,
( ~ 'c$uFinite$u$uSet$uOfinite'('c$uSet$uOimage'(X2,X0,X1,X3),X3)
| ~ 'c$uFun$uOinj$u$uon'(X2,X0,X1,X3)
| 'c$uFinite$u$uSet$uOfinite'(X0,X1) ),
inference(clausification,[status(esa)],[cls_finite__imageD_0]) ).
cnf(c843,plain,
( ~ hBOOL(hAPP(X1,X0))
| hBOOL('c$uin'(X0,X1,X2)) ),
inference(clausification,[status(esa)],[cls_mem__def_1]) ).
cnf(c844,plain,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_mem__def_0]) ).
cnf(c855,plain,
( 'c$uFinite$u$uSet$uOfinite'(X1,X0)
| ~ 'class$uFinite$u$uSet$uOfinite$uOfinite'(X0) ),
inference(clausification,[status(esa)],[cls_finite_0]) ).
cnf(c892,plain,
'class$uOrderings$uOlinorder'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(c903,plain,
'class$uFinite$u$uSet$uOfinite$uOfinite'('tc$ubool'),
inference(clausification,[status(esa)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(d0,plain,
( ~ 'class$uFinite$u$uSet$uOfinite$uOfinite'(X3)
| ~ 'c$uFun$uOinj$u$uon'(X2,X0,X1,X3)
| 'c$uFinite$u$uSet$uOfinite'(X0,X1) ),
inference(resolution,[status(thm)],[c796,c855]) ).
cnf(d1,plain,
'c$uFun$uOinj$u$uon'('c$uHilbert$u$uChoice$uOinv$u$uinto'(X0,X1,X2,X3),'c$uSet$uOimage'(X1,X0,X2,X3),X3,X2),
inference(resolution,[status(thm)],[c691,c734]) ).
cnf(d2,plain,
( ~ 'class$uFinite$u$uSet$uOfinite$uOfinite'(X2)
| 'c$uFinite$u$uSet$uOfinite'('c$uSet$uOimage'(X0,X1,X2,X3),X3) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
hBOOL(hAPP('c$uSet$uOimage'(X0,'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'(X1,'tc$ubool')),X1,X2),hAPP(X0,X3))),
inference(resolution,[status(thm)],[c767,c844]) ).
cnf(d4,plain,
'c$ufequal'(X0,X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),
inference(demodulation,[status(thm)],[c773,c664]) ).
cnf(d5,plain,
hAPP('c$uFinite$u$uSet$uOfold1'(X2,X1),'c$ufequal'(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c790,d4]) ).
cnf(d6,plain,
hBOOL(hAPP('c$uSet$uOimage'('c$uFinite$u$uSet$uOfold1'(X0,X1),'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'(X3,'tc$ubool')),X3,X4),X2)),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ hBOOL('c$uin'('c$uSuc'(hAPP('c$uFinite$u$uSet$uOlinorder$u$uclass$uOMax'('tc$unat'),X0)),X0,'tc$unat'))
| ~ 'c$uFinite$u$uSet$uOfinite'(X0,'tc$unat')
| ~ 'class$uOrderings$uOlinorder'('tc$unat') ),
inference(resolution,[status(thm)],[c579,c119]) ).
cnf(d8,plain,
( ~ hBOOL('c$uin'('c$uSuc'(hAPP('c$uFinite$u$uSet$uOlinorder$u$uclass$uOMax'('tc$unat'),X0)),X0,'tc$unat'))
| ~ 'c$uFinite$u$uSet$uOfinite'(X0,'tc$unat') ),
inference(resolution,[status(thm)],[c892,d7]) ).
cnf(d9,plain,
( ~ hBOOL(hAPP(X0,'c$uSuc'(hAPP('c$uFinite$u$uSet$uOlinorder$u$uclass$uOMax'('tc$unat'),X0))))
| ~ 'c$uFinite$u$uSet$uOfinite'(X0,'tc$unat') ),
inference(resolution,[status(thm)],[d8,c843]) ).
cnf(d10,plain,
~ 'c$uFinite$u$uSet$uOfinite'('c$uSet$uOimage'('c$uFinite$u$uSet$uOfold1'(X0,X1),'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'(X2,'tc$ubool')),X2,X3),'tc$unat'),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
~ 'class$uFinite$u$uSet$uOfinite$uOfinite'(X0),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,c903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV879-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 15:01:48 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 205.26/44.80 % SZS status Unsatisfiable for theBenchmark.p
% 205.26/44.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------