%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT069-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 02:40:42 PM UTC 2026
% Result : Unsatisfiable 88.55s 13.35s
% Output : CNFRefutation 88.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f869ERROR: Could not build tree for root c_43432ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0)
| ~ class_Lattices_Odistrib__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0)
| ~ class_Lattices_Odistrib__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f3,axiom,
! [X0,X1] :
( c_Wellfounded_Owf(X0,X1)
| c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI__pf_1) ).
fof(f4,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f5,axiom,
! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X0,X4,X2,X3),c_Relation_OImage(X1,X4,X2,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X0,X1,X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ hBOOL(hAPP(X0,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] : c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X0,X1,X2),X3) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f11,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f12,plain,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f11]) ).
fof(f18,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
fof(f19,axiom,
! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
fof(f20,axiom,
! [X2,X3,X0,X1,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,X4,X2,X3),tc_fun(X3,tc_bool)),c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f21,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f22,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f25,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f28,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f29,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f30,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) != X1
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = X2
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f33,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f34,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f35,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
fof(f37,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f38,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f40,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
fof(f41,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f42,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f43,axiom,
! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f44,axiom,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f45,axiom,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f46,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
fof(f47,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
fof(f48,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f49,axiom,
! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f50,axiom,
! [X2,X0,X1] : c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Set_Oinsert(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
fof(f51,axiom,
! [X2,X0,X1] :
( X0 = X2
| c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f52,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f57,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Set_Oinsert(X0,X3,X2),X1,tc_fun(X2,tc_bool))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f58,axiom,
! [X2,X3,X0,X1,X4] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,X2,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X3,X2,X4),tc_fun(tc_prod(X2,X4),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
fof(f59,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f63,axiom,
! [X2,X3,X0,X1] :
( c_in(X3,X0,X2)
| ~ c_lessequals(X0,c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
fof(f64,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f65,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f66,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X0,X1,X2),c_Relation_ODomain(X3,X1,X2),tc_fun(X1,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
fof(f67,axiom,
! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
fof(f68,plain,
! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f70,axiom,
! [X2,X3,X0,X1,X4] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,X2,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X3,X2,X4),tc_fun(tc_prod(X2,X4),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
fof(f71,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X4,X3,X2)
| c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X4,X3,X2)
| c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool))
| ~ c_in(X1,X0,X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
fof(f75,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X0,X3)
| c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
fof(f76,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X3,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f77,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Set_Oinsert(X3,X0,X2),X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f78,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f79,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X0,X1,X2),c_Relation_ORange(X3,X1,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
fof(f80,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
fof(f81,axiom,
! [X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
fof(f82,axiom,
! [X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) = c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
fof(f83,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(reorient_equations,[],[f82]) ).
fof(f84,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
fof(f85,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(reorient_equations,[],[f84]) ).
fof(f86,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
fof(f87,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)),
inference(reorient_equations,[],[f86]) ).
fof(f88,axiom,
! [X2,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
fof(f91,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f92,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f96,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
fof(f97,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(X1,tc_bool))
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
fof(f98,axiom,
! [X0,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f99,axiom,
! [X0,X1] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f100,axiom,
! [X2,X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
fof(f101,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f102,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f105,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f106,axiom,
! [X2,X0,X1] : c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f107,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2),
inference(reorient_equations,[],[f106]) ).
fof(f108,axiom,
! [X2,X0,X1] : c_Set_Oinsert(X0,c_Set_Oinsert(X0,X1,X2),X2) = c_Set_Oinsert(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f109,plain,
! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Set_Oinsert(X0,c_Set_Oinsert(X0,X1,X2),X2),
inference(reorient_equations,[],[f108]) ).
fof(f110,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X2,X0,X3),X1))
| X2 = X1
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X2,X0,X3),X1))
| X1 = X2
| hBOOL(hAPP(X0,X1)) ),
inference(reorient_equations,[],[f110]) ).
fof(f113,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3) = c_Set_Oinsert(X0,c_Relation_ODomain(X4,X2,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
fof(f114,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Osym(X0,X2)
| ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
fof(f115,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X0,X2,X3),c_Relation_ODomain(X1,X2,X3),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
fof(f116,axiom,
! [X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) = c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f117,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(reorient_equations,[],[f116]) ).
fof(f118,axiom,
! [X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) = c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f119,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(reorient_equations,[],[f118]) ).
fof(f120,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f121,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),
inference(reorient_equations,[],[f120]) ).
fof(f122,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f123,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(reorient_equations,[],[f122]) ).
fof(f124,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f125,axiom,
! [X2,X3,X0,X1,X4] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X0,X1,X3,X4),c_Set_Oimage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
fof(f126,axiom,
! [X2,X3,X0,X1,X4] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X0,X1,X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
fof(f127,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X0,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f128,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X0,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f129,axiom,
! [X2,X3,X0,X1,X4] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,X2,X4) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X3,X2,X4),tc_fun(tc_prod(X2,X4),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
fof(f130,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f131,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f132,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool)),
inference(reorient_equations,[],[f131]) ).
fof(f133,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X1))
| hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f134,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f135,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f136,axiom,
! [X2,X0,X1] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X2,X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X0,X1,X1),c_Relation_ORange(X2,X1,X1),tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
fof(f137,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X2,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X0,X1,X1),c_Relation_ORange(X2,X1,X1),tc_fun(X1,tc_bool)) ),
inference(reorient_equations,[],[f136]) ).
fof(f139,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Orefl__on(X0,X3,X2)
| ~ c_Relation_Orefl__on(X1,X4,X2)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
fof(f140,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f141,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f142,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f143,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f144,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f145,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f146,axiom,
! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f147,axiom,
! [X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f148,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f149,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f150,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f151,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),
inference(reorient_equations,[],[f150]) ).
fof(f152,axiom,
! [X2,X3,X0,X1,X4,X5] : c_Product__Type_OSigma(c_Set_Oinsert(X0,X1,X2),c_COMBK(c_Set_Oinsert(X3,X4,X5),tc_fun(X5,tc_bool),X2),X2,X5) = c_Set_Oinsert(c_Pair(X0,X3,X2,X5),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(c_Set_Oinsert(X3,X4,X5),tc_fun(X5,tc_bool),X2),X2,X5),c_Product__Type_OSigma(c_Set_Oinsert(X0,X1,X2),c_COMBK(X4,tc_fun(X5,tc_bool),X2),X2,X5),tc_fun(tc_prod(X2,X5),tc_bool)),tc_prod(X2,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
fof(f153,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f154,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
fof(f155,axiom,
! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
fof(f156,axiom,
! [X2,X3,X0,X1] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3
| c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) ),
inference(reorient_equations,[],[f156]) ).
fof(f158,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f159,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(reorient_equations,[],[f159]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Otrans(X0,X2)
| ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
fof(f162,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f163,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
fof(f164,axiom,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f165,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
fof(f166,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f167,plain,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) != c_HOL_Ouminus__class_Ouminus(X1,X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(reorient_equations,[],[f166]) ).
fof(f170,axiom,
! [X2,X0,X1] :
( X0 = X2
| c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
fof(f171,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Wellfounded_Oacyclic(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
fof(f172,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
fof(f173,axiom,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f174,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
fof(f175,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f176,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f177,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f178,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f179,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f180,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f181,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Orefl__on(X0,X3,X2)
| ~ c_Relation_Orefl__on(X1,X4,X2)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
fof(f182,axiom,
! [X2,X3,X0,X1,X4] :
( X0 = X3
| X0 = X4
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
fof(f183,axiom,
! [X2,X3,X0,X1,X4] :
( X0 = X3
| X1 = X3
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
fof(f184,axiom,
! [X2,X3,X0,X1,X4] :
( X1 = X4
| X0 = X4
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f185,axiom,
! [X2,X3,X0,X1] : c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X0,X2,X3),c_Relation_Oconverse(X1,X2,X3),tc_fun(tc_prod(X3,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
fof(f186,axiom,
! [X2,X3,X0,X1] :
( c_in(X1,X0,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( c_in(X1,X0,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) ),
inference(reorient_equations,[],[f186]) ).
fof(f188,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f188]) ).
fof(f190,axiom,
! [X2,X0,X1] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2)
| c_Relation_Ototal__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
fof(f191,axiom,
! [X2,X0,X1] :
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f192,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f191]) ).
fof(f193,axiom,
! [X2,X0,X1] :
( X0 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f194,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f193]) ).
fof(f195,axiom,
! [X2,X0,X1] :
( X1 = c_Orderings_Obot__class_Obot(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f196,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X1
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(reorient_equations,[],[f195]) ).
fof(f197,axiom,
! [X2,X0,X1] :
( X2 = c_Orderings_Obot__class_Obot(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f198,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X0) = X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != c_Orderings_Obot__class_Obot(X0)
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(reorient_equations,[],[f197]) ).
fof(f199,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f200,plain,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f199]) ).
fof(f201,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f202,plain,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f201]) ).
fof(f203,axiom,
! [X2,X3,X0,X1,X4,X5] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X4,X2,X3,X5),c_Relation_Orel__comp(X1,X4,X2,X3,X5),tc_fun(tc_prod(X2,X5),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
fof(f204,axiom,
! [X2,X3,X0,X1,X4,X5] : c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X1,X5,X3,X4),c_Relation_Orel__comp(X0,X2,X5,X3,X4),tc_fun(tc_prod(X5,X4),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
fof(f205,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f206,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f209,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f210,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f211,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0)
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f212,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X0),X0)
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f213,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f215,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f216,axiom,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f217,axiom,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f218,axiom,
! [X2,X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
fof(f219,axiom,
! [X2,X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
fof(f220,plain,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(reorient_equations,[],[f219]) ).
fof(f223,axiom,
! [X2,X3,X0,X1] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X0,X2,X3),c_Relation_ODomain(X1,X2,X3),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
fof(f224,axiom,
! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f225,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f226,plain,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f225]) ).
fof(f227,axiom,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f228,plain,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(reorient_equations,[],[f227]) ).
fof(f229,axiom,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f230,plain,
! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(reorient_equations,[],[f229]) ).
fof(f231,axiom,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f232,axiom,
! [X2,X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
fof(f233,axiom,
! [X2,X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
fof(f235,axiom,
! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
fof(f236,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f235]) ).
fof(f237,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X0,X2,X3),c_Relation_ORange(X1,X2,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
fof(f238,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
fof(f239,axiom,
! [X2,X0,X1] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
fof(f240,plain,
! [X2,X0,X1] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(reorient_equations,[],[f239]) ).
fof(f241,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
fof(f242,plain,
! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f241]) ).
fof(f243,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f245,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X3,tc_bool)),X1))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f246,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),X1))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f247,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3) = c_Set_Oinsert(X1,c_Relation_ORange(X4,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
fof(f248,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f248]) ).
fof(f250,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
fof(f251,plain,
! [X2,X0,X1] :
( c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f250]) ).
