TSTP Solution File: SCT006-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT006-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:12:59 EDT 2022
% Result : Unsatisfiable 73.88s 74.08s
% Output : Refutation 75.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 61
% Syntax : Number of clauses : 190 ( 86 unt; 31 nHn; 190 RR)
% Number of literals : 316 ( 0 equ; 114 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 10 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(u,v,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)),
file('SCT006-1.p',unknown),
[] ).
cnf(28,axiom,
equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v),w),
file('SCT006-1.p',unknown),
[] ).
cnf(86,axiom,
equal(hAPP(c_COMBB(u,v,w,x,y),z),hAPP(u,hAPP(v,z))),
file('SCT006-1.p',unknown),
[] ).
cnf(106,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('SCT006-1.p',unknown),
[] ).
cnf(137,axiom,
( ~ c_lessequals(c_Set_Oinsert(u,v,w),x,tc_fun(w,tc_bool))
| hBOOL(hAPP(hAPP(c_in(w),u),x)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(149,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(u)
| ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| c_lessequals(v,c_Complete__Lattice_OSup__class_OSup(w,u),u) ),
file('SCT006-1.p',unknown),
[] ).
cnf(174,axiom,
equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),c_Collect(v,u)),c_Collect(c_COMBB(c_Not,v,tc_bool,tc_bool,u),u)),
file('SCT006-1.p',unknown),
[] ).
cnf(175,axiom,
equal(c_Set_Ovimage(u,c_Collect(v,w),x,w),c_Collect(c_COMBB(v,u,w,tc_bool,x),x)),
file('SCT006-1.p',unknown),
[] ).
cnf(180,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),c_Set_OPow(w,u)))
| c_lessequals(v,w,tc_fun(u,tc_bool)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(183,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(w,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(203,axiom,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| equal(c_Lattices_Olower__semilattice__class_Oinf(v,u,tc_fun(w,tc_bool)),u) ),
file('SCT006-1.p',unknown),
[] ).
cnf(255,axiom,
( ~ class_Lattices_Oupper__semilattice(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| c_HOL_Oord__class_Oless(v,c_Lattices_Oupper__semilattice__class_Osup(x,w,u),u) ),
file('SCT006-1.p',unknown),
[] ).
cnf(261,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| ~ c_lessequals(w,x,tc_fun(u,tc_bool))
| hBOOL(hAPP(hAPP(c_in(u),v),x)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(281,axiom,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| c_HOL_Oord__class_Oless(u,c_Set_Oinsert(x,v,w),tc_fun(w,tc_bool))
| hBOOL(hAPP(hAPP(c_in(w),x),u))
| hBOOL(hAPP(hAPP(c_in(w),x),v)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(320,axiom,
equal(c_Collect(u,v),u),
file('SCT006-1.p',unknown),
[] ).
cnf(324,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(u)
| equal(c_Lattices_Olower__semilattice__class_Oinf(v,c_Complete__Lattice_OInf__class_OInf(w,u),u),c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(v,w,u),u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(347,axiom,
equal(hAPP(hAPP(c_COMBC(u,v,w,x),y),z),hAPP(hAPP(u,z),y)),
file('SCT006-1.p',unknown),
[] ).
cnf(348,axiom,
equal(hAPP(c_COMBK(u,v,w),x),u),
file('SCT006-1.p',unknown),
[] ).
cnf(355,axiom,
( ~ class_Lattices_Oboolean__algebra(u)
| equal(c_Lattices_Olower__semilattice__class_Oinf(v,hAPP(c_HOL_Ouminus__class_Ouminus(u),w),u),c_HOL_Ominus__class_Ominus(v,w,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(365,axiom,
equal(c_Set_Ovimage(u,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),w),x,v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(x,tc_bool)),c_Set_Ovimage(u,w,x,v))),
file('SCT006-1.p',unknown),
[] ).
cnf(382,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,v,tc_fun(w,tc_bool)),x))
| hBOOL(hAPP(u,x)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(385,axiom,
equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v)),v),
file('SCT006-1.p',unknown),
[] ).
cnf(429,axiom,
equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),
file('SCT006-1.p',unknown),
[] ).
cnf(452,axiom,
~ c_HOL_Oord__class_Oless(u,u,tc_fun(v,tc_bool)),
file('SCT006-1.p',unknown),
[] ).
cnf(467,axiom,
( ~ class_Lattices_Olower__semilattice(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(v,x,u),w,u) ),
file('SCT006-1.p',unknown),
[] ).
cnf(472,axiom,
( hBOOL(hAPP(hAPP(c_in(u),v),w))
| equal(c_Set_Ovimage(c_COMBK(v,u,x),w,x,u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) ),
file('SCT006-1.p',unknown),
[] ).
cnf(477,axiom,
~ equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w,u)),
file('SCT006-1.p',unknown),
[] ).
cnf(507,axiom,
equal(c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(u,v),tc_fun(v,tc_bool)),u),
file('SCT006-1.p',unknown),
[] ).
cnf(513,axiom,
equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),c_Collect(hAPP(c_fequal(v),u),v)),
file('SCT006-1.p',unknown),
[] ).
cnf(515,axiom,
equal(c_Collect(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),u),v),
file('SCT006-1.p',unknown),
[] ).
cnf(528,axiom,
( hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w)))
| hBOOL(hAPP(hAPP(c_in(u),v),w)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(529,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| ~ hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w))) ),
file('SCT006-1.p',unknown),
[] ).
