TSTP Solution File: SWW354+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW354+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:09:12 EDT 2023
% Result : ContradictoryAxioms 83.86s 13.20s
% Output : CNFRefutation 83.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of formulae : 177 ( 129 unt; 0 def)
% Number of atoms : 257 ( 165 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 150 ( 70 ~; 55 |; 9 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 44 ( 44 usr; 10 con; 0-3 aty)
% Number of variables : 353 ( 29 sgn; 189 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_vimage__Collect__eq,axiom,
! [X17,X2,X11,X5] : hAPP(c_Set_Ovimage(X5,X11,X2),hAPP(c_Set_OCollect(X11),X17)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X11,tc_HOL_Obool,X5),X17),X2)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__def,axiom,
! [X17,X5] : hAPP(c_Set_OCollect(X5),X17) = X17,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Collect__def) ).
fof(fact_vimage__id,axiom,
! [X13,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X13) = X13,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_vimage__id) ).
fof(fact_option_Oinject,axiom,
! [X200,X6,X5] :
( hAPP(c_Option_Ooption_OSome(X5),X6) = hAPP(c_Option_Ooption_OSome(X5),X200)
<=> X6 = X200 ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_option_Oinject) ).
fof(fact_not__None__eq,axiom,
! [X5,X10] :
( X10 != c_Option_Ooption_ONone(X5)
<=> ? [X97] : X10 = hAPP(c_Option_Ooption_OSome(X5),X97) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_not__None__eq) ).
fof(fact_option_Osimps_I2_J,axiom,
! [X164,X5] : c_Option_Ooption_ONone(X5) != hAPP(c_Option_Ooption_OSome(X5),X164),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_option_Osimps_I2_J) ).
fof(help_c__COMBB__1,axiom,
! [X36,X20,X17,X82,X5,X11] : hAPP(hAPP(hAPP(c_COMBB(X11,X5,X82),X17),X20),X36) = hAPP(X17,hAPP(X20,X36)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',help_c__COMBB__1) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_ext) ).
fof(fact_number__of__is__id,axiom,
! [X114] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X114) = X114,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_number__of__is__id) ).
fof(fact_Collect__empty__eq,axiom,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Collect__empty__eq) ).
fof(fact_Collect__neg__eq,axiom,
! [X17,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Collect__neg__eq) ).
fof(fact_add__Pls,axiom,
! [X114] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X114) = X114,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_add__Pls) ).
fof(help_c__fconj__2,axiom,
! [X20,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X20))
| hBOOL(X17) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',help_c__fconj__2) ).
fof(fact_Diff__eq,axiom,
! [X79,X13,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X79) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X79)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Diff__eq) ).
fof(fact_Compl__partition,axiom,
! [X13,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Compl__partition) ).
fof(help_c__fNot__1,axiom,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',help_c__fNot__1) ).
fof(fact_Compl__Un,axiom,
! [X79,X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X79)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X79)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Compl__Un) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X29,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X29))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X10))
| X10 = X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_Collect__mem__eq,axiom,
! [X13,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13)) = X13,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Collect__mem__eq) ).
fof(fact_Compl__Diff__eq,axiom,
! [X79,X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X79)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)),X79),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Compl__Diff__eq) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X13),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_double__complement,axiom,
! [X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)) = X13,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_double__complement) ).
fof(fact_UN__extend__simps_I3_J,axiom,
! [X79,X13,X11,X5,X80] :
( ( X80 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11,tc_HOL_Obool)),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X11,tc_HOL_Obool)),X80),X79)) = X13 )
& ( X80 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11,tc_HOL_Obool)),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X11,tc_HOL_Obool)),X80),X79)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X11,tc_HOL_Obool)),X80),hAPP(hAPP(c_COMBB(tc_fun(X11,tc_HOL_Obool),tc_fun(X11,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11,tc_HOL_Obool)),X13)),X79)) ) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_UN__extend__simps_I3_J) ).
fof(fact_neg__number__of__Min,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_neg__number__of__Min) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X77] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X77) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X77)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_less__eq__Suc__le__raw) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X98] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X98))
<=> ? [X144] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X98))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X144)) ) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_finite__nat__set__iff__bounded) ).
fof(help_c__COMBC__1,axiom,
! [X36,X20,X17,X5,X82,X11] : hAPP(hAPP(hAPP(c_COMBC(X11,X82,X5),X17),X20),X36) = hAPP(hAPP(X17,X36),X20),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',help_c__COMBC__1) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Pls__def) ).