fof(f252,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Osym(X0,X2)
| ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
fof(f253,axiom,
! [X2,X0,X1] :
( c_in(X0,X1,X2)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f254,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f255,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f256,axiom,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Ocut(X0,X2,X3,X4,X5) = c_Recdef_Ocut(X1,X2,X3,X4,X5)
| hAPP(X0,c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X1,X2,X3,X4,X5)) != hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X1,X2,X3,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
fof(f257,axiom,
! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
fof(f259,axiom,
! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ class_Lattices_Oboolean__algebra(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f265,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1)),X1)
| c_Wellfounded_Oacyclic(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
fof(f272,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X3)
| ~ c_in(X0,X2,X3)
| c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f274,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X2,X3)
| c_in(X0,c_Set_Oinsert(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f275,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X3)
| c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f276,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X2,X3)
| c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f280,axiom,
! [X0,X1] : ~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f281,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Set_Oinsert(X3,X1,X2),X2)
| X0 = X3
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f282,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2)
| c_in(X0,X3,X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f283,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f284,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f285,axiom,
! [X2,X0,X1] :
( c_in(X0,X1,X2)
| c_in(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
fof(f286,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
fof(f289,axiom,
! [X2,X0,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f290,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f291,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f294,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X3)
| c_in(X0,X2,X3)
| c_in(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
fof(f295,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| c_in(X0,X1,X2)
| c_in(X0,X3,X2)
| c_Set_Oinsert(X0,X1,X2) != c_Set_Oinsert(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f296,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_Set_Oinsert(X0,X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f297,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X0,X2)
| ~ c_in(X3,X4,X2)
| c_in(c_Pair(X1,X3,X2,X2),X0,tc_prod(X2,X2))
| c_Relation_OImage(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X0,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
fof(f301,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X0,X2)
| ~ c_in(c_Pair(X1,X3,X2,X2),X0,tc_prod(X2,X2))
| c_lessequals(c_Relation_OImage(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X0,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
fof(f302,axiom,
! [X0,X1] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
fof(f303,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| X0 = X1
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
fof(f304,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| c_in(c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
fof(f305,axiom,
! [X2,X3,X0,X1,X4] :
( X1 = X4
| X1 = X3
| c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
fof(f306,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f307,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0 ),
inference(reorient_equations,[],[f306]) ).
fof(f309,axiom,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f310,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X3,X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X3,X2)
| c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
inference(reorient_equations,[],[f310]) ).
fof(f312,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,X0,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f313,axiom,
! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) = c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f314,axiom,
! [X0,X1] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f315,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f316,axiom,
! [X2,X3,X0,X1] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X0,X2,X3),c_Relation_Oconverse(X1,X2,X3),tc_fun(tc_prod(X3,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
fof(f317,axiom,
! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f318,axiom,
! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f321,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
fof(f322,axiom,
! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f323,axiom,
! [X2,X0,X1] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f324,axiom,
! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f325,axiom,
! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f327,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
fof(f329,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Odistrib__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f330,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0)
| ~ class_Lattices_Odistrib__lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f331,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f332,axiom,
! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f333,axiom,
! [X2,X0,X1] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X2,X0,X1)
| c_Relation_Otrans(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
fof(f334,axiom,
! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f335,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f337,axiom,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0)
| ~ class_Lattices_Olattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f338,plain,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(reorient_equations,[],[f337]) ).
fof(f339,axiom,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f340,plain,
! [X2,X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(reorient_equations,[],[f339]) ).
fof(f341,axiom,
! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f342,plain,
! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(reorient_equations,[],[f341]) ).
fof(f343,axiom,
! [X2,X3,X0,X1] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X0,X2,X3),c_Relation_ORange(X1,X2,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
fof(f344,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
fof(f345,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
fof(f346,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
fof(f347,axiom,
! [X0,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1
| ~ class_Lattices_Olower__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f348,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f351,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f352,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f353,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f354,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f355,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f356,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f357,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,X1)
| ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_Wellfounded_Oacyclic(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
fof(f358,axiom,
! [X2,X3,X0,X1] :
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X0,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
fof(f359,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X1
| c_Set_Oimage(X0,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(reorient_equations,[],[f358]) ).
fof(f360,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f361,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
fof(f362,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
fof(f364,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
fof(f365,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0 ),
inference(reorient_equations,[],[f364]) ).
fof(f366,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X0 = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X0 ),
inference(reorient_equations,[],[f366]) ).
fof(f368,axiom,
! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
fof(f369,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f371,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f374,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f377,axiom,
! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X0,X1,X3,X4),c_Set_Oimage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f378,axiom,
! [X2,X0,X1] :
( ~ c_Order__Relation_Ostrict__linear__order__on(X2,X0,X1)
| c_Relation_Oirrefl(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
fof(f379,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X3,X2)
| c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
fof(f380,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f381,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
fof(f382,axiom,
! [X2,X3,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X3,X1,X2)
| ~ c_in(X0,X3,X2)
| c_in(X0,c_Relation_OImage(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
fof(f383,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Equiv__Relations_Oequiv(X5,X3,X2)
| ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)),X2)
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
fof(f384,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4) = c_Set_Oimage(X0,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f385,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,X2,X3)
| c_Set_Oimage(X0,X2,X3,X4) = c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4) ),
inference(reorient_equations,[],[f384]) ).
fof(f386,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X3),X3)
| c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
fof(f387,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X0,X3,X4),X1,tc_prod(X3,X4))
| c_in(X0,c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
fof(f388,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X0,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
fof(f389,axiom,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X4
| ~ c_in(X5,X1,X2)
| c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
fof(f390,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1)),X1)
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
fof(f391,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X1,X2,X3,X4),X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
fof(f392,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Transitive__Closure_Ortrancl(X1,X3),tc_prod(X3,X3))
| c_in(X0,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
fof(f393,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| c_in(X0,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
fof(f395,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X0,X2)
| ~ c_in(c_Pair(X1,X3,X2,X2),X0,tc_prod(X2,X2))
| c_Relation_OImage(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X0,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
fof(f396,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
fof(f397,axiom,
! [X2,X0,X1] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
fof(f398,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
fof(f399,axiom,
! [X2,X0,X1] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),c_Wellfounded_Oacc(X1,X2),X2)
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
fof(f400,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X0,X1,X1,X1),c_Relation_Orel__comp(X2,X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
fof(f401,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X0,X2,X2,X2),c_Relation_Orel__comp(X1,X0,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
fof(f402,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
fof(f403,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
fof(f404,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(reorient_equations,[],[f403]) ).
fof(f405,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
fof(f406,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(reorient_equations,[],[f405]) ).
fof(f407,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
fof(f408,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(reorient_equations,[],[f407]) ).
fof(f409,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f410,axiom,
! [X0,X1] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
fof(f411,axiom,
! [X0,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
fof(f412,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
fof(f413,axiom,
! [X2,X0,X1] : c_Relation_OImage(c_Relation_OId__on(X0,X1),X2,X1,X1) = c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
fof(f414,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| c_Relation_Oantisym(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
fof(f415,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
fof(f416,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Relation_Ototal__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
fof(f417,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Ototal__on(X0,X1,X2)
| c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
fof(f418,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
fof(f419,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
| X1 = X0
| c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
fof(f420,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
| X0 = X1
| c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
inference(reorient_equations,[],[f419]) ).
fof(f421,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
fof(f422,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
| X1 = X0
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
fof(f423,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
| X0 = X1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(reorient_equations,[],[f422]) ).
fof(f424,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
fof(f425,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| X0 = X1
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
fof(f426,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
fof(f427,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
fof(f428,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_in(c_Pair(X2,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
fof(f429,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
fof(f430,axiom,
! [X2,X0,X1] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X1),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X1),X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
fof(f431,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),X0,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X0,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
fof(f432,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
fof(f433,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f434,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,X1,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X2,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
fof(f435,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,X1,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X2,X3),X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
fof(f436,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Otrancl(X1,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X1,X0,X2,X3),X3,X3),X1,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
fof(f437,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
fof(f438,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,X3,X2)
| ~ c_lessequals(c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool))
| ~ c_in(X1,X4,X2)
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
fof(f439,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(c_Pair(X0,X1,X4,X5),c_Relation_Orel__comp(X2,X3,X4,X6,X5),tc_prod(X4,X5))
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X1,X2,X3,X4,X5,X6),X1,X6,X5),X3,tc_prod(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
fof(f440,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(c_Pair(X0,X1,X4,X5),c_Relation_Orel__comp(X2,X3,X4,X6,X5),tc_prod(X4,X5))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X1,X2,X3,X4,X5,X6),X4,X6),X2,tc_prod(X4,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
fof(f441,axiom,
! [X0,X1] :
( ~ c_in(X0,c_Relation_OId(X1),tc_prod(X1,X1))
| X0 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
fof(f442,plain,
! [X0,X1] :
( ~ c_in(X0,c_Relation_OId(X1),tc_prod(X1,X1))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),X1,X1) = X0 ),
inference(reorient_equations,[],[f441]) ).
fof(f443,axiom,
! [X0,X1] :
( c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1),tc_fun(X1,tc_bool))
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI__pf_0) ).
fof(f444,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_lessequals(X0,c_Relation_OImage(X2,X0,X1,X1),tc_fun(X1,tc_bool))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f445,plain,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_lessequals(X0,c_Relation_OImage(X2,X0,X1,X1),tc_fun(X1,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0 ),
inference(reorient_equations,[],[f444]) ).
fof(f446,axiom,
! [X0,X1] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X0,X1),c_Wellfounded_Oacc(X0,X1),X1)
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
fof(f447,axiom,
! [X0,X1] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X0,X1),c_Wellfounded_Oacc(X0,X1),X1)
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
fof(f448,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(X1,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X0,X1,X5,X2,X3)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X0,X1,X5,X2,X3)),tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).
fof(f449,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X0,X2,X3),c_HOL_Ouminus__class_Ouminus(X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| c_lessequals(c_Relation_OImage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).
fof(f450,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(c_Relation_OImage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool))
| c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X1,X2,X3),c_HOL_Ouminus__class_Ouminus(X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).
fof(f451,axiom,
! [X2,X0,X1] :
( ~ c_in(X1,c_Relation_OId__on(X0,X2),tc_prod(X2,X2))
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
fof(f452,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
| X0 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
fof(f453,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),X2,X2) = X0 ),
inference(reorient_equations,[],[f452]) ).
fof(f454,axiom,
! [X2,X3,X0,X1,X4,X5] :
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X5,X1,X2,X3,X4),X2,X3,X3),X1,tc_prod(X3,X3))
| c_Recdef_Ocut(X0,X1,X2,X3,X4) = c_Recdef_Ocut(X5,X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
fof(f455,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X0,X1),c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
fof(f456,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X0,X1,X2,X2,X2),X0,tc_fun(tc_prod(X2,X2),tc_bool))
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
fof(f457,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
fof(f458,axiom,
! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X1,X0,X2)
| c_lessequals(X0,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
fof(f459,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_lessequals(X0,c_Product__Type_OSigma(X5,c_COMBK(X7,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X7,c_COMBK(X6,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X0,X1,X2,X3,X4),c_Product__Type_OSigma(X5,c_COMBK(X6,tc_fun(X4,tc_bool),X2),X2,X4),tc_fun(tc_prod(X2,X4),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
fof(f460,axiom,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
fof(f461,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(reorient_equations,[],[f460]) ).
fof(f462,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
fof(f463,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(reorient_equations,[],[f462]) ).
fof(f465,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X1,X0,X2)
| c_lessequals(X0,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
fof(f466,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
fof(f468,axiom,
! [X0,X1] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1))
| c_Relation_Oirrefl(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
fof(f469,axiom,
! [X0,X1] : c_lessequals(c_Relation_OId__on(X0,X1),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
fof(f470,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X0,X3,X4),X4,X3)
| c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X0,X1,X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
fof(f471,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
fof(f472,axiom,
! [X0,X1] :
( ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1))
| c_Nitpick_Orefl_H(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
fof(f473,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Oirrefl(X1,X2)
| ~ c_Relation_Ototal__on(X0,X1,X2)
| c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
fof(f474,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X4,X1,X2)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f475,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X1,X2,X3,X4),X1,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
fof(f476,axiom,
! [X2,X0,X1] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
fof(f477,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
fof(f478,axiom,
! [X2,X0,X1] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X0,X2,X2),X1,tc_prod(X2,X2))
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
fof(f479,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f480,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X3,X2)
| c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
fof(f481,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X5,X1,X2)
| ~ c_lessequals(X0,X4,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
fof(f482,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X5,X3,X4)
| ~ c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,X4),c_Product__Type_OSigma(X1,c_COMBK(X3,tc_fun(X4,tc_bool),X2),X2,X4),tc_fun(tc_prod(X2,X4),tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
fof(f483,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X0,X1,X5,X2,X3),X0,X2)
| c_lessequals(c_Product__Type_OSigma(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).