cnf(530,axiom,
( ~ hBOOL(hAPP(u,v))
| ~ hBOOL(hAPP(hAPP(c_in(w),v),x))
| hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XbexE__1__1(x,u,w))) ),
file('SCT006-1.p',unknown),
[] ).
cnf(583,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| equal(c_Set_Oinsert(v,w,u),w) ),
file('SCT006-1.p',unknown),
[] ).
cnf(607,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),c_Equiv__Relations_Oquotient(w,x,u)))
| hBOOL(hAPP(hAPP(c_in(u),c_List_Osko__Equiv__Relations__XquotientE__1__1(w,v,x,u)),w)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(608,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),c_Set_OPow(v,u))),
file('SCT006-1.p',unknown),
[] ).
cnf(618,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(hAPP(hAPP(c_in(w),v),u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(619,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| hBOOL(hAPP(w,v)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(621,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(u)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(622,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Oupper__semilattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(623,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Olower__semilattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(624,axiom,
( ~ class_Lattices_Odistrib__lattice(u)
| class_Lattices_Odistrib__lattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(625,axiom,
( ~ class_Lattices_Obounded__lattice(u)
| class_Lattices_Obounded__lattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(626,axiom,
( ~ class_Lattices_Oboolean__algebra(u)
| class_Lattices_Oboolean__algebra(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(627,axiom,
( ~ class_Orderings_Opreorder(u)
| class_Orderings_Opreorder(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(628,axiom,
( ~ class_Lattices_Olattice(u)
| class_Lattices_Olattice(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(629,axiom,
( ~ class_Orderings_Oorder(u)
| class_Orderings_Oorder(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(630,axiom,
( ~ class_Orderings_Obot(u)
| class_Orderings_Obot(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(631,axiom,
( ~ class_HOL_Oord(u)
| class_HOL_Oord(tc_fun(v,u)) ),
file('SCT006-1.p',unknown),
[] ).
cnf(641,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(642,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(643,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(644,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(645,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(646,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(647,axiom,
class_Orderings_Opreorder(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(648,axiom,
class_Lattices_Olattice(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(649,axiom,
class_Orderings_Oorder(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(650,axiom,
class_Orderings_Obot(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(651,axiom,
class_HOL_Oord(tc_bool),
file('SCT006-1.p',unknown),
[] ).
cnf(654,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),u),c_Arrow__Order__Mirabelle_OLin)),
file('SCT006-1.p',unknown),
[] ).
cnf(657,plain,
equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v),
inference(rew,[status(thm),theory(equality)],[320,515]),
[iquote('0:Rew:320.0,515.0')] ).
cnf(658,plain,
equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),hAPP(c_fequal(v),u)),
inference(rew,[status(thm),theory(equality)],[320,513]),
[iquote('0:Rew:320.0,513.0')] ).
cnf(665,plain,
equal(c_COMBB(u,v,w,tc_bool,x),c_Set_Ovimage(v,u,x,w)),
inference(rew,[status(thm),theory(equality)],[320,175]),
[iquote('0:Rew:320.0,175.0,320.0,175.0')] ).
cnf(667,plain,
equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),c_Set_Ovimage(v,c_Not,u,tc_bool)),
inference(rew,[status(thm),theory(equality)],[320,174,665]),
[iquote('0:Rew:320.0,174.0,320.0,174.0,665.0,174.0')] ).
cnf(670,plain,
equal(c_Set_Ovimage(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),c_Not,u,tc_bool),v),
inference(rew,[status(thm),theory(equality)],[667,385]),
[iquote('0:Rew:667.0,385.0')] ).
cnf(671,plain,
equal(c_Set_Ovimage(c_Set_Ovimage(u,c_Not,v,tc_bool),c_Not,v,tc_bool),u),
inference(rew,[status(thm),theory(equality)],[667,670]),
[iquote('0:Rew:667.0,670.0')] ).
cnf(680,plain,
( hBOOL(hAPP(hAPP(c_in(u),v),w))
| hBOOL(hAPP(hAPP(c_in(u),v),c_Set_Ovimage(w,c_Not,u,tc_bool))) ),
inference(rew,[status(thm),theory(equality)],[667,528]),
[iquote('0:Rew:667.0,528.0')] ).
cnf(692,plain,
equal(c_Set_Ovimage(u,c_Set_Ovimage(v,c_Not,w,tc_bool),x,w),c_Set_Ovimage(c_Set_Ovimage(u,v,x,w),c_Not,x,tc_bool)),
inference(rew,[status(thm),theory(equality)],[667,365]),
[iquote('0:Rew:667.0,365.0,667.0,365.0')] ).
cnf(693,plain,
equal(c_Set_Ovimage(u,c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),v,tc_bool),u),
inference(rew,[status(thm),theory(equality)],[692,671]),
[iquote('0:Rew:692.0,671.0')] ).
cnf(695,plain,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| ~ hBOOL(hAPP(hAPP(c_in(u),v),c_Set_Ovimage(w,c_Not,u,tc_bool))) ),
inference(rew,[status(thm),theory(equality)],[667,529]),
[iquote('0:Rew:667.0,529.1')] ).
cnf(744,plain,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| hBOOL(hAPP(hAPP(c_in(w),x),v))
| c_HOL_Oord__class_Oless(u,c_Set_Oinsert(x,v,w),tc_fun(w,tc_bool)) ),
inference(mrr,[status(thm)],[281,261]),
[iquote('0:MRR:281.2,261.0')] ).
