TSTP Solution File: LCL801-1 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : LCL801-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:33:54 EDT 2023
% Result : Unsatisfiable 1301.11s 164.58s
% Output : CNFRefutation 1301.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 61
% Syntax : Number of clauses : 267 ( 148 unt; 31 nHn; 126 RR)
% Number of literals : 417 ( 171 equ; 156 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 8 con; 0-3 aty)
% Number of variables : 491 ( 171 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Collect__neg__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Collect__def_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_double__complement_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_COMBB__def_0) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_fun__Compl__def_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__HOL_Ouminus) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_id__apply_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_COMBK__def_0) ).
cnf(cls_Compl__partition_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Compl__partition_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Compl__empty__eq_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_top1I_0) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Collect__mem__eq_0) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_sup1E_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_compl__bot__eq_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_bot__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_Collect__imp__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Collect__imp__eq_0) ).
cnf(cls_le__bool__def__raw_0,axiom,
c_lessequals(tc_bool) = c_implies,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_le__bool__def__raw_0) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_double__compl_0) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_inf1I_0) ).
cnf(cls_Compl__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Compl__disjoint_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_bot1E_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_COMBC__def_0) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_compl__sup__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_compl__sup__top_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_inf__sup__aci_I5_J_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_COMBS__def_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Un__empty__right_0) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_insert__absorb_0) ).
cnf(cls_le__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_le__iff__inf_1) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_ComplD_0) ).
cnf(cls_sup__bot__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_sup__bot__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_le__iff__sup_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_le__iff__sup_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_inf__compl__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_inf__compl__bot_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_mem__def_1) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_sup__absorb1_0) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_uIT_0) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_insert__iff_1) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Var__IT_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_insert__code_1) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_dB_Osimps_I6_J_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_UNIV__I_0) ).
cnf(cls_Lambda_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Lambda_0) ).
cnf(cls_top__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_top__greatest_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_less__le__not__le_1) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_sup__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_sup__bot__right_0) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_exE__some_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_Int__UNIV__left_0) ).
cnf(cls_LeastI__ex_0,axiom,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X2,X1)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_LeastI__ex_0) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_COMBI__def_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_disjoint__iff__not__equal_0) ).
cnf(clsarity_nat__Orderings_Owellorder,axiom,
class_Orderings_Owellorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',clsarity_nat__Orderings_Owellorder) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
file('/export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p',cls_empty__not__insert_0) ).
cnf(c_0_61,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_62,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_63,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_64,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_62]) ).
cnf(c_0_65,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_66,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0 ).
cnf(c_0_68,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_69,plain,
hAPP(c_Not,hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(X2,X3),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,tc_bool)),X1),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_64]),c_0_65]) ).
cnf(c_0_72,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
cls_id__apply_0 ).
cnf(c_0_73,plain,
hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x))) = hAPP(X1,v_x),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
cls_COMBK__def_0 ).
cnf(c_0_75,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__partition_0 ).
cnf(c_0_76,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0 ).
cnf(c_0_77,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_78,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,plain,
hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_81,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
cls_sup1E_0 ).
cnf(c_0_82,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,plain,
hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
inference(rw,[status(thm)],[c_0_77,c_0_76]) ).
cnf(c_0_84,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_85,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_86,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_87,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_88,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
cls_Collect__imp__eq_0 ).
cnf(c_0_89,axiom,
c_lessequals(tc_bool) = c_implies,
cls_le__bool__def__raw_0 ).
cnf(c_0_90,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0 ).
cnf(c_0_91,plain,
hAPP(c_Not,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_inf1I_0 ).
cnf(c_0_93,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__disjoint_0 ).
cnf(c_0_94,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_95,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_96,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_80,c_0_62]) ).
cnf(c_0_97,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_98,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0 ).
cnf(c_0_99,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_100,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_101,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0 ).
cnf(c_0_102,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0 ).
cnf(c_0_103,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_104,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
cls_COMBS__def_0 ).
cnf(c_0_105,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_106,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_107,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X3) = hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_lessequals(tc_bool)),X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_108,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_85]) ).
cnf(c_0_109,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(X2,X3),
inference(rw,[status(thm)],[c_0_69,c_0_91]) ).