fof(f484,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,c_Product__Type_OSigma(X5,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
| c_lessequals(c_Relation_OImage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
fof(f485,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
fof(f486,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X4,X2),tc_prod(X2,X2))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| X0 = X3
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
fof(f487,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X2,X0,X1)
| c_lessequals(X0,c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
fof(f488,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Otrancl(X1,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X1,X0,X2,X3),X3,X3),X1,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
fof(f489,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X0,X1,X2,X3),X2,X3,X3),X0,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
fof(f490,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_lessequals(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
fof(f491,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool))
| c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
fof(f492,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(c_Set_Oimage(X0,X4,X5,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X5)
| c_in(hAPP(X0,X1),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f494,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(X2,tc_bool))
| c_lessequals(c_Relation_OImage(X0,X1,X2,X3),c_Relation_OImage(X4,X5,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
fof(f496,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| c_lessequals(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
fof(f497,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool))
| c_lessequals(c_Relation_ODomain(X0,X1,X2),c_Relation_ODomain(X3,X1,X2),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
fof(f498,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool))
| ~ c_Relation_Osingle__valued(X3,X1,X2)
| c_Relation_Osingle__valued(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
fof(f500,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_Relation_Oantisym(X2,X1)
| c_Relation_Oantisym(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f501,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f502,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f503,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f504,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f505,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f507,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f508,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f509,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f510,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
fof(f513,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| X1 = X2
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f515,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f516,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
fof(f517,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_lessequals(X0,X5,tc_fun(tc_prod(X2,X3),tc_bool))
| ~ c_lessequals(X1,X6,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X0,X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X2,X3,X4),tc_fun(tc_prod(X2,X4),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
fof(f518,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(X0,c_Transitive__Closure_Ortrancl(X2,X1),tc_fun(tc_prod(X1,X1),tc_bool))
| c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
fof(f519,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X0,X1),c_Wellfounded_Oacc(X2,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
fof(f520,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X1,X3,tc_fun(X4,X0))
| c_lessequals(hAPP(X1,X2),hAPP(X3,X2),X0)
| ~ class_HOL_Oord(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f524,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
fof(f525,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
fof(f526,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X0,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
fof(f527,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Otrancl(X1,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X1,X0,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X1,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
fof(f528,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| ~ c_Relation_Otrans(X0,X1)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
fof(f530,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
| ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
fof(f531,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
fof(f532,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
fof(f533,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
fof(f534,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
fof(f537,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| X0 = X1
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
fof(f538,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
fof(f539,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
fof(f540,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Osingle__valued(X3,X2,X2)
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
fof(f542,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
fof(f543,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
fof(f544,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
fof(f545,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
fof(f547,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_split(X0,X1,X2,X3),c_Pair(X4,X5,X1,X2)) = hAPP(hAPP(X0,X4),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
fof(f548,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_split(X0,X4,X5,tc_fun(X6,tc_bool)),c_Pair(X1,X2,X4,X5)),X3))
| hBOOL(hAPP(hAPP(hAPP(X0,X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).
fof(f552,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(hAPP(X3,X0),c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f553,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X1,X2)
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
fof(f554,axiom,
! [X0,X1] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
fof(f555,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f556,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,X2,X3)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
fof(f557,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Transitive__Closure_Otrancl(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
fof(f558,axiom,
! [X2,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X2)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
fof(f559,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Relation_Osym(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f560,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f561,axiom,
! [X0,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ODomain(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
fof(f562,plain,
! [X0,X1] : c_Relation_ODomain(X0,X1,X1) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),
inference(reorient_equations,[],[f561]) ).
fof(f563,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X1,X2,X3,X4),X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
fof(f564,axiom,
! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f565,axiom,
! [X0,X1] : c_Relation_Otrans(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
fof(f566,axiom,
! [X2,X0,X1] : c_Relation_Orel__comp(c_Relation_OId(X0),X1,X0,X0,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f567,axiom,
! [X2,X0,X1] : c_Relation_Orel__comp(X0,c_Relation_OId(X1),X2,X1,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f568,axiom,
! [X0,X1] : c_Relation_Oantisym(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
fof(f569,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
fof(f570,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
| c_Relation_Orefl__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f571,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Orefl__on(X0,X1,X2)
| c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f572,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f573,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f574,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| c_Wellfounded_Owf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f575,axiom,
! [X0,X1] : c_Relation_OImage(c_Relation_OId(X0),X1,X0,X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f576,axiom,
! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
fof(f577,axiom,
! [X0,X1] : c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
fof(f578,axiom,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f579,axiom,
! [X0,X1] :
( c_Relation_Osym(X0,X1)
| c_Relation_Oconverse(X0,X1,X1) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f580,axiom,
! [X0,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ORange(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f581,axiom,
! [X0,X1] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
fof(f582,axiom,
! [X2,X3,X0,X1,X4] : c_Relation_Oconverse(c_Relation_Orel__comp(X0,X1,X2,X3,X4),X2,X4) = c_Relation_Orel__comp(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X0,X2,X3),X4,X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
fof(f583,axiom,
! [X0,X1] : c_Relation_Osym(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
fof(f584,axiom,
! [X0,X1] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
fof(f585,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X2)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f586,axiom,
! [X0,X1] : c_Relation_Orel__comp(X0,c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),X0,X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
fof(f587,plain,
! [X0,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),X0,X1,X1,X1) = c_Relation_Orel__comp(X0,c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1),
inference(reorient_equations,[],[f586]) ).
fof(f588,axiom,
! [X2,X3,X0,X1] :
( ~ c_Relation_Osym(X0,X2)
| c_Relation_Osym(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f589,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
fof(f590,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),
inference(reorient_equations,[],[f589]) ).
fof(f591,axiom,
! [X0,X1] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
fof(f592,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Relation_Otrans(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
fof(f593,axiom,
! [X0,X1] :
( ~ c_Relation_Otrans(X0,X1)
| c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
fof(f594,axiom,
! [X0] : c_Relation_Oconverse(c_Relation_OId(X0),X0,X0) = c_Relation_OId(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
fof(f595,plain,
! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0),
inference(reorient_equations,[],[f594]) ).
fof(f596,axiom,
! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f597,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : c_Relation_Orel__comp(c_Relation_Orel__comp(X0,X1,X2,X3,X4),X5,X2,X4,X6) = c_Relation_Orel__comp(X0,c_Relation_Orel__comp(X1,X5,X3,X4,X6),X2,X3,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
fof(f598,axiom,
! [X2,X3,X0,X1] : c_Relation_Oconverse(c_Relation_Oinv__image(X0,X1,X2,X3),X3,X3) = c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f599,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
fof(f600,plain,
! [X0,X1] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),
inference(reorient_equations,[],[f599]) ).
fof(f601,axiom,
! [X2,X3,X0,X1] :
( ~ c_Relation_Otrans(X0,X2)
| c_Relation_Otrans(c_Relation_Oinv__image(X0,X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
fof(f602,axiom,
! [X0,X1] : c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1) = c_Relation_OId__on(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
fof(f603,plain,
! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),
inference(reorient_equations,[],[f602]) ).
fof(f604,axiom,
! [X0,X1] :
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X0,X1,X1),X0,X1)
| c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
fof(f605,axiom,
! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f606,axiom,
! [X2,X0,X1] : c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1) = c_Relation_ODomain(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f607,plain,
! [X2,X0,X1] : c_Relation_ODomain(X0,X1,X2) = c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1),
inference(reorient_equations,[],[f606]) ).
fof(f608,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X0,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
fof(f609,axiom,
! [X0,X1] : c_Relation_ORange(c_Relation_OId__on(X0,X1),X1,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
fof(f610,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Osingle__valued(X0,X2,X3)
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X1,X2,X3,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
fof(f611,axiom,
! [X2,X0,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f612,axiom,
! [X0] : c_Relation_Otrans(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
fof(f613,axiom,
! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X0,X1)
| c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
fof(f614,axiom,
! [X0,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
fof(f615,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1),
inference(reorient_equations,[],[f614]) ).
fof(f616,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1)
| c_Relation_Oantisym(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f617,axiom,
! [X0,X1] :
( ~ c_Relation_Oantisym(X0,X1)
| c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f618,axiom,
! [X2,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X2)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
fof(f619,axiom,
! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X1,X2)
| c_Relation_Orefl__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
fof(f620,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
fof(f621,axiom,
! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X0,X1)
| c_Relation_Osym(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
fof(f625,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),X0,X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
fof(f626,axiom,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Orel__comp(X0,c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
fof(f627,axiom,
! [X2,X0,X1] : c_Relation_ORange(X0,X1,X2) = c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X2),X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
fof(f628,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
| c_Relation_Ototal__on(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f629,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Ototal__on(X0,X1,X2)
| c_Relation_Ototal__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f630,axiom,
! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X0,X1)
| c_Relation_Otrans(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
fof(f631,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
fof(f632,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
fof(f633,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),
inference(reorient_equations,[],[f632]) ).
fof(f634,axiom,
! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
fof(f635,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),
inference(reorient_equations,[],[f634]) ).
fof(f636,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
fof(f637,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
| ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
fof(f639,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
| ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
fof(f640,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(c_Pair(X1,X2,X3,X4),X6,tc_prod(X3,X4))
| c_in(hAPP(hAPP(X0,X1),X2),c_Set_Oimage(c_split(X0,X3,X4,X5),X6,tc_prod(X3,X4),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).
fof(f641,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
fof(f642,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
| ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
fof(f643,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
fof(f644,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X4,X1,X2)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f645,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ODomain(X1,X2,X3),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
fof(f646,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,c_Relation_OImage(X2,X0,X3,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X1,X2,X3,X4),X1,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
fof(f647,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
fof(f648,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(X1,X3,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
fof(f649,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(X0,hAPP(hAPP(X1,X5),X6),X4)
| c_in(X0,hAPP(c_split(X1,X2,X3,tc_fun(X4,tc_bool)),c_Pair(X5,X6,X2,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
fof(f651,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Relation_Osingle__valued(X5,X3,X4)
| ~ c_in(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X3,X4),X5,tc_prod(X3,X4))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
fof(f653,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(X5,X2,X3,X3),X1,tc_prod(X3,X3))
| hAPP(c_Recdef_Ocut(X0,X1,X2,X3,X4),X5) = hAPP(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
fof(f654,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X2,X3,X4),X0,tc_prod(X3,X4))
| c_FunDef_Oin__rel(X0,X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
fof(f655,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_FunDef_Oin__rel(X4,X0,X1,X2,X3)
| c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
fof(f657,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Otrans(X3,X2)
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
fof(f659,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
fof(f660,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2))
| c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f661,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f662,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(f663,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
fof(f664,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(f665,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
fof(f667,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
fof(f669,axiom,
! [X2,X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
fof(f670,axiom,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f672,axiom,
! [X2,X3,X0,X1] :
( ~ c_Relation_Oantisym(X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
fof(f674,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
fof(f675,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_in(c_Pair(X6,X2,X3,X3),X1,tc_prod(X3,X3))
| hAPP(X0,X6) = hAPP(X5,X6)
| c_Recdef_Ocut(X0,X1,X2,X3,X4) != c_Recdef_Ocut(X5,X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
fof(f676,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
fof(f677,axiom,
! [X2,X0,X1] :
( ~ c_Nitpick_Orefl_H(X2,X1)
| c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
fof(f678,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f679,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(hAPP(X4,X0),hAPP(X4,X1),X5,X5),X3,tc_prod(X5,X5))
| c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oinv__image(X3,X4,X5,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
fof(f680,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(X1,X2,X5,X5),c_Relation_Oinv__image(X4,X0,X3,X5),tc_prod(X5,X5))
| c_in(c_Pair(hAPP(X0,X1),hAPP(X0,X2),X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
fof(f682,axiom,
! [X2,X3,X0,X1] :
( ~ c_Relation_Osym(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
fof(f683,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X0,X7,X2,X6),X4,tc_prod(X2,X6))
| ~ c_in(c_Pair(X7,X1,X6,X3),X5,tc_prod(X6,X3))
| c_in(c_Pair(X0,X1,X2,X3),c_Relation_Orel__comp(X4,X5,X2,X6,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
fof(f684,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
fof(f685,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
fof(f687,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId(X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
fof(f688,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
fof(f689,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| X1 = X3
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
fof(f691,axiom,
! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f692,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
fof(f696,axiom,
! [X2,X0,X1] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f697,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
fof(f698,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| X0 = X3
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
fof(f700,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
fof(f701,axiom,
! [X0,X1] :
( X0 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
fof(f703,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X0,X4,X2)
| ~ c_in(X1,hAPP(X5,X0),X3)
| c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
fof(f705,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
fof(f707,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X5,X2,X3)
| ~ c_in(c_Pair(X5,X0,X3,X4),X1,tc_prod(X3,X4))
| c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
fof(f708,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X3,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
fof(f709,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X2,X1)
| c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId__on(X2,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
fof(f710,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X1,X4,X2)
| ~ c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
fof(f711,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Equiv__Relations_Oequiv(X1,X4,X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
fof(f713,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3))
| c_in(X0,c_Relation_ORange(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
fof(f715,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3))
| c_in(X0,c_Relation_ODomain(X1,X2,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
fof(f716,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(X2,X0,X4,X3),c_Product__Type_OSigma(X5,X1,X4,X3),tc_prod(X4,X3))
| c_in(X0,hAPP(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
fof(f717,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Pair(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X5,X2,X4),tc_prod(X2,X4))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f718,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| ~ c_in(X1,X4,X2)
| ~ c_in(X0,X4,X2)
| X1 = X0
| c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f719,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| ~ c_in(X1,X4,X2)
| ~ c_in(X0,X4,X2)
| X0 = X1
| c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(reorient_equations,[],[f718]) ).