cnf(798,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),u),c_Set_Ovimage(c_Arrow__Order__Mirabelle_OLin,c_Not,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))),
inference(res,[status(thm),theory(equality)],[680,654]),
[iquote('0:Res:680.1,654.0')] ).
cnf(799,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,u)),
inference(res,[status(thm),theory(equality)],[618,654]),
[iquote('0:Res:618.1,654.0')] ).
cnf(819,plain,
( ~ c_lessequals(u,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| c_HOL_Oord__class_Oless(u,c_Set_Oinsert(v,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
inference(res,[status(thm),theory(equality)],[744,654]),
[iquote('0:Res:744.2,654.0')] ).
cnf(1039,plain,
hBOOL(hAPP(c_Set_OPow(u,v),u)),
inference(res,[status(thm),theory(equality)],[608,619]),
[iquote('0:Res:608.0,619.0')] ).
cnf(1766,plain,
equal(c_Set_Oinsert(u,c_Set_OPow(u,v),tc_fun(v,tc_bool)),c_Set_OPow(u,v)),
inference(res,[status(thm),theory(equality)],[608,583]),
[iquote('0:Res:608.0,583.0')] ).
cnf(1813,plain,
~ equal(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool)),c_Set_OPow(v,u)),
inference(spl,[status(thm),theory(equality)],[1766,477]),
[iquote('0:SpL:1766.0,477.0')] ).
cnf(2160,plain,
equal(hAPP(c_Set_Ovimage(u,v,w,x),y),hAPP(v,hAPP(u,y))),
inference(spr,[status(thm),theory(equality)],[665,86]),
[iquote('0:SpR:665.0,86.0')] ).
cnf(2165,plain,
equal(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),hAPP(u,v)),hAPP(u,v)),
inference(spr,[status(thm),theory(equality)],[693,2160]),
[iquote('0:SpR:693.0,2160.0')] ).
cnf(2167,plain,
equal(hAPP(c_Not,hAPP(c_Not,hAPP(u,v))),hAPP(u,v)),
inference(rew,[status(thm),theory(equality)],[2160,2165]),
[iquote('0:Rew:2160.0,2165.0')] ).
cnf(2172,plain,
equal(hAPP(c_Not,hAPP(c_Not,u)),u),
inference(spr,[status(thm),theory(equality)],[28,2167]),
[iquote('0:SpR:28.0,2167.0')] ).
cnf(2467,plain,
( ~ class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w),tc_fun(u,tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[355,13]),
[iquote('0:SpR:355.1,13.0')] ).
cnf(2503,plain,
( ~ class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Set_Ovimage(w,c_Not,u,tc_bool),tc_fun(u,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[667,2467]),
[iquote('0:Rew:667.0,2467.1')] ).
cnf(2504,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Ovimage(v,c_Not,w,tc_bool),tc_fun(w,tc_bool)),
inference(ssi,[status(thm)],[2503,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:2503.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(2590,plain,
c_lessequals(u,c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Not,v,tc_bool),tc_fun(v,tc_bool)),
inference(spr,[status(thm),theory(equality)],[429,2504]),
[iquote('0:SpR:429.0,2504.0')] ).
cnf(3183,plain,
( ~ class_Lattices_Olower__semilattice(tc_fun(u,tc_bool))
| ~ c_HOL_Oord__class_Oless(v,c_Lattices_Olower__semilattice__class_Oinf(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) ),
inference(res,[status(thm),theory(equality)],[467,452]),
[iquote('0:Res:467.2,452.0')] ).
cnf(3197,plain,
~ c_HOL_Oord__class_Oless(u,c_Lattices_Olower__semilattice__class_Oinf(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),
inference(ssi,[status(thm)],[3183,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:3183.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(3210,plain,
( ~ c_lessequals(u,v,tc_fun(w,tc_bool))
| ~ c_HOL_Oord__class_Oless(v,u,tc_fun(w,tc_bool)) ),
inference(spl,[status(thm),theory(equality)],[203,3197]),
[iquote('0:SpL:203.1,3197.0')] ).
cnf(3841,plain,
( ~ class_Lattices_Oupper__semilattice(tc_fun(u,tc_bool))
| ~ c_HOL_Oord__class_Oless(v,w,tc_fun(u,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(x,w,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) ),
inference(res,[status(thm),theory(equality)],[255,3210]),
[iquote('0:Res:255.2,3210.1')] ).
cnf(3862,plain,
( ~ c_HOL_Oord__class_Oless(u,v,tc_fun(w,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(x,v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool)) ),
inference(ssi,[status(thm)],[3841,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:3841.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(5315,plain,
equal(hAPP(hAPP(c_in(u),v),w),hAPP(w,v)),
inference(spr,[status(thm),theory(equality)],[657,347]),
[iquote('0:SpR:657.0,347.0')] ).
cnf(5334,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),c_Equiv__Relations_Oquotient(w,x,u)))
| hBOOL(hAPP(w,c_List_Osko__Equiv__Relations__XquotientE__1__1(w,v,x,u))) ),
inference(rew,[status(thm),theory(equality)],[5315,607]),
[iquote('0:Rew:5315.0,607.1')] ).
cnf(5432,plain,
( ~ c_lessequals(c_Set_Oinsert(u,v,w),x,tc_fun(w,tc_bool))
| hBOOL(hAPP(x,u)) ),
inference(rew,[status(thm),theory(equality)],[5315,137]),
[iquote('0:Rew:5315.0,137.1')] ).