cnf(c_0_110,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_111,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_insert__absorb_0 ).
cnf(c_0_112,plain,
hAPP(X1,X2) = hAPP(hAPP(c_in(X3),X2),X1),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_113,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_64]),c_0_65]) ).
cnf(c_0_114,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_76]),c_0_100]) ).
cnf(c_0_115,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_85]),c_0_100]) ).
cnf(c_0_116,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_117,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_118,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_119,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplD_0 ).
cnf(c_0_120,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)))
| hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_97,c_0_70]) ).
cnf(c_0_121,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x) = hAPP(hAPP(X4,v_x),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_122,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_lessequals(tc_bool)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_123,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_124,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0 ).
cnf(c_0_125,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)))
| ~ hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_110,c_0_70]) ).
cnf(c_0_127,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_128,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_72]) ).
cnf(c_0_129,plain,
hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_83,c_0_114]) ).
cnf(c_0_130,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_131,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__iff__sup_0 ).
cnf(c_0_132,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) != X1 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_133,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_134,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0 ).
cnf(c_0_135,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_119,c_0_112]) ).
cnf(c_0_136,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_137,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_74]) ).
cnf(c_0_138,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_sup__absorb1_0 ).
cnf(c_0_139,plain,
hAPP(hAPP(c_lessequals(tc_bool),hAPP(X1,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]),c_0_65]) ).
cnf(c_0_140,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_141,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_74]) ).
cnf(c_0_142,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Not) = c_Not
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_143,plain,
hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_144,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = X2
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133])]) ).
cnf(c_0_145,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_134,c_0_85]) ).
cnf(c_0_146,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Not,hAPP(X3,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_64]),c_0_65]) ).
cnf(c_0_147,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ouminus__class_Ouminus(tc_bool)))
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_148,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
cls_uIT_0 ).
cnf(c_0_149,plain,
( hAPP(X1,v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]),c_0_133])]) ).
cnf(c_0_150,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
cls_insert__iff_1 ).
cnf(c_0_151,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
cls_Var__IT_0 ).
cnf(c_0_152,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2)),c_Not) = c_Not
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_153,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| c_Orderings_Obot__class_Obot(tc_bool) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_154,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_155,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_u____),c_InductTermi_OIT)),
inference(spm,[status(thm)],[c_0_136,c_0_148]) ).
cnf(c_0_156,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_149,c_0_74]) ).
cnf(c_0_157,plain,
~ hBOOL(hAPP(c_Not,hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2))),
inference(spm,[status(thm)],[c_0_146,c_0_150]) ).
cnf(c_0_158,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Lambda_OdB_OVar(X2)),c_InductTermi_OIT) = c_InductTermi_OIT,
inference(spm,[status(thm)],[c_0_127,c_0_151]) ).
cnf(c_0_159,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
cls_insert__code_1 ).
cnf(c_0_160,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Not) = c_Not
| c_Orderings_Obot__class_Obot(tc_bool) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_108]) ).
cnf(c_0_161,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_154,c_0_108]) ).
cnf(c_0_162,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_InductTermi_OIT),hAPP(c_in(X2),v_u____))),
inference(spm,[status(thm)],[c_0_136,c_0_155]) ).
cnf(c_0_163,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_137]) ).
cnf(c_0_164,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1)))),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_165,plain,
( hBOOL(hAPP(c_Not,X1))
| c_Orderings_Obot__class_Obot(tc_bool) != X1 ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_166,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Not,X1)))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_161,c_0_78]) ).
cnf(c_0_167,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_InductTermi_OIT,v_u____))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_162]),c_0_112]) ).
cnf(c_0_168,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
cls_dB_Osimps_I6_J_0 ).
cnf(c_0_169,plain,
( X1 = X2
| hBOOL(X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_163]) ).
cnf(c_0_170,plain,
hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_171,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_166]),c_0_91]) ).
cnf(c_0_172,plain,
hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_Not,hAPP(c_InductTermi_OIT,v_u____))),c_Not) = c_Not,
inference(spm,[status(thm)],[c_0_167,c_0_142]) ).
cnf(c_0_173,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_UNIV__I_0 ).