fof(f721,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Orefl__on(X1,X4,X2)
| ~ c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
fof(f722,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Orefl__on(X1,X4,X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
fof(f723,axiom,
! [X2,X3,X0,X1] :
( ~ c_Relation_Orefl__on(X3,X2,X1)
| ~ c_in(X0,X3,X1)
| c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
fof(f726,axiom,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X5
| c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f727,axiom,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X4
| c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f732,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f733,axiom,
! [X2,X0,X1] :
( ~ c_in(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f738,axiom,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f739,axiom,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f740,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f741,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f743,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).
fof(f744,axiom,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_3) ).
fof(f745,axiom,
! [X2,X3,X0,X1] :
( X1 = X0
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2) ).
fof(f746,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(reorient_equations,[],[f745]) ).
fof(f747,axiom,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_05) ).
fof(f748,axiom,
! [X2,X3,X0,X1] :
( X1 = X0
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_06) ).
fof(f749,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(reorient_equations,[],[f748]) ).
fof(f750,axiom,
v_b____ = v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_07) ).
fof(f751,axiom,
v_a____ = v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_08) ).
fof(f752,negated_conjecture,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f753,negated_conjecture,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f754,axiom,
! [X0,X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f755,axiom,
! [X0,X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f756,axiom,
! [X0,X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f757,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f758,axiom,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f759,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f760,axiom,
! [X0,X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f761,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f762,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f763,axiom,
! [X0,X1] :
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f764,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f765,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f766,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f767,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f768,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f769,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f770,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f771,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f772,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f773,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f774,axiom,
! [X0,X1] : c_fequal(X0,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f775,axiom,
! [X2,X0,X1] :
( ~ c_fequal(X0,X1,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f777,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),
inference(definition_unfolding,[],[f625,f461]) ).
fof(f778,plain,
! [X2,X3,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1),c_Relation_ORange(c_Relation_Oconverse(X3,X1,X2),X2,X1),tc_fun(X1,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),X2,X1),tc_fun(X1,tc_bool)),
inference(definition_unfolding,[],[f66,f607,f607,f607]) ).
fof(f779,plain,
! [X2,X0,X1] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f88,f461,f461,f461]) ).
fof(f780,plain,
! [X2,X3,X0,X1,X4] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2),
inference(definition_unfolding,[],[f113,f607,f607]) ).
fof(f781,plain,
! [X2,X3,X0,X1] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(definition_unfolding,[],[f115,f607,f607,f607]) ).
fof(f782,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(X2,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),c_Relation_ORange(X2,X1,X1),tc_fun(X1,tc_bool)) ),
inference(definition_unfolding,[],[f137,f607]) ).
fof(f783,plain,
! [X2,X3,X0,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),tc_fun(X2,tc_bool)),
inference(definition_unfolding,[],[f223,f607,f607,f607]) ).
fof(f784,plain,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f240,f461,f461,f461,f461]) ).
fof(f785,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3))
| X0 = X1
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f303,f461]) ).
fof(f786,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| c_in(c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| hBOOL(hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f304,f461,f461]) ).
fof(f787,plain,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X3,X2)
| c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(definition_unfolding,[],[f379,f461]) ).
fof(f788,plain,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f380,f461]) ).
fof(f789,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4),X4,X4),X3,tc_prod(X4,X4))
| hBOOL(hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f381,f461]) ).
fof(f790,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3))
| c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f392,f461,f461]) ).
fof(f791,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3))
| c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f393,f461,f461]) ).
fof(f792,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f404,f461,f461]) ).
fof(f793,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f406,f461,f461]) ).
fof(f794,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f408,f461,f461]) ).
fof(f795,plain,
! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
inference(definition_unfolding,[],[f409,f461]) ).
fof(f796,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f418,f461]) ).
fof(f797,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a))
| X0 = X1
| c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a)) ),
inference(definition_unfolding,[],[f420,f461,f461]) ).
fof(f798,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X2,X1,X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f421,f461]) ).
fof(f799,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a))
| X0 = X1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(definition_unfolding,[],[f423,f461]) ).
fof(f800,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X1,X2,X4,X4),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X2,X3,X4)))
| hBOOL(hAPP(X0,X1)) ),
inference(definition_unfolding,[],[f424,f461]) ).
fof(f801,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X3,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3))
| X0 = X1
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X3,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f425,f461,f461]) ).
fof(f802,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(definition_unfolding,[],[f463,f461]) ).
fof(f804,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X1),c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f466,f461,f461]) ).
fof(f806,plain,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f479,f461]) ).
fof(f807,plain,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X3,X2)
| c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(definition_unfolding,[],[f480,f461]) ).
fof(f808,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(definition_unfolding,[],[f485,f461,f461]) ).
fof(f809,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X3,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X4,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| X0 = X3
| c_in(X0,X1,X2) ),
inference(definition_unfolding,[],[f486,f461]) ).
fof(f810,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool))
| c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1),c_Relation_ORange(c_Relation_Oconverse(X3,X1,X2),X2,X1),tc_fun(X1,tc_bool)) ),
inference(definition_unfolding,[],[f497,f607,f607]) ).
fof(f811,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(definition_unfolding,[],[f510,f461,f461,f461]) ).
fof(f812,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(definition_unfolding,[],[f516,f461,f461]) ).
fof(f813,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(definition_unfolding,[],[f518,f461,f461,f461]) ).
fof(f814,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X0,X1,X2,X3),X2,X3,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f526,f461]) ).
fof(f815,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Otrancl(X1,X3),tc_prod(X3,X3))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X1,X0,X2,X3),X3,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X3),c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f527,f461]) ).
fof(f817,plain,
! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_prod(X2,X2))
| c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f531,f461]) ).
fof(f818,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f533,f461]) ).
fof(f819,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f534,f461]) ).
fof(f822,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| X0 = X1
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f537,f461]) ).
fof(f823,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f538,f461,f461]) ).
fof(f824,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f539,f461,f461]) ).
fof(f825,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Osingle__valued(X3,X2,X2)
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f540,f461,f461,f461,f461]) ).
fof(f827,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f542,f461]) ).
fof(f828,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f543,f461]) ).
fof(f829,plain,
! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1,X1),
inference(definition_unfolding,[],[f562,f607,f607]) ).
fof(f830,plain,
! [X0,X1] :
( ~ c_Relation_Osym(X0,X1)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
inference(definition_unfolding,[],[f572,f461]) ).
fof(f831,plain,
! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),X1,X1) = X0,
inference(definition_unfolding,[],[f577,f607]) ).
fof(f832,plain,
! [X0,X1] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1),
inference(definition_unfolding,[],[f587,f461,f461]) ).
fof(f833,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(definition_unfolding,[],[f590,f461,f461]) ).
fof(f834,plain,
! [X0,X1] : c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(definition_unfolding,[],[f591,f461]) ).
fof(f835,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),X0,X1)
| c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1) != X0 ),
inference(definition_unfolding,[],[f604,f607]) ).
fof(f836,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1),
inference(definition_unfolding,[],[f615,f461,f461,f461]) ).
fof(f837,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1),
inference(definition_unfolding,[],[f620,f461,f461]) ).
fof(f838,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X0,X1) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1),
inference(definition_unfolding,[],[f626,f461]) ).
fof(f839,plain,
! [X2,X0,X1] : c_Relation_ORange(X0,X1,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1),X1,X2),
inference(definition_unfolding,[],[f627,f607]) ).
fof(f840,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f633,f461,f461]) ).
fof(f841,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(definition_unfolding,[],[f635,f461,f461,f461]) ).
fof(f842,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(definition_unfolding,[],[f636,f461]) ).
fof(f844,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3)) ),
inference(definition_unfolding,[],[f641,f607]) ).
fof(f845,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2)
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3)) ),
inference(definition_unfolding,[],[f645,f607]) ).
fof(f846,plain,
! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| X0 = X1 ),
inference(definition_unfolding,[],[f647,f461,f607]) ).
fof(f847,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f664,f461,f461]) ).
fof(f848,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f665,f461,f461]) ).
fof(f849,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(definition_unfolding,[],[f667,f461,f461,f461]) ).
fof(f851,plain,
! [X2,X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_prod(X1,X1)),
inference(definition_unfolding,[],[f669,f461]) ).
fof(f853,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3))
| c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2) ),
inference(definition_unfolding,[],[f715,f607]) ).
fof(f863,plain,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition_unfolding,[],[f738,f751,f750]) ).
fof(f864,plain,
! [X0] :
( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition_unfolding,[],[f739,f751,f750]) ).
fof(f865,plain,
v_a_H____ != v_b_H____,
inference(definition_unfolding,[],[f743,f751,f750]) ).
fof(f866,plain,
( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition_unfolding,[],[f752,f751,f750]) ).
fof(f867,plain,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition_unfolding,[],[f753,f751,f750]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1) = c_Transitive__Closure_Otrancl(X0,X1),
inference(cnf_transformation,[],[f777]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) )
| ~ class_Lattices_Odistrib__lattice(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X2,X0) )
| ~ class_Lattices_Odistrib__lattice(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(X1,X0)
| ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X1,X0) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 )
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X0,X1,X2,X3),c_Relation_OImage(X4,X1,X2,X3),tc_fun(X3,tc_bool)) = c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X1,X2,X3),
inference(cnf_transformation,[],[f6]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X0,X1,X2,X3),c_Relation_OImage(X0,X4,X2,X3),tc_fun(X3,tc_bool)) = c_Relation_OImage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X0,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(c_COMBK(X0,X1,X2),X3) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ominus__class_Ominus(X1,X2,X0) )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,X4,X2,X3),tc_fun(X3,tc_bool)),c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) )
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) )
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)) = X0 )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = X0 )
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) = X0 )
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_782,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_783,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_784,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) )
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1 )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] : c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Set_Oinsert(X0,X1,X2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,X2,X3),
inference(cnf_transformation,[],[f58]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(c_Set_Oinsert(X2,X0,X3),X1))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X1,X0,X3)
| c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f65]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1),c_Relation_ORange(c_Relation_Oconverse(X3,X1,X2),X2,X1),tc_fun(X1,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),X2,X1),tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f778]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)) = X0 )
| ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,X2,X3),
inference(cnf_transformation,[],[f70]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X0,X3)
| ~ c_lessequals(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool))
| ~ c_in(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X3,X2),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)) )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X0,X1,X2),c_Relation_ORange(X3,X1,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_Orderings_Obot__class_Obot(X0) )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) = c_Orderings_Obot__class_Obot(X0) )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f85]) ).