cnf(5445,plain,
( ~ hBOOL(hAPP(u,v))
| ~ hBOOL(hAPP(w,v))
| hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XbexE__1__1(w,u,x))) ),
inference(rew,[status(thm),theory(equality)],[5315,530]),
[iquote('0:Rew:5315.0,530.1')] ).
cnf(5453,plain,
( ~ hBOOL(hAPP(u,v))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(u,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[5315,183]),
[iquote('0:Rew:5315.0,183.0')] ).
cnf(5454,plain,
( ~ hBOOL(hAPP(c_Set_OPow(u,v),w))
| c_lessequals(w,u,tc_fun(v,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[5315,180]),
[iquote('0:Rew:5315.0,180.0')] ).
cnf(5468,plain,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| ~ hBOOL(hAPP(c_Set_Ovimage(w,c_Not,u,tc_bool),v)) ),
inference(rew,[status(thm),theory(equality)],[5315,695]),
[iquote('0:Rew:5315.0,695.1')] ).
cnf(5469,plain,
( hBOOL(hAPP(hAPP(c_in(u),v),w))
| hBOOL(hAPP(c_Set_Ovimage(w,c_Not,u,tc_bool),v)) ),
inference(rew,[status(thm),theory(equality)],[5315,680]),
[iquote('0:Rew:5315.0,680.1')] ).
cnf(5483,plain,
hBOOL(hAPP(c_Set_Ovimage(c_Arrow__Order__Mirabelle_OLin,c_Not,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),u)),
inference(rew,[status(thm),theory(equality)],[5315,798]),
[iquote('0:Rew:5315.0,798.0')] ).
cnf(5514,plain,
( hBOOL(hAPP(u,v))
| equal(c_Set_Ovimage(c_COMBK(v,w,x),u,x,w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) ),
inference(rew,[status(thm),theory(equality)],[5315,472]),
[iquote('0:Rew:5315.0,472.0')] ).
cnf(5516,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(u)
| ~ hBOOL(hAPP(v,w))
| c_lessequals(w,c_Complete__Lattice_OSup__class_OSup(v,u),u) ),
inference(rew,[status(thm),theory(equality)],[5315,149]),
[iquote('0:Rew:5315.0,149.1')] ).
cnf(5519,plain,
hBOOL(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u))),
inference(rew,[status(thm),theory(equality)],[2160,5483]),
[iquote('0:Rew:2160.0,5483.0')] ).
cnf(5523,plain,
( hBOOL(hAPP(hAPP(c_in(u),v),w))
| hBOOL(hAPP(c_Not,hAPP(w,v))) ),
inference(rew,[status(thm),theory(equality)],[2160,5469]),
[iquote('0:Rew:2160.0,5469.1')] ).
cnf(5524,plain,
( hBOOL(hAPP(u,v))
| hBOOL(hAPP(c_Not,hAPP(u,v))) ),
inference(rew,[status(thm),theory(equality)],[5315,5523]),
[iquote('0:Rew:5315.0,5523.0')] ).
cnf(5531,plain,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
| ~ hBOOL(hAPP(c_Not,hAPP(w,v))) ),
inference(rew,[status(thm),theory(equality)],[2160,5468]),
[iquote('0:Rew:2160.0,5468.1')] ).
cnf(5532,plain,
( ~ hBOOL(hAPP(u,v))
| ~ hBOOL(hAPP(c_Not,hAPP(u,v))) ),
inference(rew,[status(thm),theory(equality)],[5315,5531]),
[iquote('0:Rew:5315.0,5531.0')] ).
cnf(5555,plain,
( ~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(u,v,w),x))
| hBOOL(hAPP(u,c_List_Osko__Equiv__Relations__XquotientE__1__1(u,x,v,w))) ),
inference(rew,[status(thm),theory(equality)],[5315,5334]),
[iquote('0:Rew:5315.0,5334.0')] ).
cnf(5620,plain,
( hBOOL(hAPP(c_Not,u))
| hBOOL(u) ),
inference(spr,[status(thm),theory(equality)],[2172,5524]),
[iquote('0:SpR:2172.0,5524.1')] ).
cnf(5655,plain,
( ~ hBOOL(hAPP(c_Not,u))
| ~ hBOOL(u) ),
inference(spl,[status(thm),theory(equality)],[2172,5532]),
[iquote('0:SpL:2172.0,5532.1')] ).
cnf(5738,plain,
( ~ c_lessequals(hAPP(c_fequal(u),v),w,tc_fun(u,tc_bool))
| hBOOL(hAPP(w,v)) ),
inference(spl,[status(thm),theory(equality)],[658,5432]),
[iquote('0:SpL:658.0,5432.0')] ).
cnf(5882,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,tc_bool))
| ~ hBOOL(hAPP(v,hAPP(c_fequal(u),w)))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(v,tc_fun(u,tc_bool)),w)) ),
inference(res,[status(thm),theory(equality)],[5516,5738]),
[iquote('0:Res:5516.2,5738.0')] ).
cnf(5887,plain,
( ~ hBOOL(hAPP(u,hAPP(c_fequal(v),w)))
| hBOOL(hAPP(c_Complete__Lattice_OSup__class_OSup(u,tc_fun(v,tc_bool)),w)) ),
inference(ssi,[status(thm)],[5882,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:5882.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(6975,plain,
( ~ hBOOL(hAPP(c_Set_OPow(u,v),hAPP(c_fequal(v),w)))
| hBOOL(hAPP(u,w)) ),
inference(spr,[status(thm),theory(equality)],[507,5887]),
[iquote('0:SpR:507.0,5887.1')] ).
