%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT084-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:07:41 PM UTC 2026
% Result : Unsatisfiable 40.91s 21.68s
% Output : CNFRefutation 40.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of clauses : 161 ( 75 unt; 20 nHn; 80 RR)
% Number of literals : 260 ( 93 equ; 105 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-5 aty)
% Number of variables : 347 ( 156 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_UNIV__eq__I_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)),X2))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_fun__Compl__def_0,axiom,
( ~ class_HOL_Ouminus(X1)
| 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(cls_bex__UNIV_2,axiom,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
cnf(cls_ComplI_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/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
cnf(cls_bex__UNIV_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))))
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_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/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_compl__top__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__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/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_insert__absorb_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_insert__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(c_0_29,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)),X2))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_UNIV__eq__I_0]) ).
cnf(c_0_30,plain,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_31,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_top__fun__eq_0]) ).
cnf(c_0_32,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)),X2))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
c_0_29 ).
cnf(c_0_33,plain,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_30 ).
cnf(c_0_34,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
c_0_31 ).
cnf(c_0_35,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_36,plain,
( ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_38,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_41,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_0]) ).
cnf(c_0_42,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ hBOOL(X2)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_44,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
c_0_41 ).
cnf(c_0_45,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
cls_CHAINED_0 ).
cnf(c_0_46,plain,
( ~ hBOOL(X1)
| X1 = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40]) ).
cnf(c_0_47,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
cls_CHAINED_0_01 ).
cnf(c_0_50,plain,
( ~ class_HOL_Ouminus(X1)
| 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)) ),
inference(fof_simplification,[status(thm)],[cls_fun__Compl__def_0]) ).
cnf(c_0_51,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
inference(fof_simplification,[status(thm)],[cls_bex__UNIV_2]) ).
cnf(c_0_52,plain,
( ~ hBOOL(X1)
| X1 = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) ),
inference(rw,[status(thm)],[c_0_46,c_0_48]) ).
cnf(c_0_53,plain,
hBOOL(hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_44,c_0_49]) ).
cnf(c_0_54,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_ComplI_0 ).
cnf(c_0_55,plain,
( ~ class_HOL_Ouminus(X1)
| 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)) ),
c_0_50 ).
cnf(c_0_56,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_57,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))))
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2))) ),
inference(fof_simplification,[status(thm)],[cls_bex__UNIV_0]) ).
cnf(c_0_58,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
c_0_51 ).
cnf(c_0_59,plain,
hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ComplD_0]) ).
cnf(c_0_61,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_44,c_0_54]) ).
cnf(c_0_62,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_55,c_0_56]) ).
cnf(c_0_63,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))))
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2))) ),
c_0_57 ).
cnf(c_0_64,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_65,plain,
hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_Lab____,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_47])]) ).
cnf(c_0_66,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_60 ).
cnf(c_0_67,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)))
| hBOOL(hAPP(hAPP(c_in(t_a),v_x),X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_compl__top__eq_0]) ).
cnf(c_0_69,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_70,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_71,plain,
hAPP(v_Lab____,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_Lab____,X1)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
cnf(c_0_72,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_66,c_0_33]) ).
cnf(c_0_73,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_74,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_double__compl_0]) ).
cnf(c_0_75,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_COMBK(X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_67,c_0_40]) ).
cnf(c_0_76,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1) ),
c_0_68 ).
cnf(c_0_77,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_78,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Arrow__Order__Mirabelle_OLin,X1))),
inference(spm,[status(thm)],[c_0_58,c_0_47]) ).
cnf(c_0_79,plain,
( ~ hBOOL(hAPP(hAPP(X1,X7),X5))
| hBOOL(hAPP(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6)),X5)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_69]),c_0_69]) ).
cnf(c_0_80,plain,
( ~ hBOOL(hAPP(X3,X2))
| hAPP(hAPP(c_in(X1),X2),X3) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) ),
inference(spm,[status(thm)],[c_0_52,c_0_33]) ).
cnf(c_0_81,plain,
hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(v_Lab____,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_47])]) ).
cnf(c_0_82,plain,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
c_0_74 ).
cnf(c_0_84,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_75]),c_0_40]) ).
cnf(c_0_85,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Arrow__Order__Mirabelle_OLin,X1)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_78]) ).
cnf(c_0_87,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_insert__absorb_0]) ).