tcf(c_821,plain,
! [X0: $i,X1: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f87]) ).
tcf(c_822,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f779]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2),
inference(cnf_transformation,[],[f91]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X3),
inference(cnf_transformation,[],[f92]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X0,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
| ~ class_Orderings_Obot(X0) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_831,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f100]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f101]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f102]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2),
inference(cnf_transformation,[],[f105]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_OImage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f107]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i,X2: $i] : c_Set_Oinsert(X0,c_Set_Oinsert(X0,X1,X2),X2) = c_Set_Oinsert(X0,X1,X2),
inference(cnf_transformation,[],[f109]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| ( X0 = X3 )
| ~ hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2),
inference(cnf_transformation,[],[f780]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Osym(X2,X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f781]) ).
tcf(c_843,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X0),X0) = c_Orderings_Obot__class_Obot(X0) )
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_844,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X1,X0) = c_Orderings_Obot__class_Obot(X0) )
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_845,plain,
! [X0: $i,X1: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_846,plain,
! [X0: $i,X1: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_lessequals(c_Set_Oimage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X0,X1,X3,X4),c_Set_Oimage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_lessequals(c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X0,X1,X3,X4),c_Relation_OImage(X0,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(cnf_transformation,[],[f126]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_fun(X2,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,X2,X3),
inference(cnf_transformation,[],[f129]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f130]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f132]) ).
tcf(c_855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X1))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X1))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X2,X1)
| ~ c_Wellfounded_Owf(X0,X1)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),c_Relation_ORange(X2,X1,X1),tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ) ),
inference(cnf_transformation,[],[f782]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Orefl__on(X3,X4,X2)
| ~ c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) )
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) )
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(cnf_transformation,[],[f145]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 )
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 )
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = X1,
inference(cnf_transformation,[],[f148]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f149]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
inference(cnf_transformation,[],[f151]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Set_Oinsert(c_Pair(X0,X1,X2,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X4,c_COMBK(c_Set_Oinsert(X1,X5,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X0,X4,X2),c_COMBK(X5,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3)) = c_Product__Type_OSigma(c_Set_Oinsert(X0,X4,X2),c_COMBK(c_Set_Oinsert(X1,X5,X3),tc_fun(X3,tc_bool),X2),X2,X3),
inference(cnf_transformation,[],[f152]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[],[f153]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f154]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3 )
| ( c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Otrans(X2,X1)
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f163]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ class_Lattices_Oboolean__algebra(X1)
| ( c_HOL_Ouminus__class_Ouminus(X0,X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)) ) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X0,X1,X1),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
inference(cnf_transformation,[],[f174]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,X0,X2) = X1 )
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_891,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) = X1 )
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = X1 )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)) = X1 )
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != X1 ) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Orefl__on(X3,X4,X2)
| ~ c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( X0 = X3 )
| ( c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ( X0 = X3 )
| ( c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( X0 = X4 )
| ( c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X0,X1,X2),c_Relation_Oconverse(X3,X1,X2),tc_fun(tc_prod(X2,X1),tc_bool)) = c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),
inference(cnf_transformation,[],[f185]) ).
tcf(c_901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X1,X0,X3)
| ( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)) ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Ototal__on(X0,X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X1 )
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0 )
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(X2) = X0 )
| ~ class_Lattices_Obounded__lattice(X2)
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) != c_Orderings_Obot__class_Obot(X2) ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(X2) = X1 )
| ~ class_Lattices_Obounded__lattice(X2)
| ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) != c_Orderings_Obot__class_Obot(X2) ) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_908,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f200]) ).
tcf(c_909,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f202]) ).
tcf(c_910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X1,X2,X3,X4),c_Relation_Orel__comp(X5,X1,X2,X3,X4),tc_fun(tc_prod(X2,X4),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X5,tc_fun(tc_prod(X2,X3),tc_bool)),X1,X2,X3,X4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X1,X2,X3,X4),c_Relation_Orel__comp(X0,X5,X2,X3,X4),tc_fun(tc_prod(X2,X4),tc_bool)) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X5,tc_fun(tc_prod(X3,X4),tc_bool)),X2,X3,X4),
inference(cnf_transformation,[],[f204]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f213]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f215]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f218]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X2),X2,X1),c_Relation_ORange(c_Relation_Oconverse(X3,X1,X2),X2,X1),tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),X2,X1),
inference(cnf_transformation,[],[f783]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X2,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X0,X2,X1),
inference(cnf_transformation,[],[f224]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f226]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) )
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_931,plain,
! [X0: $i,X1: $i,X2: $i] : c_Set_Oimage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f231]) ).
tcf(c_932,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f232]) ).
tcf(c_933,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_934,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f236]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X0,X2,X3),c_Relation_ORange(X1,X2,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(cnf_transformation,[],[f237]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_937,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f784]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i,X2: $i] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f242]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ( c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X3),X2,tc_fun(X3,tc_bool)) ) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X3)) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3) = c_Set_Oinsert(X1,c_Relation_ORange(X4,X2,X3),X3),
inference(cnf_transformation,[],[f247]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) )
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Osym(X2,X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X1,X2)
| ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X0,X1,X2),c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X1 ) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Recdef_Ocut(X0,X2,X3,X4,X5) = c_Recdef_Ocut(X1,X2,X3,X4,X5) )
| ( hAPP(X0,c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X1,X2,X3,X4,X5)) != hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X1,X2,X3,X4,X5)) ) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f257]) ).
tcf(c_952,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Wellfounded_Oacyclic(X3,X2)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i] : ~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[],[f280]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ( X0 = X1 )
| ~ c_in(X0,c_Set_Oinsert(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f281]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| c_in(X0,X1,X3)
| ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c_in(X0,X2,X3)
| ~ c_in(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_968,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X1,X2)
| c_in(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2) ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_972,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f289]) ).
tcf(c_973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| c_in(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| c_in(X0,X1,X2)
| ( X1 = X3 )
| ( c_Set_Oinsert(X0,X1,X2) != c_Set_Oinsert(X0,X3,X2) ) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Set_Oinsert(X0,X1,X2) = X1 )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X1,X3,X2,X2),X0,tc_prod(X2,X2))
| ~ c_Equiv__Relations_Oequiv(X4,X0,X2)
| ~ c_in(X3,X4,X2)
| ( c_Relation_OImage(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X0,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Relation_OImage(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(cnf_transformation,[],[f302]) ).
tcf(c_986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),X3,tc_prod(X2,X2))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f785]) ).
tcf(c_987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X4,X1))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ hBOOL(hAPP(X4,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f786]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( X1 = X3 )
| ( c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0 )
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_991,plain,
! [X0: $i,X1: $i,X2: $i] : c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f309]) ).
tcf(c_992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X3,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2) )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4) = c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),
inference(cnf_transformation,[],[f313]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0),
inference(cnf_transformation,[],[f314]) ).
tcf(c_996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X0,X1,X2),c_Relation_Oconverse(X3,X1,X2),tc_fun(tc_prod(X2,X1),tc_bool)) = c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),
inference(cnf_transformation,[],[f316]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X2,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X1,X0)
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f324]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f325]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X2,X0) )
| ~ class_Lattices_Odistrib__lattice(X0) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) )
| ~ class_Lattices_Odistrib__lattice(X0) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f331]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f332]) ).
tcf(c_1014,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Otrans(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[],[f334]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Set_Oinsert(X3,X0,X2),X1,tc_fun(X2,tc_bool))
| ~ c_in(X3,X1,X2)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) )
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) )
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f340]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f342]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X0,X1,X2),c_Relation_ORange(X3,X1,X2),tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),
inference(cnf_transformation,[],[f343]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_1024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = X1 )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 )
| ~ class_Lattices_Olower__semilattice(X0) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[],[f348]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_1030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,X3,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f355]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_1035,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Oacyclic(X0,X2)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f357]) ).
tcf(c_1036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X1 )
| ( c_Set_Oimage(X0,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ) ),
inference(cnf_transformation,[],[f359]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X3,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f361]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(cnf_transformation,[],[f362]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0 )
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_1042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0 )
| ( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X0 )
| ~ c_lessequals(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_1043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[],[f368]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X3,tc_bool)),X1))
| ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_1045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X3 )
| ~ c_lessequals(X3,X0,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Set_Oinsert(X3,X0,X2),c_Set_Oinsert(X3,X1,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f374]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X0,X1,X2,X3),c_Set_Oimage(X0,X4,X2,X3),tc_fun(X3,tc_bool)) = c_Set_Oimage(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool)),X2,X3),
inference(cnf_transformation,[],[f377]) ).
tcf(c_1049,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Oirrefl(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f378]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X2,X3,X1,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_prod(X1,X1))
| ~ c_Wellfounded_Oacyclic(X0,X1) ),
inference(cnf_transformation,[],[f787]) ).
tcf(c_1051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f788]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X4,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ hBOOL(hAPP(X4,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f789]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Relation_OImage(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2)
| ~ c_Equiv__Relations_Oequiv(X1,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f382]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3)
| ~ c_in(X0,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Set_Oinsert(hAPP(X3,X0),c_Set_Oimage(X3,X1,X2,X4),X4) = c_Set_Oimage(X3,X1,X2,X4) )
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f385]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X2,X0,X3,X4),X1,tc_prod(X3,X4))
| ~ c_in(X0,c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X1,c_Relation_OImage(X4,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X3,X2),X1,X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0 = X4 )
| ~ c_in(X5,X1,X2)
| ( c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) ) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_1060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,X1,X3,X4),X2,X3)
| ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
inference(cnf_transformation,[],[f391]) ).
tcf(c_1062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f790]) ).
tcf(c_1063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f791]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Relation_OImage(X3,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) )
| ~ c_Equiv__Relations_Oequiv(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X3,X0))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X0,X2,X2,X2),c_Relation_Orel__comp(X1,X0,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_1071,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X0,X0,X1,X1,X1),c_Relation_Orel__comp(X2,X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X0,X1),X0,X1,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(X0,X1),
inference(cnf_transformation,[],[f402]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f792]) ).
tcf(c_1074,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f793]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f794]) ).
tcf(c_1076,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Wellfounded_Oacyclic(X0,X1) ),
inference(cnf_transformation,[],[f795]) ).
tcf(c_1077,plain,
! [X0: $i,X1: $i] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(cnf_transformation,[],[f410]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Relation_Oconverse(X0,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(cnf_transformation,[],[f411]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f412]) ).
tcf(c_1080,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_OImage(c_Relation_OId__on(X0,X1),X2,X1,X1) = c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f413]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Oantisym(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Ototal__on(X0,X1,X2)
| ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_1084,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Ototal__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f417]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X4,X0))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f796]) ).
tcf(c_1086,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f797]) ).
tcf(c_1087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2)))
| ~ hBOOL(hAPP(X4,X0))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f798]) ).
tcf(c_1088,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,t_a),c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f799]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X4,X0))
| ~ hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2)))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f800]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f801]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f426]) ).
tcf(c_1092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f427]) ).
tcf(c_1093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(c_Pair(X0,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f428]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X1),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X1),X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f430]) ).
tcf(c_1096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f431]) ).
tcf(c_1097,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f432]) ).
tcf(c_1098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Wellfounded_Oacyclic(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f433]) ).
tcf(c_1099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f434]) ).
tcf(c_1100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f435]) ).