cnf(c_0_174,plain,
( hBOOL(c_Lambda_OdB_OAbs(X1))
| hBOOL(X2)
| X2 != c_Lambda_OdB_OVar(X3) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_175,plain,
( hBOOL(c_InductTermi_OIT)
| hBOOL(X1)
| hAPP(X1,c_Lambda_OdB_OVar(X2)) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_170,c_0_169]) ).
cnf(c_0_176,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_171,c_0_163]) ).
cnf(c_0_177,plain,
hBOOL(hAPP(c_Not,hAPP(c_Not,hAPP(c_InductTermi_OIT,v_u____)))),
inference(spm,[status(thm)],[c_0_159,c_0_172]) ).
cnf(c_0_178,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))),
inference(rw,[status(thm)],[c_0_173,c_0_76]) ).
cnf(c_0_179,plain,
( hBOOL(c_Lambda_OdB_OVar(X1))
| hBOOL(c_Lambda_OdB_OAbs(X2)) ),
inference(er,[status(thm)],[c_0_174]) ).
cnf(c_0_180,plain,
( c_Lambda_OdB_OVar(X1) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_InductTermi_OIT) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_181,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_94,c_0_105]) ).
cnf(c_0_182,plain,
hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Not,hAPP(c_InductTermi_OIT,v_u____)))),
inference(spm,[status(thm)],[c_0_161,c_0_177]) ).
cnf(c_0_183,plain,
~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2))),
inference(spm,[status(thm)],[c_0_146,c_0_178]) ).
cnf(c_0_184,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(X1)
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_169]) ).
cnf(c_0_185,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
cls_Lambda_0 ).
cnf(c_0_186,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_Lambda_OdB_OAbs(X1))
| hBOOL(c_InductTermi_OIT) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).
cnf(c_0_187,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_InductTermi_OIT,v_u____)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_182]),c_0_91]) ).
cnf(c_0_188,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))),
inference(spm,[status(thm)],[c_0_183,c_0_114]) ).
cnf(c_0_189,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_190,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_InductTermi_OIT)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).
cnf(c_0_191,plain,
hAPP(c_InductTermi_OIT,v_u____) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_108,c_0_187]) ).
cnf(c_0_192,plain,
~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)))),
inference(spm,[status(thm)],[c_0_188,c_0_130]) ).
cnf(c_0_193,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_less__le__not__le_1 ).
cnf(c_0_194,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_99]),c_0_100]) ).
cnf(c_0_195,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_196,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_compl__eq__compl__iff_0 ).
cnf(c_0_197,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_InductTermi_OIT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_129])]) ).
cnf(c_0_198,plain,
( c_Orderings_Obot__class_Obot(tc_bool) != X1
| ~ hBOOL(hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_144]),c_0_145]) ).
cnf(c_0_199,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_64]),c_0_65]) ).
cnf(c_0_200,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_195])]) ).
cnf(c_0_201,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_202,plain,
( X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2) ),
inference(spm,[status(thm)],[c_0_196,c_0_85]) ).
cnf(c_0_203,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_InductTermi_OIT) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_171,c_0_197]) ).
cnf(c_0_204,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_198,c_0_108]) ).
cnf(c_0_205,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_199,c_0_105]) ).
cnf(c_0_206,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))),X2)),
inference(spm,[status(thm)],[c_0_200,c_0_130]) ).
cnf(c_0_207,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_201,c_0_125]) ).
cnf(c_0_208,plain,
( c_InductTermi_OIT = X1
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_209,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_InductTermi_OIT),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_203]),c_0_207]) ).
cnf(c_0_211,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_InductTermi_OIT = X1
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_208,c_0_176]) ).
cnf(c_0_212,plain,
( hBOOL(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != X1 ),
inference(spm,[status(thm)],[c_0_209,c_0_163]) ).
cnf(c_0_213,plain,
( hAPP(c_HOL_Oord__class_Oless(tc_bool),c_InductTermi_OIT) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_214,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != X1 ),
inference(spm,[status(thm)],[c_0_212,c_0_108]) ).
cnf(c_0_215,plain,
( hAPP(c_HOL_Oord__class_Oless(tc_bool),c_InductTermi_OIT) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_191]),c_0_129])]) ).
cnf(c_0_216,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_214]),c_0_212]) ).