cnf(c_0_88,plain,
( ~ hBOOL(hAPP(X5,X7))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(c_in(X1),X2,X3,X4),X5),X6)),X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_47])]) ).
cnf(c_0_89,plain,
hAPP(v_Lab____,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(v_Lab____,X1)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_81]) ).
cnf(c_0_90,plain,
( ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_33]) ).
cnf(c_0_91,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_83,c_0_77]) ).
cnf(c_0_92,plain,
( hBOOL(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) ),
inference(spm,[status(thm)],[c_0_52,c_0_84]) ).
cnf(c_0_93,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[c_0_85,c_0_48]) ).
cnf(c_0_94,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_95,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Arrow__Order__Mirabelle_OLin,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_86]),c_0_47])]) ).
cnf(c_0_96,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(fof_simplification,[status(thm)],[cls_empty__not__insert_0]) ).
cnf(c_0_97,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
c_0_87 ).
cnf(c_0_98,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(c_in(X1),X2,X3,X4),v_Lab____),X5)),v_Lab____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_47])]) ).
cnf(c_0_99,plain,
( ~ hBOOL(hAPP(X1,v_x))
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x))) ),
inference(spm,[status(thm)],[c_0_90,c_0_62]) ).
cnf(c_0_100,plain,
( hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_101,plain,
( ~ hBOOL(hAPP(X1,hAPP(X2,X7)))
| hBOOL(hAPP(X1,hAPP(X2,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_COMBB(X1,X2,X3,X4,X5),X6)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_94]),c_0_94]) ).
cnf(c_0_102,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Arrow__Order__Mirabelle_OLin,X1)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_95]) ).
cnf(c_0_103,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
c_0_96 ).
cnf(c_0_104,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(c_in(X1),X2,X3,X4),v_Lab____),X5)),v_Lab____) = v_Lab____,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_99,c_0_40]) ).
cnf(c_0_106,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_100,c_0_100]) ).
cnf(c_0_107,plain,
( ~ hBOOL(X3)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = X3 ),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_108,plain,
( ~ hBOOL(hAPP(X1,hAPP(X2,X7)))
| hBOOL(hAPP(X1,hAPP(X2,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_COMBB(X1,X2,X3,X4,X5),X6)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_94]),c_0_94]) ).
cnf(c_0_109,plain,
( ~ hBOOL(X6)
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2,X3,X4),X5)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_73]),c_0_73]) ).
cnf(c_0_110,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(c_in(X1),X2,X3,X4),c_Arrow__Order__Mirabelle_OLin),X5)),c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_102]),c_0_47])]) ).
cnf(c_0_111,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X4)
| c_COMBK(X1,X2,X3) = c_COMBK(X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_43,c_0_43]) ).
cnf(c_0_112,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != v_Lab____,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_113,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(X1)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_107,c_0_47]) ).
cnf(c_0_115,plain,
( ~ hBOOL(X6)
| hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2,X3,X4),X5)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_73]),c_0_73]) ).
cnf(c_0_116,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2,X3,X4),X5)),
inference(spm,[status(thm)],[c_0_109,c_0_47]) ).
cnf(c_0_117,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(fof_simplification,[status(thm)],[cls_UNIV__not__empty_0]) ).
cnf(c_0_118,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5) ),
inference(fof_simplification,[status(thm)],[cls_insert__image_0]) ).
cnf(c_0_119,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_compl__bot__eq_0]) ).
cnf(c_0_120,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_COMBC(c_in(X1),X2,X3,X4),c_Arrow__Order__Mirabelle_OLin),X5)),c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_97,c_0_110]) ).
cnf(c_0_121,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_111]),c_0_40]) ).
cnf(c_0_122,plain,
( hBOOL(v_Lab____)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_106])]) ).
cnf(c_0_123,plain,
( ~ hBOOL(X2)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_47])]) ).
cnf(c_0_124,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2,X3,X4),X5)),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_125,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_117 ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5) ),
c_0_118 ).
cnf(c_0_127,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1) ),
c_0_119 ).
cnf(c_0_128,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_103,c_0_120]) ).
cnf(c_0_129,plain,
( ~ hBOOL(X1)
| hBOOL(v_Lab____)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_125,c_0_39]) ).
cnf(c_0_132,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_103,c_0_126]) ).
cnf(c_0_133,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_127,c_0_77]) ).
cnf(c_0_134,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_106])]) ).
cnf(c_0_135,plain,
( hBOOL(v_Lab____)
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_136,plain,
( ~ hBOOL(hAPP(X4,X5))
| hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_80]),c_0_47])]) ).