tcf(c_1101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X0,X1,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f436]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f437]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X3,X1,X2,X2),X0,tc_prod(X2,X2))
| ~ c_Equiv__Relations_Oequiv(X4,X0,X2)
| ~ c_in(X1,X4,X2)
| ~ c_lessequals(c_Relation_OImage(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X0,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f438]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X1,X4,X5,X2,X3,X6),X1,X6,X3),X5,tc_prod(X6,X3))
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Orel__comp(X4,X5,X2,X6,X3),tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X0,X1,X4,X5,X2,X3,X6),X2,X6),X4,tc_prod(X2,X6))
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Orel__comp(X4,X5,X2,X6,X3),tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_1106,plain,
! [X0: $i,X1: $i] :
( ( c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X0,X1),X1,X1) = X0 )
| ~ c_in(X0,c_Relation_OId(X1),tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_1107,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(X0,X1)
| c_lessequals(c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),c_Relation_OImage(X0,c_ATP__Linkup_Osko__Wellfounded__XwfI__pf__1__1(X0,X1),X1,X1),tc_fun(X1,tc_bool)) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_1108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0 )
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X0,c_Relation_OImage(X1,X0,X2,X2),tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f445]) ).
tcf(c_1109,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X0,X1),c_Wellfounded_Oacc(X0,X1),X1) ),
inference(cnf_transformation,[],[f446]) ).
tcf(c_1110,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X0,X1),c_Wellfounded_Oacc(X0,X1),X1) ),
inference(cnf_transformation,[],[f447]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(c_Product__Type_OSigma(X1,X0,X3,X4),c_Product__Type_OSigma(X5,X2,X3,X4),tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(X0,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X0,X2,X3,X4)),hAPP(X2,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X0,X2,X3,X4)),tc_fun(X4,tc_bool)) ),
inference(cnf_transformation,[],[f448]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Relation_OImage(X1,X0,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X1,X2,X3),c_HOL_Ouminus__class_Ouminus(X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f449]) ).
tcf(c_1113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X0,X2,X3),c_HOL_Ouminus__class_Ouminus(X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f450]) ).
tcf(c_1114,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),X1,X2)
| ~ c_in(X0,c_Relation_OId__on(X1,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_1115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X0,X2),X2,X2) = X0 )
| ~ c_in(X0,c_Relation_OId__on(X1,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f453]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X0,X5,X1,X2,X3,X4),X2,X3,X3),X1,tc_prod(X3,X3))
| ( c_Recdef_Ocut(X0,X1,X2,X3,X4) = c_Recdef_Ocut(X5,X1,X2,X3,X4) ) ),
inference(cnf_transformation,[],[f454]) ).
tcf(c_1117,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Transitive__Closure_Otrancl(X0,X2),c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X0,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f455]) ).
tcf(c_1118,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X0,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X0,X1,X2,X2,X2),X0,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f456]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(X0,X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(cnf_transformation,[],[f457]) ).
tcf(c_1120,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X0,X1,X2) ),
inference(cnf_transformation,[],[f458]) ).
tcf(c_1121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_lessequals(c_Relation_Orel__comp(X0,X5,X4,X3,X7),c_Product__Type_OSigma(X1,c_COMBK(X6,tc_fun(X7,tc_bool),X4),X4,X7),tc_fun(tc_prod(X4,X7),tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X2,c_COMBK(X6,tc_fun(X7,tc_bool),X3),X3,X7),tc_fun(tc_prod(X3,X7),tc_bool))
| ~ c_lessequals(X0,c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool)) ),
inference(cnf_transformation,[],[f459]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(cnf_transformation,[],[f802]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f465]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X1,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(cnf_transformation,[],[f804]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oirrefl(X0,X1)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f468]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i] : c_lessequals(c_Relation_OId__on(X0,X1),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f469]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X0,X3,X1,X2),c_Relation_OImage(X0,X4,X1,X2),tc_fun(X2,tc_bool)) = c_Relation_OImage(X0,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1,X2) )
| ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X0,X1,X2),X2,X1) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i] :
( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X0,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i] :
( c_Nitpick_Orefl_H(X0,X1)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X0,X1),X1,X1),X0,tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Order__Relation_Ostrict__linear__order__on(X0,X1,X2)
| ~ c_Relation_Oirrefl(X1,X2)
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Ototal__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f473]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X0,X1,X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_1133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X0,X1,X3,X4),X0,X3,X4),X1,tc_prod(X3,X4))
| ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_1136,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f806]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X2,X3,X1,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f807]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X4,tc_fun(X5,tc_bool),X2),X2,X5),c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X2),X2,X5),tc_fun(tc_prod(X2,X5),tc_bool))
| ~ c_in(X3,X4,X5)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_1140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(X0,X4,tc_fun(X3,tc_bool))
| ~ c_in(X5,X1,X2)
| ~ c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X0,X3,X5,X2,X4),X0,X2)
| c_lessequals(c_Product__Type_OSigma(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X5,X2,X4),tc_fun(tc_prod(X2,X4),tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f483]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(c_Relation_OImage(X0,X5,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X0,c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool)) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(cnf_transformation,[],[f808]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X0,X4,X2)
| ( X0 = X1 )
| ~ c_lessequals(X3,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f809]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X0,X1,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f488]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X3,X0,X1,X2),X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f489]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f491]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(hAPP(X0,X5),X4,X3)
| ~ c_in(X5,X1,X2)
| ~ c_lessequals(c_Set_Oimage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f492]) ).
tcf(c_1151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_lessequals(c_Relation_OImage(X0,X4,X2,X3),c_Relation_OImage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Set_Oimage(X3,X0,X2,X4),c_Set_Oimage(X3,X1,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f496]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(cnf_transformation,[],[f810]) ).
tcf(c_1155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Relation_Osingle__valued(X0,X2,X3)
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(cnf_transformation,[],[f498]) ).
tcf(c_1157,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Oantisym(X0,X2)
| ~ c_Relation_Oantisym(X1,X2)
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Wellfounded_Owf(X0,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_1161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X0,X3))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_1162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_1164,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,X0,tc_fun(X1,tc_bool)),
inference(cnf_transformation,[],[f507]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X1,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_1166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X1,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f811]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f513]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f812]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_lessequals(c_Relation_Orel__comp(X0,X4,X2,X3,X6),c_Relation_Orel__comp(X1,X5,X2,X3,X6),tc_fun(tc_prod(X2,X6),tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) )
| ~ c_lessequals(X1,X0,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f813]) ).
tcf(c_1176,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Wellfounded_Oacc(X1,X2),c_Wellfounded_Oacc(X0,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X0,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(cnf_transformation,[],[f519]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(hAPP(X0,X4),hAPP(X1,X4),X3)
| ~ class_HOL_Oord(X3)
| ~ c_lessequals(X0,X1,tc_fun(X2,X3)) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[],[f524]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X0,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f525]) ).
tcf(c_1183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X0,X1,X2),X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f814]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X3,X0,X1,X2),X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f815]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1),X0,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_Relation_Otrans(X0,X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f528]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,X0))
| ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f530]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f817]) ).
tcf(c_1189,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f532]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f818]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f819]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f822]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f823]) ).
tcf(c_1196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X1,X0,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f824]) ).
tcf(c_1197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| c_in(c_Pair(X1,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X3,X2,X2)
| ~ c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f825]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f827]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f828]) ).
tcf(c_1201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f544]) ).
tcf(c_1202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP(c_split(X0,X1,X2,X3),c_Pair(X4,X5,X1,X2)) = hAPP(hAPP(X0,X4),X5),
inference(cnf_transformation,[],[f547]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( hBOOL(hAPP(hAPP(hAPP(X0,X4),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_split(X0,X1,X2,tc_fun(X3,tc_bool)),c_Pair(X4,X5,X1,X2)),X6)) ),
inference(cnf_transformation,[],[f548]) ).
tcf(c_1209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(hAPP(X3,X0),c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f552]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f553]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X1),X1,X1),
inference(cnf_transformation,[],[f554]) ).
tcf(c_1212,plain,
! [X0: $i,X1: $i] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f555]) ).
tcf(c_1213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,X3))
| ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f556]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i] :
( ( c_Transitive__Closure_Otrancl(X0,X1) = X0 )
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f557]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,X2))
| ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
| ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1))) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_1216,plain,
! [X0: $i,X1: $i] :
( c_Relation_Osym(X0,X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_1217,plain,
! [X0: $i,X1: $i] :
( c_Relation_Osym(c_Relation_Oconverse(X0,X1,X1),X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f560]) ).
tcf(c_1218,plain,
! [X0: $i,X1: $i] : c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1,X1) = c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),
inference(cnf_transformation,[],[f829]) ).
tcf(c_1219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X0,X1,X3,X4),X2,X3)
| ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
inference(cnf_transformation,[],[f563]) ).
tcf(c_1220,plain,
! [X0: $i] : c_Relation_Osym(c_Relation_OId(X0),X0),
inference(cnf_transformation,[],[f564]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] : c_Relation_Otrans(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[],[f565]) ).
tcf(c_1222,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_Orel__comp(c_Relation_OId(X0),X1,X0,X0,X2) = X1,
inference(cnf_transformation,[],[f566]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_Orel__comp(X0,c_Relation_OId(X1),X2,X1,X1) = X0,
inference(cnf_transformation,[],[f567]) ).
tcf(c_1224,plain,
! [X0: $i,X1: $i] : c_Relation_Oantisym(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[],[f568]) ).
tcf(c_1225,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X0,X1,X1),X1) ),
inference(cnf_transformation,[],[f569]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(cnf_transformation,[],[f570]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f571]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f830]) ).
tcf(c_1229,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f573]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(X0,X1)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X0,X0,X1,X1,X1),X1) ),
inference(cnf_transformation,[],[f574]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i] : c_Relation_OImage(c_Relation_OId(X0),X1,X0,X0) = X1,
inference(cnf_transformation,[],[f575]) ).
tcf(c_1232,plain,
! [X0: $i] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0),
inference(cnf_transformation,[],[f576]) ).
tcf(c_1233,plain,
! [X0: $i,X1: $i] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),X1,X1) = X0,
inference(cnf_transformation,[],[f831]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i] :
( ( c_Relation_Oconverse(X0,X1,X1) = X0 )
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f578]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i] :
( c_Relation_Osym(X0,X1)
| ( c_Relation_Oconverse(X0,X1,X1) != X0 ) ),
inference(cnf_transformation,[],[f579]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ORange(X0,X1,X1),
inference(cnf_transformation,[],[f580]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X0,X1),X1),
inference(cnf_transformation,[],[f581]) ).
tcf(c_1238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X2),c_Relation_Oconverse(X3,X4,X1),X2,X1,X4) = c_Relation_Oconverse(c_Relation_Orel__comp(X3,X0,X4,X1,X2),X4,X2),
inference(cnf_transformation,[],[f582]) ).
tcf(c_1239,plain,
! [X0: $i,X1: $i] : c_Relation_Osym(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[],[f583]) ).
tcf(c_1240,plain,
! [X0: $i,X1: $i] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[],[f584]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X0,X2,X1,X3),X3)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f585]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X0,X1,X1,X1) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1),
inference(cnf_transformation,[],[f832]) ).
tcf(c_1243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Relation_Osym(c_Relation_Oinv__image(X0,X2,X1,X3),X3)
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[],[f588]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f833]) ).
tcf(c_1245,plain,
! [X0: $i,X1: $i] : c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(cnf_transformation,[],[f834]) ).
tcf(c_1246,plain,
! [X0: $i,X1: $i] :
( c_Relation_Otrans(X0,X1)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1) ),
inference(cnf_transformation,[],[f592]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( c_Relation_Otrans(c_Relation_Oconverse(X0,X1,X1),X1)
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f593]) ).
tcf(c_1248,plain,
! [X0: $i] : c_Relation_Oconverse(c_Relation_OId(X0),X0,X0) = c_Relation_OId(X0),
inference(cnf_transformation,[],[f595]) ).
tcf(c_1249,plain,
! [X0: $i,X1: $i] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X0,X1),X1)
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[],[f596]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Relation_Orel__comp(c_Relation_Orel__comp(X0,X1,X2,X3,X4),X5,X2,X4,X6) = c_Relation_Orel__comp(X0,c_Relation_Orel__comp(X1,X5,X3,X4,X6),X2,X3,X6),
inference(cnf_transformation,[],[f597]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Relation_Oconverse(c_Relation_Oinv__image(X0,X1,X2,X3),X3,X3) = c_Relation_Oinv__image(c_Relation_Oconverse(X0,X2,X2),X1,X2,X3),
inference(cnf_transformation,[],[f598]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),
inference(cnf_transformation,[],[f600]) ).