cnf(c_0_217,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_210,c_0_215]) ).
cnf(c_0_218,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(X1)
| hAPP(X1,X2) != X2 ),
inference(spm,[status(thm)],[c_0_216,c_0_169]) ).
cnf(c_0_219,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_211]),c_0_197]) ).
cnf(c_0_220,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| c_Orderings_Obot__class_Obot(tc_bool) != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_181]) ).
cnf(c_0_221,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_222,plain,
hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)),
inference(er,[status(thm)],[c_0_220]) ).
cnf(c_0_223,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
cls_Int__UNIV__left_0 ).
cnf(c_0_224,plain,
hAPP(hAPP(c_in(X1),X2),c_Fun_Oid(X3)) = X2,
inference(spm,[status(thm)],[c_0_72,c_0_112]) ).
cnf(c_0_225,axiom,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X2,X1)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
cls_LeastI__ex_0 ).
cnf(c_0_226,plain,
hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1))),
inference(spm,[status(thm)],[c_0_221,c_0_199]) ).
cnf(c_0_227,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_228,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_HOL_Ouminus__class_Ouminus(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_171,c_0_222]) ).
cnf(c_0_229,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_230,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X2) = X2,
inference(rw,[status(thm)],[c_0_223,c_0_76]) ).
cnf(c_0_231,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_224]),c_0_72]) ).
cnf(c_0_232,plain,
( hBOOL(hAPP(c_Not,c_Orderings_Oord__class_OLeast(c_Not,X1)))
| ~ class_Orderings_Owellorder(X1) ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_233,plain,
hAPP(hAPP(c_in(X1),X2),c_COMBI(X3)) = X2,
inference(spm,[status(thm)],[c_0_227,c_0_112]) ).
cnf(c_0_234,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(spm,[status(thm)],[c_0_108,c_0_228]) ).
cnf(c_0_235,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_178]),c_0_230]) ).
cnf(c_0_236,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_Orderings_Obot__class_Obot(tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_bool))),
inference(spm,[status(thm)],[c_0_136,c_0_129]) ).
cnf(c_0_237,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4))),
inference(spm,[status(thm)],[c_0_136,c_0_159]) ).
cnf(c_0_238,plain,
( ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(c_Orderings_Oord__class_OLeast(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_239,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_COMBI(X3)) = c_COMBI(X3)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_233]) ).
cnf(c_0_240,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(rw,[status(thm)],[c_0_130,c_0_234]) ).
cnf(c_0_241,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_242,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_93,c_0_64]) ).
cnf(c_0_243,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Not))
| c_Orderings_Obot__class_Obot(tc_bool) != X2 ),
inference(spm,[status(thm)],[c_0_237,c_0_160]) ).
cnf(c_0_244,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Not))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_231,c_0_112]) ).
cnf(c_0_245,plain,
( c_Orderings_Oord__class_OLeast(c_Not,X1) = X2
| hBOOL(X2)
| ~ class_Orderings_Owellorder(X1) ),
inference(spm,[status(thm)],[c_0_238,c_0_169]) ).
cnf(c_0_246,axiom,
class_Orderings_Owellorder(tc_nat),
clsarity_nat__Orderings_Owellorder ).
cnf(c_0_247,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
cls_empty__not__insert_0 ).
cnf(c_0_248,plain,
hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_InductTermi_OIT,v_u____)),c_COMBI(X2)) = c_COMBI(X2),
inference(spm,[status(thm)],[c_0_239,c_0_148]) ).
cnf(c_0_249,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| X1 = c_HOL_Ouminus__class_Ouminus(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_176]),c_0_207]) ).
cnf(c_0_250,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) != c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_251,plain,
( hBOOL(hAPP(hAPP(hAPP(c_in(X1),X2),c_in(X3)),c_Not))
| c_Orderings_Obot__class_Obot(tc_bool) != X2 ),
inference(spm,[status(thm)],[c_0_243,c_0_112]) ).
cnf(c_0_252,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),hAPP(c_in(X5),X6)),c_COMBI(X7)) = hAPP(hAPP(X4,c_COMBI(X7)),X6),
inference(spm,[status(thm)],[c_0_104,c_0_233]) ).