cnf(8238,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,tc_bool))
| ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x))
| hBOOL(hAPP(v,x)) ),
inference(spl,[status(thm),theory(equality)],[324,382]),
[iquote('0:SpL:324.1,382.0')] ).
cnf(8261,plain,
( ~ hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x))
| hBOOL(hAPP(u,x)) ),
inference(ssi,[status(thm)],[8238,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:8238.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(8985,plain,
~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(c_Arrow__Order__Mirabelle_OLin,u,v),w)),
inference(res,[status(thm),theory(equality)],[5555,799]),
[iquote('0:Res:5555.1,799.0')] ).
cnf(9042,plain,
~ hBOOL(hAPP(c_Equiv__Relations_Oquotient(c_Equiv__Relations_Oquotient(c_Arrow__Order__Mirabelle_OLin,u,v),w,x),y)),
inference(res,[status(thm),theory(equality)],[5555,8985]),
[iquote('0:Res:5555.1,8985.0')] ).
cnf(11402,plain,
( ~ hBOOL(hAPP(u,hAPP(c_Arrow__Order__Mirabelle_OLin,v)))
| hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__XbexE__1__1(u,c_Not,w))) ),
inference(res,[status(thm),theory(equality)],[5519,5445]),
[iquote('0:Res:5519.0,5445.0')] ).
cnf(12565,plain,
hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(hAPP(c_Arrow__Order__Mirabelle_OLin,u),v),c_Not,w))),
inference(res,[status(thm),theory(equality)],[1039,11402]),
[iquote('0:Res:1039.0,11402.0')] ).
cnf(12696,plain,
~ hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(hAPP(c_Arrow__Order__Mirabelle_OLin,u),v),c_Not,w)),
inference(res,[status(thm),theory(equality)],[12565,5655]),
[iquote('0:Res:12565.0,5655.0')] ).
cnf(13450,plain,
( hBOOL(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),u))
| equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_COMBK(u,tc_bool,v)) ),
inference(spr,[status(thm),theory(equality)],[5514,693]),
[iquote('0:SpR:5514.1,693.0')] ).
cnf(13459,plain,
( hBOOL(u)
| equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_COMBK(u,tc_bool,v)) ),
inference(rew,[status(thm),theory(equality)],[2172,13450,2160]),
[iquote('0:Rew:2172.0,13450.0,2160.0,13450.0')] ).
cnf(13525,plain,
( hBOOL(u)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w),u) ),
inference(spr,[status(thm),theory(equality)],[13459,348]),
[iquote('0:SpR:13459.1,348.0')] ).
cnf(13552,plain,
( ~ equal(c_COMBK(u,tc_bool,tc_fun(v,tc_bool)),c_Set_OPow(w,v))
| hBOOL(u) ),
inference(spl,[status(thm),theory(equality)],[13459,1813]),
[iquote('0:SpL:13459.1,1813.0')] ).
cnf(13597,plain,
( hBOOL(u)
| hBOOL(v)
| equal(u,v) ),
inference(spr,[status(thm),theory(equality)],[13525]),
[iquote('0:SpR:13525.1,13525.1')] ).
cnf(15864,plain,
( hBOOL(c_Set_OPow(u,v))
| hBOOL(w)
| hBOOL(hAPP(w,u)) ),
inference(spr,[status(thm),theory(equality)],[13597,1039]),
[iquote('0:SpR:13597.2,1039.0')] ).
cnf(16992,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(u,v),c_Not,w))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,x))
| hBOOL(u) ),
inference(spl,[status(thm),theory(equality)],[13597,12696]),
[iquote('0:SpL:13597.2,12696.0')] ).
cnf(18034,plain,
( hBOOL(u)
| equal(hAPP(c_Arrow__Order__Mirabelle_OLin,v),u) ),
inference(res,[status(thm),theory(equality)],[13597,799]),
[iquote('0:Res:13597.0,799.0')] ).
cnf(18035,plain,
( ~ hBOOL(u)
| hBOOL(v)
| equal(hAPP(c_Not,u),v) ),
inference(res,[status(thm),theory(equality)],[13597,5655]),
[iquote('0:Res:13597.0,5655.0')] ).
cnf(18439,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_Set_OPow(u,v),c_Not,w))
| hBOOL(u) ),
inference(mrr,[status(thm)],[16992,799]),
[iquote('0:MRR:16992.1,799.0')] ).
cnf(19745,plain,
( hBOOL(c_Set_OPow(u,v))
| hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,w),u)) ),
inference(spr,[status(thm),theory(equality)],[18034,1039]),
[iquote('0:SpR:18034.1,1039.0')] ).
cnf(20513,plain,
( ~ hBOOL(u)
| equal(hAPP(c_Arrow__Order__Mirabelle_OLin,v),hAPP(c_Not,u)) ),
inference(res,[status(thm),theory(equality)],[18034,5655]),
[iquote('0:Res:18034.0,5655.0')] ).
cnf(30873,plain,
( ~ hBOOL(u)
| equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v)),u) ),
inference(spr,[status(thm),theory(equality)],[20513,2172]),
[iquote('0:SpR:20513.1,2172.0')] ).
cnf(31044,plain,
equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u)),hAPP(c_Set_OPow(v,w),v)),
inference(res,[status(thm),theory(equality)],[1039,30873]),
[iquote('0:Res:1039.0,30873.0')] ).