fof(fact_Un__empty__left,axiom,
! [X79,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X79) = X79,
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Un__empty__left) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(fact_le__refl,axiom,
! [X81] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X81),X81)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_le__refl) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_One__nat__def) ).
fof(fact_nat__number__of__def,axiom,
! [X146] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X146) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X146)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_nat__number__of__def) ).
fof(fact_rangeI,axiom,
! [X11,X10,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X10)),hAPP(c_Set_Oimage(X11,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_rangeI) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_one__is__num__one) ).
fof(fact_Un__Diff__cancel,axiom,
! [X79,X13,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X79),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X79),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Un__Diff__cancel) ).
fof(fact_card__infinite,axiom,
! [X13,X5] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
=> hAPP(c_Finite__Set_Ocard(X5),X13) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_card__infinite) ).
fof(fact_card__UNIV__bool,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_card__UNIV__bool) ).
fof(fact_finite__imageI,axiom,
! [X78,X11,X67,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X67))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X11),hAPP(c_Set_Oimage(X5,X11,X78),X67))) ),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_finite__imageI) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_semiring__norm_I115_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X111),
file('/export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p',fact_Zero__not__Suc) ).
fof(c_0_43,plain,
! [X6848,X6849,X6850,X6851] : hAPP(c_Set_Ovimage(X6851,X6850,X6849),hAPP(c_Set_OCollect(X6850),X6848)) = hAPP(c_Set_OCollect(X6851),hAPP(hAPP(c_COMBB(X6850,tc_HOL_Obool,X6851),X6848),X6849)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_44,plain,
! [X2595,X2596] : hAPP(c_Set_OCollect(X2596),X2595) = X2595,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_45,plain,
! [X6946,X6947] : hAPP(c_Set_Ovimage(X6947,X6947,c_Fun_Oid(X6947)),X6946) = X6946,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_46,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_48,plain,
! [X2752,X2753,X2754] :
( ( hAPP(c_Option_Ooption_OSome(X2754),X2753) != hAPP(c_Option_Ooption_OSome(X2754),X2752)
| X2753 = X2752 )
& ( X2753 != X2752
| hAPP(c_Option_Ooption_OSome(X2754),X2753) = hAPP(c_Option_Ooption_OSome(X2754),X2752) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])]) ).
fof(c_0_49,plain,
! [X2755,X2756,X2758,X2759,X2760] :
( ( X2756 = c_Option_Ooption_ONone(X2755)
| X2756 = hAPP(c_Option_Ooption_OSome(X2755),esk68_2(X2755,X2756)) )
& ( X2759 != hAPP(c_Option_Ooption_OSome(X2758),X2760)
| X2759 != c_Option_Ooption_ONone(X2758) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__None__eq])])])])]) ).
fof(c_0_50,plain,
! [X2769,X2770] : c_Option_Ooption_ONone(X2770) != hAPP(c_Option_Ooption_OSome(X2770),X2769),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).
fof(c_0_51,plain,
! [X1075,X1076,X1077,X1078,X1079,X1080] : hAPP(hAPP(hAPP(c_COMBB(X1080,X1079,X1078),X1077),X1076),X1075) = hAPP(X1077,hAPP(X1076,X1075)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_52,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_47]) ).
cnf(c_0_54,plain,
( X2 = X3
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( X1 = c_Option_Ooption_ONone(X2)
| X1 = hAPP(c_Option_Ooption_OSome(X2),esk68_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_59,plain,
! [X387,X388] :
( hAPP(X388,esk5_2(X387,X388)) != hAPP(X387,esk5_2(X387,X388))
| X388 = X387 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_60,plain,
esk68_2(X1,hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55])]),c_0_56]) ).
cnf(c_0_61,plain,
hAPP(X1,hAPP(c_Fun_Oid(X2),X3)) = hAPP(X1,X3),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
( X1 = X2
| hAPP(X1,esk5_2(X2,X1)) != hAPP(X2,esk5_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_60]) ).
fof(c_0_64,plain,
! [X4388] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4388) = X4388,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_65,plain,
( c_Fun_Oid(X1) = X2
| hAPP(X2,esk5_2(X2,c_Fun_Oid(X1))) != esk5_2(X2,c_Fun_Oid(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_67,plain,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_68,plain,
! [X2003,X2004] : hAPP(c_Set_OCollect(X2004),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2004),c_fNot),X2003)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2004,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2004),X2003)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
cnf(c_0_69,plain,
c_Fun_Oid(X1) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
fof(c_0_70,plain,
! [X6512] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X6512) = X6512,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_71,plain,
! [X20,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X20))
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(c_0_72,plain,
! [X2583,X2584,X2585,X2586,X2588] :
( ( hAPP(c_Set_OCollect(X2584),X2583) != c_Orderings_Obot__class_Obot(tc_fun(X2584,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2583,X2585)) )
& ( hBOOL(hAPP(X2586,esk60_1(X2586)))
| hAPP(c_Set_OCollect(X2588),X2586) = c_Orderings_Obot__class_Obot(tc_fun(X2588,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])])]) ).