cnf(c_0_253,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_in(X1),X2),c_in(X3)),c_Not))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_244,c_0_112]) ).
cnf(c_0_254,plain,
hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),c_COMBI(X2)) = c_COMBI(X2),
inference(spm,[status(thm)],[c_0_239,c_0_205]) ).
cnf(c_0_255,plain,
( c_Orderings_Oord__class_OLeast(c_Not,tc_nat) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_256,plain,
c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
cnf(c_0_257,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),X6)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))) = hAPP(hAPP(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))),X6),
inference(spm,[status(thm)],[c_0_104,c_0_106]) ).
cnf(c_0_258,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_249]),c_0_250]) ).
cnf(c_0_259,plain,
c_COMBI(X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_249]),c_0_216]) ).
cnf(c_0_260,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_in(X1)),hAPP(c_in(X7),c_in(X3))),c_COMBI(X2)),c_Not))
| c_COMBI(X2) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_261,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_in(X1)),hAPP(c_in(X7),c_in(X3))),c_COMBI(X2)),c_Not))
| ~ hBOOL(c_COMBI(X2)) ),
inference(spm,[status(thm)],[c_0_253,c_0_252]) ).
cnf(c_0_262,plain,
( c_Orderings_Oord__class_OLeast(c_Not,tc_nat) = c_COMBI(X2)
| hBOOL(c_COMBI(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_254]) ).
cnf(c_0_263,plain,
( hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| c_COMBI(X1) != c_Orderings_Oord__class_OLeast(c_Not,tc_nat) ),
inference(spm,[status(thm)],[c_0_256,c_0_255]) ).
cnf(c_0_264,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_in(X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_in(X3))),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Not))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_251,c_0_257]) ).
cnf(c_0_265,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_in(X1)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_in(X3))),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Not))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(spm,[status(thm)],[c_0_253,c_0_257]) ).
cnf(c_0_266,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_258,c_0_259,c_0_260,c_0_261,c_0_262,c_0_263,c_0_264,c_0_265]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : LCL801-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 2400
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Oct 2 12:53:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.44/0.62 Running first-order model finding
% 0.44/0.62 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.nTXwPf8Wfj/E---3.1_5047.p
% 1301.11/164.58 # Version: 3.1pre001
% 1301.11/164.58 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1301.11/164.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1301.11/164.58 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1301.11/164.58 # Starting new_bool_3 with 600s (2) cores
% 1301.11/164.58 # Starting new_bool_1 with 300s (1) cores
% 1301.11/164.58 # Starting sh5l with 300s (1) cores
% 1301.11/164.58 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 5124 completed with status 0
% 1301.11/164.58 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 1301.11/164.58 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1301.11/164.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1301.11/164.58 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1301.11/164.58 # No SInE strategy applied
% 1301.11/164.58 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1301.11/164.58 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 1301.11/164.58 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 1301.11/164.58 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 1301.11/164.58 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 1301.11/164.58 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1301.11/164.58 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 5133 completed with status 7
% 1301.11/164.58 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 90s (1) cores
% 1301.11/164.58 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 5134 completed with status 7
% 1301.11/164.58 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 90s (1) cores
% 1301.11/164.58 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 5131 completed with status 7
% 1301.11/164.58 # Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1301.11/164.58 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 5132 completed with status 7
% 1301.11/164.58 # Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1301.11/164.58 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 5875 completed with status 0
% 1301.11/164.58 # Result found by G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y
% 1301.11/164.58 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1301.11/164.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1301.11/164.58 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1301.11/164.58 # No SInE strategy applied
% 1301.11/164.58 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1301.11/164.58 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 1301.11/164.58 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 1301.11/164.58 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 1301.11/164.58 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 1301.11/164.58 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1301.11/164.58 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 5133 completed with status 7
% 1301.11/164.58 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 90s (1) cores
% 1301.11/164.58 # Preprocessing time : 0.013 s
% 1301.11/164.58 # Presaturation interreduction done
% 1301.11/164.58 # SatCheck found unsatisfiable ground set
% 1301.11/164.58
% 1301.11/164.58 # Proof found!