cnf(31047,plain,
( hBOOL(u)
| equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v)),hAPP(c_Not,u)) ),
inference(res,[status(thm),theory(equality)],[5620,30873]),
[iquote('0:Res:5620.0,30873.0')] ).
cnf(31550,plain,
( ~ class_Orderings_Opreorder(tc_fun(u,tc_bool))
| ~ c_lessequals(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Not,u,tc_bool),v,tc_fun(u,tc_bool))
| c_lessequals(w,v,tc_fun(u,tc_bool)) ),
inference(res,[status(thm),theory(equality)],[2590,106]),
[iquote('0:Res:2590.0,106.1')] ).
cnf(31601,plain,
( ~ c_lessequals(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Not,u,tc_bool),v,tc_fun(u,tc_bool))
| c_lessequals(w,v,tc_fun(u,tc_bool)) ),
inference(ssi,[status(thm)],[31550,630,650,651,644,645,646,649,647,641,643,642,648,631,624,625,626,629,627,621,623,622,628]),
[iquote('0:SSi:31550.0,630.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,631.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,624.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,625.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,626.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,629.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,627.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,621.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,623.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,622.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1,628.0,650.0,651.0,644.0,645.0,646.0,649.0,647.0,641.0,643.0,642.0,648.1')] ).
cnf(32194,plain,
( hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,u),v))
| equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,w)),c_Set_OPow(v,x)) ),
inference(res,[status(thm),theory(equality)],[19745,30873]),
[iquote('0:Res:19745.0,30873.0')] ).
cnf(33039,plain,
( hBOOL(c_Set_OPow(hAPP(c_Not,u),v))
| hBOOL(c_Not)
| hBOOL(u) ),
inference(spr,[status(thm),theory(equality)],[2172,15864]),
[iquote('0:SpR:2172.0,15864.2')] ).
cnf(33051,plain,
( hBOOL(c_Set_OPow(u,v))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(res,[status(thm),theory(equality)],[15864,799]),
[iquote('0:Res:15864.2,799.0')] ).
cnf(33143,plain,
hBOOL(c_Set_OPow(u,v)),
inference(spt,[spt(split,[position(s1)])],[33051]),
[iquote('1:Spt:33051.0')] ).
cnf(33154,plain,
equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u)),c_Set_OPow(v,w)),
inference(res,[status(thm),theory(equality)],[33143,30873]),
[iquote('1:Res:33143.0,30873.0')] ).
cnf(33231,plain,
hBOOL(hAPP(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u)),v)),
inference(spr,[status(thm),theory(equality)],[33154,1039]),
[iquote('1:SpR:33154.0,1039.0')] ).
cnf(33295,plain,
( ~ hBOOL(hAPP(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u)),hAPP(c_fequal(v),w)))
| hBOOL(hAPP(x,w)) ),
inference(spl,[status(thm),theory(equality)],[33154,6975]),
[iquote('1:SpL:33154.0,6975.0')] ).
cnf(33308,plain,
hBOOL(hAPP(u,v)),
inference(mrr,[status(thm)],[33295,33231]),
[iquote('1:MRR:33295.0,33231.0')] ).
cnf(33309,plain,
$false,
inference(unc,[status(thm)],[33308,9042]),
[iquote('1:UnC:33308.0,9042.0')] ).
cnf(33312,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(spt,[spt(split,[position(s2)])],[33051]),
[iquote('1:Spt:33309.0,33051.1')] ).
cnf(33313,plain,
( hBOOL(u)
| equal(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),u) ),
inference(res,[status(thm),theory(equality)],[33312,18035]),
[iquote('1:Res:33312.0,18035.0')] ).
cnf(33314,plain,
equal(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,u)),c_Arrow__Order__Mirabelle_OLin),
inference(res,[status(thm),theory(equality)],[33312,30873]),
[iquote('1:Res:33312.0,30873.0')] ).
cnf(33331,plain,
( ~ hBOOL(u)
| equal(c_Arrow__Order__Mirabelle_OLin,u) ),
inference(rew,[status(thm),theory(equality)],[33314,30873]),
[iquote('1:Rew:33314.0,30873.1')] ).
cnf(33352,plain,
equal(hAPP(c_Set_OPow(u,v),u),c_Arrow__Order__Mirabelle_OLin),
inference(rew,[status(thm),theory(equality)],[33314,31044]),
[iquote('1:Rew:33314.0,31044.0')] ).
cnf(33474,plain,
( hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,u),v))
| equal(c_Set_OPow(v,w),c_Arrow__Order__Mirabelle_OLin) ),
inference(rew,[status(thm),theory(equality)],[33314,32194]),
[iquote('1:Rew:33314.0,32194.1')] ).
cnf(33483,plain,
( hBOOL(u)
| equal(hAPP(c_Not,u),c_Arrow__Order__Mirabelle_OLin) ),
inference(rew,[status(thm),theory(equality)],[33314,31047]),
[iquote('1:Rew:33314.0,31047.1')] ).
cnf(33506,plain,
( hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,u))
| hBOOL(c_Not)
| hBOOL(v) ),
inference(rew,[status(thm),theory(equality)],[33483,33039]),
[iquote('1:Rew:33483.1,33039.0')] ).
cnf(33523,plain,
( hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,u))
| hBOOL(c_Not) ),
inference(con,[status(thm)],[33506]),
[iquote('1:Con:33506.2')] ).
cnf(33739,plain,
hBOOL(c_Not),
inference(spt,[spt(split,[position(s2s1)])],[33523]),
[iquote('2:Spt:33523.1')] ).