fof(c_0_73,plain,
! [X2545,X2546,X2547] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2547,tc_HOL_Obool)),X2546),X2545) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2547,tc_HOL_Obool)),X2546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2547,tc_HOL_Obool)),X2545)),
inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).
cnf(c_0_74,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_75,plain,
! [X2731,X2732] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2732,tc_HOL_Obool)),X2731),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2732,tc_HOL_Obool)),X2731)) = c_Orderings_Otop__class_Otop(tc_fun(X2732,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).
cnf(c_0_76,plain,
( c_Int_Onumber__class_Onumber__of(tc_Int_Oint) = X1
| hAPP(X1,esk5_2(X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint))) != esk5_2(X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_69]),c_0_69]),c_0_69]) ).
cnf(c_0_77,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_78,plain,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_79,plain,
! [X2082,X2083] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X2083),X2082))
| hBOOL(X2083) ),
inference(variable_rename,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
( hBOOL(hAPP(X1,esk60_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_81,plain,
! [X2421,X2422,X2423] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2423,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2423,tc_HOL_Obool)),X2422),X2421)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2423,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2423,tc_HOL_Obool)),X2422)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2423,tc_HOL_Obool)),X2421)),
inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).
cnf(c_0_82,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_47]),c_0_47]) ).
cnf(c_0_84,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) = X2,
inference(rw,[status(thm)],[c_0_58,c_0_69]) ).
cnf(c_0_86,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint) = hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
fof(c_0_87,plain,
! [X2013] :
( ~ hBOOL(hAPP(c_fNot,X2013))
| ~ hBOOL(X2013) ),
inference(variable_rename,[status(thm)],[c_0_78]) ).
cnf(c_0_88,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk60_1(X1))) ),
inference(rw,[status(thm)],[c_0_80,c_0_47]) ).
fof(c_0_90,plain,
! [X29,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X29))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X10))
| X10 = X29 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(c_0_91,plain,
! [X2597,X2598] : hAPP(c_Set_OCollect(X2598),hAPP(hAPP(c_COMBC(X2598,tc_fun(X2598,tc_HOL_Obool),tc_HOL_Obool),c_member(X2598)),X2597)) = X2597,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_92,plain,
! [X2424,X2425,X2426] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2426,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2426,tc_HOL_Obool)),X2425),X2424)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2426,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2426,tc_HOL_Obool)),X2425)),X2424),
inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).
cnf(c_0_93,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_94,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_95,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_84,c_0_83]) ).
cnf(c_0_96,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls)) = X2,
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_97,plain,
! [X2735,X2736] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2736,tc_HOL_Obool)),X2735) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2736,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2736,tc_HOL_Obool))),X2735),
inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(c_0_98,plain,
! [X4225,X4226] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4226,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4226,tc_HOL_Obool)),X4225)) = X4225,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(c_0_99,plain,
! [X4763,X4764,X4765,X4766,X4767] :
( ( X4767 != c_Orderings_Obot__class_Obot(tc_fun(X4766,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4765,tc_HOL_Obool)),X4764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4766,tc_fun(X4765,tc_HOL_Obool)),X4767),X4763)) = X4764 )
& ( X4767 = c_Orderings_Obot__class_Obot(tc_fun(X4766,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4765,tc_HOL_Obool)),X4764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4766,tc_fun(X4765,tc_HOL_Obool)),X4767),X4763)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4766,tc_fun(X4765,tc_HOL_Obool)),X4767),hAPP(hAPP(c_COMBB(tc_fun(X4765,tc_HOL_Obool),tc_fun(X4765,tc_HOL_Obool),X4766),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4765,tc_HOL_Obool)),X4764)),X4763)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).
cnf(c_0_100,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_101,plain,
( hAPP(c_fconj,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_102,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min]) ).
fof(c_0_103,plain,
! [X7387,X7388,X7389] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7389),X7388),X7387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7389),X7387),X7388))
| X7388 = X7387
| ~ class_Orderings_Olinorder(X7389) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7389),X7387),X7388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7389),X7388),X7387))
| ~ class_Orderings_Olinorder(X7389) )
& ( X7388 != X7387
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7389),X7388),X7387))
| ~ class_Orderings_Olinorder(X7389) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])]) ).