tcf(c_1253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Relation_Otrans(c_Relation_Oinv__image(X0,X2,X1,X3),X3)
| ~ c_Relation_Otrans(X0,X1) ),
inference(cnf_transformation,[],[f601]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1) = c_Relation_OId__on(X0,X1),
inference(cnf_transformation,[],[f603]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X0,X1,X1),X1,X1),X0,X1)
| ( c_Relation_Orel__comp(c_Relation_Oconverse(X0,X1,X1),X0,X1,X1,X1) != X0 ) ),
inference(cnf_transformation,[],[f835]) ).
tcf(c_1256,plain,
! [X0: $i] : c_Relation_Oantisym(c_Relation_OId(X0),X0),
inference(cnf_transformation,[],[f605]) ).
tcf(c_1257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X3,X2),X1,X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f608]) ).
tcf(c_1258,plain,
! [X0: $i,X1: $i] : c_Relation_ORange(c_Relation_OId__on(X0,X1),X1,X1) = X0,
inference(cnf_transformation,[],[f609]) ).
tcf(c_1259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X0,X3,X1,X2,X4),X1,X4)
| ~ c_Relation_Osingle__valued(X3,X2,X4)
| ~ c_Relation_Osingle__valued(X0,X1,X2) ),
inference(cnf_transformation,[],[f610]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1) = X0,
inference(cnf_transformation,[],[f611]) ).
tcf(c_1261,plain,
! [X0: $i] : c_Relation_Otrans(c_Relation_OId(X0),X0),
inference(cnf_transformation,[],[f612]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) = X1 )
| ~ c_Equiv__Relations_Oequiv(X0,X1,X2) ),
inference(cnf_transformation,[],[f613]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f836]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oantisym(X0,X1)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1) ),
inference(cnf_transformation,[],[f616]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i] :
( c_Relation_Oantisym(c_Relation_Oconverse(X0,X1,X1),X1)
| ~ c_Relation_Oantisym(X0,X1) ),
inference(cnf_transformation,[],[f617]) ).
tcf(c_1266,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,X2))
| ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
| ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1))) ),
inference(cnf_transformation,[],[f618]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Equiv__Relations_Oequiv(X0,X1,X2) ),
inference(cnf_transformation,[],[f619]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1),
inference(cnf_transformation,[],[f837]) ).
tcf(c_1269,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Osym(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X0,X1,X2) ),
inference(cnf_transformation,[],[f621]) ).
tcf(c_1270,plain,
! [X0: $i,X1: $i] : c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1,X1) = c_Transitive__Closure_Otrancl(X0,X1),
inference(cnf_transformation,[],[f838]) ).
tcf(c_1271,plain,
! [X0: $i,X1: $i,X2: $i] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1),X1,X2) = c_Relation_ORange(X0,X1,X2),
inference(cnf_transformation,[],[f839]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Ototal__on(X0,X1,X2)
| ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(cnf_transformation,[],[f628]) ).
tcf(c_1273,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Ototal__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Ototal__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f629]) ).
tcf(c_1274,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Relation_Otrans(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X0,X1,X2) ),
inference(cnf_transformation,[],[f630]) ).
tcf(c_1275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X3,X0))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X3,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(cnf_transformation,[],[f631]) ).
tcf(c_1276,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f840]) ).
tcf(c_1277,plain,
! [X0: $i,X1: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X0,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(cnf_transformation,[],[f841]) ).
tcf(c_1278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
| ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f842]) ).
tcf(c_1279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| c_in(X0,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f637]) ).
tcf(c_1281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,X0))
| ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f639]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_in(hAPP(hAPP(X5,X0),X1),c_Set_Oimage(c_split(X5,X2,X3,X6),X4,tc_prod(X2,X3),X6),X6)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f640]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2) ),
inference(cnf_transformation,[],[f844]) ).
tcf(c_1284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X1,X3))
| c_in(X0,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f642]) ).
tcf(c_1285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,X0))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f643]) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ c_Wellfounded_Owf(X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X0,X1,X3)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f644]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X0,X1,X2,X3),X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2) ),
inference(cnf_transformation,[],[f845]) ).
tcf(c_1288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X0,X1,X3,X4),X0,X3,X4),X1,tc_prod(X3,X4))
| ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
inference(cnf_transformation,[],[f646]) ).
tcf(c_1289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f846]) ).
tcf(c_1290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X0,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(X0,c_Relation_ORange(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f648]) ).
tcf(c_1291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_in(X0,hAPP(c_split(X1,X5,X6,tc_fun(X4,tc_bool)),c_Pair(X2,X3,X5,X6)),X4)
| ~ c_in(X0,hAPP(hAPP(X1,X2),X3),X4) ),
inference(cnf_transformation,[],[f649]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X5 )
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_in(c_Pair(X0,X5,X2,X3),X4,tc_prod(X2,X3))
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f651]) ).
tcf(c_1294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( hAPP(c_Recdef_Ocut(X4,X3,X1,X2,X5),X0) = hAPP(X4,X0) )
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f653]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_FunDef_Oin__rel(X4,X0,X1,X2,X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f654]) ).
tcf(c_1296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X1,X2,X3,X4),X0,tc_prod(X3,X4))
| ~ c_FunDef_Oin__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f655]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X3,X2)
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f657]) ).
tcf(c_1300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2))
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f659]) ).
tcf(c_1301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f660]) ).
tcf(c_1302,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f661]) ).
tcf(c_1303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f662]) ).
tcf(c_1304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f663]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f847]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f848]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X3,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f849]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),tc_prod(X1,X1)),
inference(cnf_transformation,[],[f851]) ).
tcf(c_1311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f670]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f672]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f674]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( hAPP(X0,X6) = hAPP(X5,X6) )
| ~ c_in(c_Pair(X6,X2,X3,X3),X1,tc_prod(X3,X3))
| ( c_Recdef_Ocut(X0,X1,X2,X3,X4) != c_Recdef_Ocut(X5,X1,X2,X3,X4) ) ),
inference(cnf_transformation,[],[f675]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f676]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(X0,X1) ),
inference(cnf_transformation,[],[f677]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[],[f678]) ).
tcf(c_1319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_Pair(X1,X2,X5,X5),c_Relation_Oinv__image(X4,X0,X3,X5),tc_prod(X5,X5))
| ~ c_in(c_Pair(hAPP(X0,X1),hAPP(X0,X2),X3,X3),X4,tc_prod(X3,X3)) ),
inference(cnf_transformation,[],[f679]) ).
tcf(c_1320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_Pair(hAPP(X4,X0),hAPP(X4,X1),X5,X5),X3,tc_prod(X5,X5))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oinv__image(X3,X4,X5,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f680]) ).
tcf(c_1322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Osym(X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f682]) ).
tcf(c_1323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_in(c_Pair(X0,X5,X2,X6),c_Relation_Orel__comp(X4,X7,X2,X3,X6),tc_prod(X2,X6))
| ~ c_in(c_Pair(X1,X5,X3,X6),X7,tc_prod(X3,X6))
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f683]) ).
tcf(c_1324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f684]) ).
tcf(c_1325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f685]) ).
tcf(c_1327,plain,
! [X0: $i,X1: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId(X1),tc_prod(X1,X1)),
inference(cnf_transformation,[],[f687]) ).
tcf(c_1328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X3 )
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f688]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X1 = X3 )
| ( X0 = X3 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f689]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[],[f691]) ).
tcf(c_1332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X1 = X3 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f692]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f868]) ).
tcf(c_1335,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[],[f696]) ).
tcf(c_1336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X1 = X3 )
| ( X0 = X1 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f697]) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X1 = X3 )
| ( X0 = X3 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f698]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f869]) ).
tcf(c_1339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X3 )
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f700]) ).
tcf(c_1340,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f701]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(c_Pair(X2,X0,X5,X3),c_Product__Type_OSigma(X4,X1,X5,X3),tc_prod(X5,X3))
| ~ c_in(X2,X4,X5)
| ~ c_in(X0,hAPP(X1,X2),X3) ),
inference(cnf_transformation,[],[f703]) ).
tcf(c_1344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
| ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f705]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f707]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f708]) ).
tcf(c_1348,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f709]) ).
tcf(c_1349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X1,X4,X2)
| ~ c_Equiv__Relations_Oequiv(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f710]) ).
tcf(c_1350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X0,X4,X2)
| ~ c_Equiv__Relations_Oequiv(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f711]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X1,c_Relation_ORange(X4,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f713]) ).
tcf(c_1354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X0,c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f853]) ).
tcf(c_1355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X1,hAPP(X5,X0),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f716]) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X0,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f717]) ).
tcf(c_1357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))
| c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))
| ( X0 = X3 )
| ~ c_Relation_Ototal__on(X1,X4,X2)
| ~ c_in(X3,X1,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f719]) ).
tcf(c_1359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X1,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f721]) ).
tcf(c_1360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X0,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f722]) ).
tcf(c_1361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Orefl__on(X1,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f723]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X5 )
| ( c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ) ),
inference(cnf_transformation,[],[f726]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0 = X4 )
| ( c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ) ),
inference(cnf_transformation,[],[f727]) ).
tcf(c_1368,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f732]) ).
tcf(c_1369,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X1,X0))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f733]) ).
tcf(c_1370,plain,
! [X0: $i] :
( c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f863]) ).
tcf(c_1371,plain,
! [X0: $i] :
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f864]) ).
tcf(c_1372,plain,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(cnf_transformation,[],[f740]) ).
tcf(c_1373,plain,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(cnf_transformation,[],[f741]) ).
tcf(c_1375,plain,
v_a_H____ != v_b_H____,
inference(cnf_transformation,[],[f865]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 )
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f744]) ).
tcf(c_1377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 )
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f746]) ).
tcf(c_1378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 )
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f747]) ).
tcf(c_1379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( X0 = X1 )
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f749]) ).
tcf(c_1380,negated_conjecture,
( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f866]) ).
tcf(c_1381,negated_conjecture,
( c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[],[f867]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(X1,X0))
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f754]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Olower__semilattice(tc_fun(X1,X0))
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f755]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Odistrib__lattice(tc_fun(X1,X0))
| ~ class_Lattices_Odistrib__lattice(X0) ),
inference(cnf_transformation,[],[f756]) ).
tcf(c_1385,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Obounded__lattice(tc_fun(X1,X0))
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f757]) ).
tcf(c_1386,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(X1,X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f758]) ).
tcf(c_1387,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Opreorder(tc_fun(X1,X0))
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[],[f759]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Olattice(tc_fun(X1,X0))
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f760]) ).
tcf(c_1389,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oorder(tc_fun(X1,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f761]) ).
tcf(c_1390,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Obot(tc_fun(X1,X0))
| ~ class_Orderings_Obot(X0) ),
inference(cnf_transformation,[],[f762]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i] :
( class_HOL_Oord(tc_fun(X1,X0))
| ~ class_HOL_Oord(X0) ),
inference(cnf_transformation,[],[f763]) ).
tcf(c_1392,plain,
class_Lattices_Oupper__semilattice(tc_bool),
inference(cnf_transformation,[],[f764]) ).
tcf(c_1393,plain,
class_Lattices_Olower__semilattice(tc_bool),
inference(cnf_transformation,[],[f765]) ).
tcf(c_1394,plain,
class_Lattices_Odistrib__lattice(tc_bool),
inference(cnf_transformation,[],[f766]) ).
tcf(c_1395,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(cnf_transformation,[],[f767]) ).
tcf(c_1396,plain,
class_Lattices_Oboolean__algebra(tc_bool),
inference(cnf_transformation,[],[f768]) ).
tcf(c_1397,plain,
class_Orderings_Opreorder(tc_bool),
inference(cnf_transformation,[],[f769]) ).
tcf(c_1398,plain,
class_Lattices_Olattice(tc_bool),
inference(cnf_transformation,[],[f770]) ).