cnf(33751,plain,
equal(c_Arrow__Order__Mirabelle_OLin,c_Not),
inference(res,[status(thm),theory(equality)],[33739,33331]),
[iquote('2:Res:33739.0,33331.0')] ).
cnf(34029,plain,
( ~ c_lessequals(u,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| c_HOL_Oord__class_Oless(u,c_Set_Oinsert(v,c_Not,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[33751,819]),
[iquote('2:Rew:33751.0,819.1')] ).
cnf(40347,plain,
equal(hAPP(c_Not,hAPP(c_Not,u)),c_Not),
inference(rew,[status(thm),theory(equality)],[33751,33314]),
[iquote('2:Rew:33751.0,33314.0')] ).
cnf(40501,plain,
equal(u,c_Not),
inference(rew,[status(thm),theory(equality)],[2172,40347]),
[iquote('2:Rew:2172.0,40347.0')] ).
cnf(40514,plain,
( ~ hBOOL(c_Not)
| hBOOL(u) ),
inference(rew,[status(thm),theory(equality)],[40501,18439]),
[iquote('2:Rew:40501.0,18439.0')] ).
cnf(40671,plain,
( ~ hBOOL(hAPP(c_Not,u))
| c_lessequals(u,v,tc_fun(w,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[40501,5454]),
[iquote('2:Rew:40501.0,5454.0')] ).
cnf(46114,plain,
( ~ c_HOL_Oord__class_Oless(u,v,tc_fun(w,tc_bool))
| ~ c_lessequals(c_Not,u,tc_fun(w,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[40501,3862]),
[iquote('2:Rew:40501.0,3862.1')] ).
cnf(47194,plain,
hBOOL(u),
inference(mrr,[status(thm)],[40514,33739]),
[iquote('2:MRR:40514.0,33739.0')] ).
cnf(47555,plain,
c_lessequals(u,v,tc_fun(w,tc_bool)),
inference(mrr,[status(thm)],[40671,47194]),
[iquote('2:MRR:40671.0,47194.0')] ).
cnf(47844,plain,
~ c_HOL_Oord__class_Oless(u,v,tc_fun(w,tc_bool)),
inference(mrr,[status(thm)],[46114,47555]),
[iquote('2:MRR:46114.1,47555.0')] ).
cnf(48151,plain,
$false,
inference(mrr,[status(thm)],[34029,47555,47844]),
[iquote('2:MRR:34029.0,34029.1,47555.0,47844.0')] ).
cnf(48152,plain,
~ hBOOL(c_Not),
inference(spt,[spt(split,[position(s2sa)])],[48151,33739]),
[iquote('2:Spt:48151.0,33523.1,33739.0')] ).
cnf(48153,plain,
hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,u)),
inference(spt,[spt(split,[position(s2s2)])],[33523]),
[iquote('2:Spt:48151.0,33523.0')] ).
cnf(48182,plain,
equal(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,u),c_Arrow__Order__Mirabelle_OLin),
inference(res,[status(thm),theory(equality)],[48153,33331]),
[iquote('2:Res:48153.0,33331.0')] ).
cnf(48218,plain,
equal(hAPP(c_Arrow__Order__Mirabelle_OLin,u),hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin)),
inference(res,[status(thm),theory(equality)],[33313,799]),
[iquote('1:Res:33313.0,799.0')] ).
cnf(49703,plain,
( hBOOL(hAPP(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),u))
| equal(c_Set_OPow(u,v),c_Arrow__Order__Mirabelle_OLin) ),
inference(rew,[status(thm),theory(equality)],[48218,33474]),
[iquote('1:Rew:48218.0,33474.0')] ).
cnf(58592,plain,
equal(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin),c_Arrow__Order__Mirabelle_OLin),
inference(spr,[status(thm),theory(equality)],[48182,33352]),
[iquote('2:SpR:48182.0,33352.0')] ).
cnf(58593,plain,
equal(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),c_Arrow__Order__Mirabelle_OLin),
inference(rew,[status(thm),theory(equality)],[48218,58592]),
[iquote('2:Rew:48218.0,58592.0')] ).
cnf(58594,plain,
( hBOOL(u)
| equal(c_Arrow__Order__Mirabelle_OLin,u) ),
inference(rew,[status(thm),theory(equality)],[58593,33313]),
[iquote('2:Rew:58593.0,33313.1')] ).
cnf(58702,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,u))
| equal(c_Set_OPow(u,v),c_Arrow__Order__Mirabelle_OLin) ),
inference(rew,[status(thm),theory(equality)],[58593,49703]),
[iquote('2:Rew:58593.0,49703.0')] ).
cnf(60017,plain,
equal(c_Arrow__Order__Mirabelle_OLin,u),
inference(mrr,[status(thm)],[58594,33331]),
[iquote('2:MRR:58594.0,33331.0')] ).
cnf(61291,plain,
( ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,u,tc_fun(v,tc_bool))
| c_lessequals(w,u,tc_fun(v,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[60017,31601]),
[iquote('2:Rew:60017.0,31601.0')] ).
cnf(61430,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,u))
| hBOOL(hAPP(v,u)) ),
inference(rew,[status(thm),theory(equality)],[60017,8261]),
[iquote('2:Rew:60017.0,8261.0')] ).
cnf(61440,plain,
( ~ hBOOL(hAPP(u,v))
| c_lessequals(c_Arrow__Order__Mirabelle_OLin,v,tc_fun(w,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[60017,5453]),
[iquote('2:Rew:60017.0,5453.1')] ).