fof(c_0_104,plain,
! [X3781] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3781) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3781)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_105,plain,
! [X1297,X1299,X1300,X1301] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1299),X1297))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1299),esk29_1(X1297))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk30_2(X1300,X1301)),X1300))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1300)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk30_2(X1300,X1301)),X1301))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1300)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])]) ).
fof(c_0_106,plain,
! [X1106,X1107,X1108,X1109,X1110,X1111] : hAPP(hAPP(hAPP(c_COMBC(X1111,X1110,X1109),X1108),X1107),X1106) = hAPP(hAPP(X1108,X1106),X1107),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_107,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_108,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_109,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_110,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_111,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_83]),c_0_83]),c_0_94]),c_0_83]) ).
cnf(c_0_112,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls)),c_fNot) = c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_113,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_114,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_98]) ).
fof(c_0_115,plain,
! [X2327,X2328] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2328,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2328,tc_HOL_Obool))),X2327) = X2327,
inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).
cnf(c_0_116,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = X4
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_117,plain,
( hAPP(c_fconj,hAPP(c_fNot,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_118,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
inference(rw,[status(thm)],[c_0_102,c_0_66]) ).
cnf(c_0_119,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_120,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_121,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(c_0_122,plain,
! [X1189] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1189),X1189)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
cnf(c_0_123,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk29_1(X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_124,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_125,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_107,c_0_47]) ).
cnf(c_0_126,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_127,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_128,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
fof(c_0_129,plain,
! [X4337] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4337) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4337)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
cnf(c_0_130,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_83]),c_0_83]) ).
cnf(c_0_131,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),c_fNot),c_fNot),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_96]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[c_0_113,c_0_83]) ).
cnf(c_0_133,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_83]),c_0_83]) ).
cnf(c_0_134,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_135,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = X2,
inference(er,[status(thm)],[c_0_116]) ).
cnf(c_0_136,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_137,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_120])]) ).
cnf(c_0_138,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_139,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk29_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)) ),
inference(rw,[status(thm)],[c_0_123,c_0_120]) ).
cnf(c_0_140,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
fof(c_0_141,plain,
! [X2202,X2203,X2204,X2205] : hBOOL(hAPP(hAPP(c_member(X2205),hAPP(X2204,X2203)),hAPP(c_Set_Oimage(X2202,X2205,X2204),c_Orderings_Otop__class_Otop(tc_fun(X2202,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_142,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(c_0_143,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_144,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
fof(c_0_145,plain,
! [X1332,X1333,X1334] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1334,tc_HOL_Obool)),X1333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1334,tc_HOL_Obool)),X1332),X1333)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1334,tc_HOL_Obool)),X1333),X1332),
inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).
cnf(c_0_146,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),c_fNot),c_fNot)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]),c_0_133]) ).
cnf(c_0_147,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))),X3) = hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_136]) ).
cnf(c_0_148,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_149,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk29_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_150,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
fof(c_0_151,plain,
! [X13,X5] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
=> hAPP(c_Finite__Set_Ocard(X5),X13) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_152,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).
cnf(c_0_153,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_66]),c_0_143]) ).
cnf(c_0_154,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_144,c_0_66]) ).
cnf(c_0_155,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_156,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),c_fNot),c_fNot) = hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_146]),c_0_136]),c_0_147]) ).
cnf(c_0_157,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk29_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_158,plain,
hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
inference(rw,[status(thm)],[c_0_150,c_0_140]) ).
fof(c_0_159,plain,
! [X2086,X2087,X2088,X2089] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2089),X2088))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X2087),hAPP(c_Set_Oimage(X2089,X2087,X2086),X2088))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(c_0_160,plain,
! [X5688,X5689] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5689),X5688))
| hAPP(c_Finite__Set_Ocard(X5689),X5688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])]) ).
cnf(c_0_161,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_162,plain,
hAPP(c_Int_Onat,c_Int_OBit0(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_163,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_146]),c_0_146]),c_0_156]) ).
fof(c_0_164,plain,
! [X3783] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3783),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_165,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(X1,X2,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_166,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_167,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_168,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_153]),c_0_154]),c_0_162]),c_0_128]) ).
cnf(c_0_169,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))),
inference(spm,[status(thm)],[c_0_132,c_0_163]) ).
cnf(c_0_170,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_171,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_172,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(c_Int_Onat,c_Int_OPls)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(rw,[status(thm)],[c_0_167,c_0_128]) ).
cnf(c_0_173,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_174,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_170,c_0_128]) ).
cnf(c_0_175,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))))),
inference(spm,[status(thm)],[c_0_171,c_0_169]) ).
cnf(c_0_176,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_175]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.85/0.90 % Problem : SWW354+1 : TPTP v8.1.2. Released v5.2.0.