tcf(c_1399,plain,
class_Orderings_Oorder(tc_bool),
inference(cnf_transformation,[],[f771]) ).
tcf(c_1400,plain,
class_Orderings_Obot(tc_bool),
inference(cnf_transformation,[],[f772]) ).
tcf(c_1401,plain,
class_HOL_Oord(tc_bool),
inference(cnf_transformation,[],[f773]) ).
tcf(c_1402,plain,
! [X0: $i,X1: $i] : c_fequal(X0,X0,X1),
inference(cnf_transformation,[],[f774]) ).
tcf(c_1403,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_fequal(X0,X1,X2) ),
inference(cnf_transformation,[],[f775]) ).
tcf(c_35630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_Set_Oinsert(c_Pair(X0,c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X6,c_COMBK(c_Product__Type_OSigma(c_Set_Oinsert(X1,X7,X3),c_COMBK(c_Set_Oinsert(X2,X8,X4),tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool),X5),X5,tc_prod(X3,X4)),c_Product__Type_OSigma(c_Set_Oinsert(X0,X6,X5),c_COMBK(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X7,c_COMBK(c_Set_Oinsert(X2,X8,X4),tc_fun(X4,tc_bool),X3),X3,X4),c_Product__Type_OSigma(c_Set_Oinsert(X1,X7,X3),c_COMBK(X8,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)),tc_fun(tc_prod(X3,X4),tc_bool),X5),X5,tc_prod(X3,X4)),tc_fun(tc_prod(X5,tc_prod(X3,X4)),tc_bool)),tc_prod(X5,tc_prod(X3,X4))) = c_Product__Type_OSigma(c_Set_Oinsert(X0,X6,X5),c_COMBK(c_Product__Type_OSigma(c_Set_Oinsert(X1,X7,X3),c_COMBK(c_Set_Oinsert(X2,X8,X4),tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool),X5),X5,tc_prod(X3,X4)),
inference(superposition,[status(thm)],[c_872,c_872]) ).
tcf(c_35631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_Set_Oinsert(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),X5),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X6,c_COMBK(c_Set_Oinsert(X1,X7,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X0,X6,X2),c_COMBK(X7,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),c_COMBK(c_Set_Oinsert(X4,X8,X5),tc_fun(X5,tc_bool),tc_prod(X2,X3)),tc_prod(X2,X3),X5),c_Product__Type_OSigma(c_Product__Type_OSigma(c_Set_Oinsert(X0,X6,X2),c_COMBK(c_Set_Oinsert(X1,X7,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_COMBK(X8,tc_fun(X5,tc_bool),tc_prod(X2,X3)),tc_prod(X2,X3),X5),tc_fun(tc_prod(tc_prod(X2,X3),X5),tc_bool)),tc_prod(tc_prod(X2,X3),X5)) = c_Product__Type_OSigma(c_Product__Type_OSigma(c_Set_Oinsert(X0,X6,X2),c_COMBK(c_Set_Oinsert(X1,X7,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_COMBK(c_Set_Oinsert(X4,X8,X5),tc_fun(X5,tc_bool),tc_prod(X2,X3)),tc_prod(X2,X3),X5),
inference(superposition,[status(thm)],[c_872,c_872]) ).
tcf(c_43432,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_35631,c_35630,c_1403,c_1402,c_1401,c_1400,c_1399,c_1398,c_1397,c_1396,c_1395,c_1394,c_1393,c_1392,c_1391,c_1390,c_1389,c_1388,c_1387,c_1386,c_1385,c_1384,c_1383,c_1382,c_1381,c_1380,c_1379,c_1378,c_1377,c_1376,c_1373,c_1372,c_1369,c_1368,c_1370,c_1371,c_1365,c_1364,c_1375,c_1360,c_1359,c_1361,c_1357,c_1356,c_1355,c_1354,c_1352,c_1350,c_1349,c_1348,c_1347,c_1346,c_1344,c_1342,c_1340,c_1339,c_1338,c_1337,c_1336,c_1335,c_1333,c_1332,c_1331,c_1329,c_1328,c_1327,c_1325,c_1310,c_1308,c_1306,c_1305,c_1289,c_1287,c_1283,c_1277,c_1276,c_1270,c_1268,c_1263,c_1255,c_1245,c_1244,c_1242,c_1233,c_1228,c_1218,c_1200,c_1199,c_1197,c_1196,c_1195,c_1194,c_1191,c_1190,c_1188,c_1278,c_1184,c_1183,c_1175,c_1173,c_1167,c_1166,c_1154,c_1144,c_1143,c_1138,c_1137,c_1124,c_1122,c_1090,c_1089,c_1088,c_1087,c_1086,c_1085,c_1076,c_1075,c_1074,c_1073,c_1063,c_1062,c_1052,c_1051,c_1050,c_1045,c_987,c_986,c_937,c_926,c_858,c_842,c_840,c_822,c_805,c_745,c_1271,c_1324,c_1323,c_1322,c_1320,c_1319,c_1318,c_1317,c_1316,c_1315,c_1314,c_1313,c_1311,c_1304,c_1303,c_1302,c_1301,c_1300,c_1298,c_1296,c_1295,c_1294,c_1292,c_1291,c_1290,c_1288,c_1286,c_1285,c_1284,c_1282,c_1281,c_1279,c_1275,c_1274,c_1273,c_1272,c_1269,c_1267,c_1266,c_1265,c_1264,c_1262,c_1261,c_1260,c_1259,c_1258,c_1257,c_1256,c_1254,c_1253,c_1252,c_1251,c_1250,c_1249,c_1248,c_1247,c_1246,c_1243,c_1241,c_1240,c_1239,c_1238,c_1237,c_1236,c_1235,c_1234,c_1232,c_1231,c_1230,c_1229,c_1227,c_1226,c_1225,c_1224,c_1223,c_1222,c_1221,c_1220,c_1219,c_1217,c_1216,c_1215,c_1214,c_1213,c_1212,c_1211,c_1210,c_1209,c_1205,c_1204,c_1202,c_1201,c_1189,c_1187,c_1185,c_1182,c_1181,c_1177,c_1176,c_1174,c_1172,c_1170,c_1165,c_1164,c_1162,c_1160,c_1159,c_1158,c_1157,c_1161,c_1155,c_1153,c_1151,c_1150,c_1149,c_1148,c_1147,c_1146,c_1145,c_1142,c_1141,c_1140,c_1139,c_1136,c_1135,c_1134,c_1133,c_1132,c_1131,c_1130,c_1129,c_1128,c_1127,c_1126,c_1123,c_1121,c_1120,c_1119,c_1118,c_1117,c_1116,c_1115,c_1114,c_1113,c_1112,c_1111,c_1110,c_1109,c_1108,c_1107,c_1106,c_1105,c_1104,c_1103,c_1102,c_1101,c_1100,c_1099,c_1098,c_1097,c_1096,c_1095,c_1094,c_1093,c_1092,c_1091,c_1084,c_1083,c_1082,c_1081,c_1080,c_1079,c_1078,c_1077,c_1072,c_1071,c_1070,c_1069,c_1068,c_1067,c_1066,c_1065,c_1061,c_1060,c_1059,c_1058,c_1057,c_1056,c_1055,c_1054,c_1053,c_1049,c_1048,c_1046,c_1044,c_1043,c_1042,c_1041,c_1039,c_1038,c_1037,c_1035,c_1034,c_1033,c_1030,c_1029,c_1032,c_1031,c_1026,c_1025,c_1024,c_1023,c_1022,c_1021,c_1020,c_1019,c_1018,c_1016,c_1015,c_1014,c_1013,c_1012,c_1011,c_1010,c_1008,c_1006,c_1005,c_1004,c_1003,c_1002,c_999,c_998,c_997,c_996,c_995,c_994,c_993,c_992,c_989,c_988,c_985,c_984,c_980,c_979,c_978,c_977,c_974,c_973,c_972,c_969,c_968,c_967,c_966,c_965,c_964,c_963,c_959,c_958,c_957,c_955,c_953,c_952,c_951,c_950,c_949,c_948,c_947,c_946,c_945,c_944,c_943,c_942,c_941,c_939,c_938,c_936,c_935,c_934,c_933,c_932,c_930,c_929,c_928,c_927,c_925,c_924,c_923,c_922,c_921,c_920,c_917,c_916,c_919,c_918,c_913,c_912,c_911,c_910,c_909,c_908,c_907,c_906,c_905,c_904,c_903,c_902,c_901,c_900,c_899,c_898,c_897,c_896,c_895,c_894,c_893,c_892,c_891,c_890,c_889,c_888,c_887,c_886,c_885,c_884,c_883,c_882,c_881,c_880,c_879,c_878,c_877,c_876,c_875,c_874,c_873,c_872,c_871,c_870,c_869,c_868,c_867,c_866,c_865,c_864,c_863,c_862,c_861,c_860,c_857,c_856,c_855,c_854,c_853,c_852,c_851,c_850,c_849,c_848,c_847,c_846,c_845,c_844,c_843,c_841,c_838,c_837,c_836,c_835,c_991,c_833,c_832,c_831,c_830,c_829,c_827,c_828,c_825,c_824,c_1036,c_821,c_820,c_819,c_818,c_817,c_816,c_815,c_814,c_813,c_812,c_810,c_809,c_808,c_807,c_806,c_804,c_803,c_802,c_798,c_797,c_796,c_793,c_792,c_791,c_790,c_789,c_788,c_787,c_786,c_785,c_784,c_783,c_782,c_779,c_778,c_781,c_775,c_774,c_776,c_772,c_771,c_770,c_769,c_768,c_767,c_766,c_765,c_764,c_763,c_762,c_761,c_760,c_759,c_931,c_756,c_755,c_754,c_753,c_752,c_751,c_750,c_749,c_748,c_747,c_746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT069-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 08:42:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 88.55/13.35 % SZS status Started for theBenchmark.p
% 88.55/13.35 % SZS status Unsatisfiable for theBenchmark.p
% 88.55/13.35
% 88.55/13.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 88.55/13.35
% 88.55/13.35 % ------ iProver source info
% 88.55/13.35
% 88.55/13.35 % git: date: 2026-07-19 20:42:38 +0200
% 88.55/13.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 88.55/13.35 % git: non_committed_changes: false
% 88.55/13.35
% 88.55/13.35 % ------ Parsing...% successful
% 88.55/13.35
% 88.55/13.35
% 88.55/13.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 88.55/13.35
% 88.55/13.35 % ------ Preprocessing...%
% 88.55/13.35
% 88.55/13.35 % ------ Preprocessing...%
% 88.55/13.35
% 88.55/13.35 % ------ Preprocessing...
% 88.55/13.35 % ------ Proving...
% 88.55/13.35 % ------ Problem Properties
% 88.55/13.35
% 88.55/13.35 %
% 88.55/13.35 % clauses 577
% 88.55/13.35 % conjectures 2
% 88.55/13.35 % EPR 26
% 88.55/13.35 % Horn 507
% 88.55/13.35 % unary 157
% 88.55/13.35 % binary 251
% 88.55/13.35 % lits 1223
% 88.55/13.35 % lits eq 266
% 88.55/13.35 % fd_pure 0
% 88.55/13.35 % fd_pseudo 0
% 88.55/13.35 % fd_cond 0
% 88.55/13.35 % fd_pseudo_cond 52
% 88.55/13.35 % AC symbols 0
% 88.55/13.35
% 88.55/13.35 % ------ Input Options Time Limit: Unbounded
% 88.55/13.35
% 88.55/13.35
% 88.55/13.35 % ------
% 88.55/13.35 % Current options:
% 88.55/13.35 % ------
% 88.55/13.35
% 88.55/13.35
% 88.55/13.35 %
% 88.55/13.35
% 88.55/13.35 % ------ Proving...
% 88.55/13.35 %
% 88.55/13.35
% 88.55/13.35 % SZS status Unsatisfiable for theBenchmark.p
% 88.55/13.35
% 88.55/13.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 88.55/13.38
% 88.55/13.38
%------------------------------------------------------------------------------