cnf(c_0_137,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(rw,[status(thm)],[c_0_133,c_0_48]) ).
cnf(c_0_138,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) ),
inference(spm,[status(thm)],[c_0_52,c_0_134]) ).
cnf(c_0_139,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
cls_empty__is__image_1 ).
cnf(c_0_140,plain,
( hBOOL(v_Lab____)
| c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_129,c_0_135]) ).
cnf(c_0_141,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ouminus__class_Ouminus(tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_47])]) ).
cnf(c_0_142,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) != v_Lab____
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_112,c_0_138]) ).
cnf(c_0_143,plain,
hBOOL(v_Lab____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]) ).
cnf(c_0_144,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(fof_simplification,[status(thm)],[cls_Lin__irrefl_0]) ).
cnf(c_0_145,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))),
inference(spm,[status(thm)],[c_0_64,c_0_39]) ).
cnf(c_0_146,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) != v_Lab____
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) = c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_52,c_0_142]) ).
cnf(c_0_147,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) = v_Lab____,
inference(spm,[status(thm)],[c_0_52,c_0_143]) ).
cnf(c_0_148,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_144 ).
cnf(c_0_149,plain,
hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_52,c_0_145]) ).
cnf(c_0_150,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) ),
inference(spm,[status(thm)],[c_0_52,c_0_100]) ).
cnf(c_0_151,plain,
v_Lab____ = c_Arrow__Order__Mirabelle_OLin,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_147])]) ).
cnf(c_0_152,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_47]),c_0_149]),c_0_47])]) ).
cnf(c_0_153,plain,
( X1 = c_Arrow__Order__Mirabelle_OLin
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_147]),c_0_151]) ).
cnf(c_0_154,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_80]),c_0_47])]) ).
cnf(c_0_155,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_153]),c_0_128]) ).
cnf(c_0_156,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_154,c_0_100]) ).
cnf(c_0_157,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_155,c_0_153]) ).
cnf(c_0_158,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_151]),c_0_151]) ).
cnf(c_0_159,plain,
c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OLin,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_153]),c_0_128]) ).
cnf(c_0_160,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_159]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT084-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/15.43 % Computer : n015.cluster.edu
% 0.14/15.43 % Model : x86_64 x86_64
% 0.14/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/15.43 % Memory : 8046.5625MB
% 0.14/15.43 % OS : Linux 6.8.0-71-generic
% 0.14/15.43 % CPULimit : 300
% 0.14/15.43 % WCLimit : 300
% 0.14/15.43 % DateTime : Mon Sep 21 04:33:37 UTC 2026
% 0.14/15.43 % CPUTime :
% 0.14/15.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/15.50 Running first-order theorem proving
% 0.18/15.50 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.91/21.68 % Version: 3.5.1
% 40.91/21.68 % Preprocessing class: FSLMSMSMSSSNFFN.
% 40.91/21.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.91/21.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 40.91/21.68 % Starting new_bool_3 with 600s (2) cores
% 40.91/21.68 % Starting new_bool_1 with 300s (1) cores
% 40.91/21.68 % Starting sh5l with 300s (1) cores
% 40.91/21.68 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 560569 completed with status 0
% 40.91/21.68 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 40.91/21.68 % Preprocessing class: FSLMSMSMSSSNFFN.
% 40.91/21.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.91/21.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 40.91/21.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 40.91/21.68 % No SInE strategy applied
% 40.91/21.68 % Search class: FGHSM-FSLM32-DFFFFFNN
% 40.91/21.68 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 40.91/21.68 % Starting SubtermCWHack with 109s (1) cores
% 40.91/21.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 40.91/21.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 40.91/21.68 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 40.91/21.68 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 560579 completed with status 0
% 40.91/21.68 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 40.91/21.68 % Preprocessing class: FSLMSMSMSSSNFFN.
% 40.91/21.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 40.91/21.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 40.91/21.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 40.91/21.68 % No SInE strategy applied
% 40.91/21.68 % Search class: FGHSM-FSLM32-DFFFFFNN
% 40.91/21.68 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 40.91/21.68 % Starting SubtermCWHack with 109s (1) cores
% 40.91/21.68 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 40.91/21.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 40.91/21.68 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 40.91/21.68 % Preprocessing time : 0.021 s
% 40.91/21.68 % Presaturation interreduction done
% 40.91/21.68
% 40.91/21.68 % Proof found!