% 1301.11/164.58 # SZS status Unsatisfiable
% 1301.11/164.58 # SZS output start CNFRefutation
% See solution above
% 1301.11/164.58 # Parsed axioms : 796
% 1301.11/164.58 # Removed by relevancy pruning/SinE : 0
% 1301.11/164.58 # Initial clauses : 796
% 1301.11/164.58 # Removed in clause preprocessing : 0
% 1301.11/164.58 # Initial clauses in saturation : 796
% 1301.11/164.58 # Processed clauses : 40365
% 1301.11/164.58 # ...of these trivial : 584
% 1301.11/164.58 # ...subsumed : 29781
% 1301.11/164.58 # ...remaining for further processing : 10000
% 1301.11/164.58 # Other redundant clauses eliminated : 400
% 1301.11/164.58 # Clauses deleted for lack of memory : 0
% 1301.11/164.58 # Backward-subsumed : 1070
% 1301.11/164.58 # Backward-rewritten : 1057
% 1301.11/164.58 # Generated clauses : 1822294
% 1301.11/164.58 # ...of the previous two non-redundant : 1788177
% 1301.11/164.58 # ...aggressively subsumed : 0
% 1301.11/164.58 # Contextual simplify-reflections : 63
% 1301.11/164.58 # Paramodulations : 1821703
% 1301.11/164.58 # Factorizations : 18
% 1301.11/164.58 # NegExts : 0
% 1301.11/164.58 # Equation resolutions : 573
% 1301.11/164.58 # Total rewrite steps : 325982
% 1301.11/164.58 # Propositional unsat checks : 2
% 1301.11/164.58 # Propositional check models : 0
% 1301.11/164.58 # Propositional check unsatisfiable : 1
% 1301.11/164.58 # Propositional clauses : 1744076
% 1301.11/164.58 # Propositional clauses after purity: 58944
% 1301.11/164.58 # Propositional unsat core size : 8
% 1301.11/164.58 # Propositional preprocessing time : 0.000
% 1301.11/164.58 # Propositional encoding time : 11.859
% 1301.11/164.58 # Propositional solver time : 0.582
% 1301.11/164.58 # Success case prop preproc time : 0.000
% 1301.11/164.58 # Success case prop encoding time : 11.298
% 1301.11/164.58 # Success case prop solver time : 0.334
% 1301.11/164.58 # Current number of processed clauses : 7234
% 1301.11/164.58 # Positive orientable unit clauses : 1113
% 1301.11/164.58 # Positive unorientable unit clauses: 324
% 1301.11/164.58 # Negative unit clauses : 1202
% 1301.11/164.58 # Non-unit-clauses : 4595
% 1301.11/164.58 # Current number of unprocessed clauses: 1736842
% 1301.11/164.58 # ...number of literals in the above : 3566329
% 1301.11/164.58 # Current number of archived formulas : 0
% 1301.11/164.58 # Current number of archived clauses : 2766
% 1301.11/164.58 # Clause-clause subsumption calls (NU) : 2499441
% 1301.11/164.58 # Rec. Clause-clause subsumption calls : 1444863
% 1301.11/164.58 # Non-unit clause-clause subsumptions : 14035
% 1301.11/164.58 # Unit Clause-clause subsumption calls : 365855
% 1301.11/164.58 # Rewrite failures with RHS unbound : 378297
% 1301.11/164.58 # BW rewrite match attempts : 459283
% 1301.11/164.58 # BW rewrite match successes : 118537
% 1301.11/164.58 # Condensation attempts : 0
% 1301.11/164.58 # Condensation successes : 0
% 1301.11/164.58 # Termbank termtop insertions : 104261644
% 1301.11/164.58
% 1301.11/164.58 # -------------------------------------------------
% 1301.11/164.58 # User time : 455.832 s
% 1301.11/164.58 # System time : 8.754 s
% 1301.11/164.58 # Total time : 464.586 s
% 1301.11/164.58 # Maximum resident set size: 3608 pages
% 1301.11/164.58
% 1301.11/164.58 # -------------------------------------------------
% 1301.11/164.58 # User time : 637.084 s
% 1301.11/164.58 # System time : 12.776 s
% 1301.11/164.58 # Total time : 649.860 s
% 1301.11/164.58 # Maximum resident set size: 2536 pages
% 1301.11/164.58 % E---3.1 exiting
%------------------------------------------------------------------------------