cnf(62270,plain,
( ~ c_lessequals(u,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(c_Arrow__Order__Mirabelle_OLin,tc_bool),tc_bool))
| c_HOL_Oord__class_Oless(u,c_Set_Oinsert(v,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[60017,819]),
[iquote('2:Rew:60017.0,819.0')] ).
cnf(62334,plain,
( ~ equal(c_Set_OPow(u,v),c_Arrow__Order__Mirabelle_OLin)
| hBOOL(w) ),
inference(rew,[status(thm),theory(equality)],[60017,13552]),
[iquote('2:Rew:60017.0,13552.0')] ).
cnf(62442,plain,
( ~ c_HOL_Oord__class_Oless(u,v,tc_fun(w,tc_bool))
| ~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,u,tc_fun(w,tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[60017,3862]),
[iquote('2:Rew:60017.0,3862.1')] ).
cnf(64225,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,u)),
inference(mrr,[status(thm)],[58702,62334]),
[iquote('2:MRR:58702.1,62334.0')] ).
cnf(64244,plain,
hBOOL(hAPP(u,v)),
inference(mrr,[status(thm)],[61430,64225]),
[iquote('2:MRR:61430.0,64225.0')] ).
cnf(64455,plain,
c_lessequals(c_Arrow__Order__Mirabelle_OLin,u,tc_fun(v,tc_bool)),
inference(mrr,[status(thm)],[61440,64244]),
[iquote('2:MRR:61440.0,64244.0')] ).
cnf(64712,plain,
c_lessequals(u,v,tc_fun(w,tc_bool)),
inference(mrr,[status(thm)],[61291,64455]),
[iquote('2:MRR:61291.0,64455.0')] ).
cnf(64943,plain,
~ c_HOL_Oord__class_Oless(u,v,tc_fun(w,tc_bool)),
inference(mrr,[status(thm)],[62442,64712]),
[iquote('2:MRR:62442.1,64712.0')] ).
cnf(65398,plain,
$false,
inference(mrr,[status(thm)],[62270,64712,64943]),
[iquote('2:MRR:62270.0,62270.1,64712.0,64943.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SCT006-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 01:14:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 73.88/74.08
% 73.88/74.08 SPASS V 3.9
% 73.88/74.08 SPASS beiseite: Proof found.
% 73.88/74.08 % SZS status Theorem
% 73.88/74.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.88/74.08 SPASS derived 57352 clauses, backtracked 13892 clauses, performed 3 splits and kept 30662 clauses.
% 73.88/74.08 SPASS allocated 134585 KBytes.
% 73.88/74.08 SPASS spent 0:1:13.66 on the problem.
% 73.88/74.08 0:00:00.06 for the input.
% 73.88/74.08 0:00:00.00 for the FLOTTER CNF translation.
% 73.88/74.08 0:00:00.34 for inferences.
% 73.88/74.08 0:00:08.00 for the backtracking.
% 73.88/74.08 0:01:05.04 for the reduction.
% 73.88/74.08
% 73.88/74.08
% 73.88/74.08 Here is a proof with depth 8, length 190 :
% 73.88/74.08 % SZS output start Refutation
% See solution above
% 75.37/75.53 Formulae used in the proof : cls_Int__lower2_0 cls_fun__upd__same_0 cls_COMBB__def_0 cls_order__trans_0 cls_insert__subset_0 cls_Sup__upper_0 cls_Collect__neg__eq_0 cls_vimage__Collect__eq_0 cls_PowD_0 cls_Inter__lower_0 cls_Int__absorb1_0 cls_less__supI2_0 cls_subset__iff_0 cls_psubset__insert__iff_3 cls_Collect__def_0 cls_Inf__insert_0 cls_COMBC__def_0 cls_COMBK__def_0 cls_diff__eq_0 cls_vimage__Compl_0 cls_inf1E_0 cls_double__complement_0 cls_Diff__empty_0 cls_psubset__eq_1 cls_less__infI1_0 cls_vimage__const_1 cls_empty__not__insert_0 cls_Union__Pow__eq_0 cls_singleton__conv2_0 cls_Collect__mem__eq_0 cls_ComplI_0 cls_ComplD_0 cls_bexE_1 cls_insert__absorb_0 cls_quotientE_1 cls_Pow__top_0 cls_mem__def_1 cls_mem__def_0 clsarity_fun__Complete__Lattice_Ocomplete__lattice clsarity_fun__Lattices_Oupper__semilattice clsarity_fun__Lattices_Olower__semilattice clsarity_fun__Lattices_Odistrib__lattice clsarity_fun__Lattices_Obounded__lattice clsarity_fun__Lattices_Oboolean__algebra clsarity_fun__Orderings_Opreorder clsarity_fun__Lattices_Olattice clsarity_fun__Orderings_Oorder clsarity_fun__Orderings_Obot clsarity_fun__HOL_Oord clsarity_bool__Complete__Lattice_Ocomplete__lattice clsarity_bool__Lattices_Oupper__semilattice clsarity_bool__Lattices_Olower__semilattice clsarity_bool__Lattices_Odistrib__lattice clsarity_bool__Lattices_Obounded__lattice clsarity_bool__Lattices_Oboolean__algebra clsarity_bool__Orderings_Opreorder clsarity_bool__Lattices_Olattice clsarity_bool__Orderings_Oorder clsarity_bool__Orderings_Obot clsarity_bool__HOL_Oord cls_conjecture_0
% 75.37/75.53
%------------------------------------------------------------------------------