% 40.91/21.68 % SZS status Unsatisfiable
% 40.91/21.68 % SZS output start CNFRefutation
% See solution above
% 40.91/21.68 % Parsed axioms : 772
% 40.91/21.68 % Removed by relevancy pruning/SinE : 0
% 40.91/21.68 % Initial clauses : 772
% 40.91/21.68 % Removed in clause preprocessing : 0
% 40.91/21.68 % Initial clauses in saturation : 772
% 40.91/21.68 % Processed clauses : 7471
% 40.91/21.68 % ...of these trivial : 276
% 40.91/21.68 % ...subsumed : 4233
% 40.91/21.68 % ...remaining for further processing : 2962
% 40.91/21.68 % Other redundant clauses eliminated : 1240
% 40.91/21.68 % Clauses deleted for lack of memory : 0
% 40.91/21.68 % Backward-subsumed : 87
% 40.91/21.68 % Backward-rewritten : 636
% 40.91/21.68 % Generated clauses : 151508
% 40.91/21.68 % ...of the previous two non-redundant : 141814
% 40.91/21.68 % ...aggressively subsumed : 0
% 40.91/21.68 % Contextual simplify-reflections : 6
% 40.91/21.68 % Paramodulations : 150245
% 40.91/21.68 % Factorizations : 12
% 40.91/21.68 % NegExts : 0
% 40.91/21.68 % Equation resolutions : 1251
% 40.91/21.68 % Disequality decompositions : 0
% 40.91/21.68 % Total rewrite steps : 21496
% 40.91/21.68 % ...of those cached : 18186
% 40.91/21.68 % Propositional unsat checks : 0
% 40.91/21.68 % Propositional check models : 0
% 40.91/21.68 % Propositional check unsatisfiable : 0
% 40.91/21.68 % Propositional clauses : 0
% 40.91/21.68 % Propositional clauses after purity: 0
% 40.91/21.68 % Propositional unsat core size : 0
% 40.91/21.68 % Propositional preprocessing time : 0.000
% 40.91/21.68 % Propositional encoding time : 0.000
% 40.91/21.68 % Propositional solver time : 0.000
% 40.91/21.68 % Success case prop preproc time : 0.000
% 40.91/21.68 % Success case prop encoding time : 0.000
% 40.91/21.68 % Success case prop solver time : 0.000
% 40.91/21.68 % Current number of processed clauses : 1618
% 40.91/21.68 % Positive orientable unit clauses : 343
% 40.91/21.68 % Positive unorientable unit clauses: 14
% 40.91/21.68 % Negative unit clauses : 99
% 40.91/21.68 % Non-unit-clauses : 1162
% 40.91/21.68 % Current number of unprocessed clauses: 133212
% 40.91/21.68 % ...number of literals in the above : 400176
% 40.91/21.68 % Current number of archived formulas : 0
% 40.91/21.68 % Current number of archived clauses : 1344
% 40.91/21.68 % Clause-clause subsumption calls (NU) : 588702
% 40.91/21.68 % Rec. Clause-clause subsumption calls : 263811
% 40.91/21.68 % Non-unit clause-clause subsumptions : 3427
% 40.91/21.68 % Unit Clause-clause subsumption calls : 20317
% 40.91/21.68 % Rewrite failures with RHS unbound : 415
% 40.91/21.68 % BW rewrite match attempts : 2615
% 40.91/21.68 % BW rewrite match successes : 345
% 40.91/21.68 % Condensation attempts : 0
% 40.91/21.68 % Condensation successes : 0
% 40.91/21.68 % Termbank termtop insertions : 2977593
% 40.91/21.68 % Search garbage collected termcells : 1596
% 40.91/21.68
% 40.91/21.68 % -------------------------------------------------
% 40.91/21.68 % User time : 5.723 s
% 40.91/21.68 % System time : 0.194 s
% 40.91/21.68 % Total time : 5.918 s
% 40.91/21.68 % Maximum resident set size: 4848 pages
% 40.91/21.68
% 40.91/21.68 % -------------------------------------------------
% 40.91/21.68 % User time : 23.000 s
% 40.91/21.68 % System time : 0.631 s
% 40.91/21.68 % Total time : 23.630 s
% 40.91/21.68 % Maximum resident set size: 5376 pages
% 40.91/21.68 % E exiting
%------------------------------------------------------------------------------