% 0.85/0.91 % Command : run_E %s %d THM
% 0.90/1.12 % Computer : n013.cluster.edu
% 0.90/1.12 % Model : x86_64 x86_64
% 0.90/1.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.90/1.12 % Memory : 8042.1875MB
% 0.90/1.12 % OS : Linux 3.10.0-693.el7.x86_64
% 0.90/1.12 % CPULimit : 2400
% 0.90/1.12 % WCLimit : 300
% 0.90/1.12 % DateTime : Mon Oct 2 22:30:45 EDT 2023
% 0.90/1.12 % CPUTime :
% 1.71/2.02 Running first-order theorem proving
% 1.71/2.02 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.qOD6JF2uk3/E---3.1_14007.p
% 83.86/13.20 # Version: 3.1pre001
% 83.86/13.20 # Preprocessing class: FMLMSMSMSSSNFFN.
% 83.86/13.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.86/13.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 83.86/13.20 # Starting new_bool_3 with 300s (1) cores
% 83.86/13.20 # Starting new_bool_1 with 300s (1) cores
% 83.86/13.20 # Starting sh5l with 300s (1) cores
% 83.86/13.20 # new_bool_3 with pid 14174 completed with status 0
% 83.86/13.20 # Result found by new_bool_3
% 83.86/13.20 # Preprocessing class: FMLMSMSMSSSNFFN.
% 83.86/13.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.86/13.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 83.86/13.20 # Starting new_bool_3 with 300s (1) cores
% 83.86/13.20 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 83.86/13.20 # Search class: FGHSM-SMLM33-DFFFFFNN
% 83.86/13.20 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 83.86/13.20 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 83.86/13.20 # SAT001_MinMin_p005000_rr with pid 14178 completed with status 0
% 83.86/13.20 # Result found by SAT001_MinMin_p005000_rr
% 83.86/13.20 # Preprocessing class: FMLMSMSMSSSNFFN.
% 83.86/13.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.86/13.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 83.86/13.20 # Starting new_bool_3 with 300s (1) cores
% 83.86/13.20 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 83.86/13.20 # Search class: FGHSM-SMLM33-DFFFFFNN
% 83.86/13.20 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 83.86/13.20 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 83.86/13.20 # Preprocessing time : 0.046 s
% 83.86/13.20 # Presaturation interreduction done
% 83.86/13.20
% 83.86/13.20 # Proof found!
% 83.86/13.20 # SZS status ContradictoryAxioms
% 83.86/13.20 # SZS output start CNFRefutation
% See solution above
% 83.86/13.20 # Parsed axioms : 5245
% 83.86/13.20 # Removed by relevancy pruning/SinE : 3192
% 83.86/13.20 # Initial clauses : 3006
% 83.86/13.20 # Removed in clause preprocessing : 89
% 83.86/13.20 # Initial clauses in saturation : 2917
% 83.86/13.20 # Processed clauses : 23447
% 83.86/13.20 # ...of these trivial : 841
% 83.86/13.20 # ...subsumed : 13402
% 83.86/13.20 # ...remaining for further processing : 9204
% 83.86/13.20 # Other redundant clauses eliminated : 2776
% 83.86/13.20 # Clauses deleted for lack of memory : 0
% 83.86/13.20 # Backward-subsumed : 212
% 83.86/13.20 # Backward-rewritten : 625
% 83.86/13.20 # Generated clauses : 462856
% 83.86/13.20 # ...of the previous two non-redundant : 443369
% 83.86/13.20 # ...aggressively subsumed : 0
% 83.86/13.20 # Contextual simplify-reflections : 23
% 83.86/13.20 # Paramodulations : 460020
% 83.86/13.20 # Factorizations : 14
% 83.86/13.20 # NegExts : 0
% 83.86/13.20 # Equation resolutions : 2853
% 83.86/13.20 # Total rewrite steps : 90404
% 83.86/13.20 # Propositional unsat checks : 1
% 83.86/13.20 # Propositional check models : 0
% 83.86/13.20 # Propositional check unsatisfiable : 0
% 83.86/13.20 # Propositional clauses : 0
% 83.86/13.20 # Propositional clauses after purity: 0
% 83.86/13.20 # Propositional unsat core size : 0
% 83.86/13.20 # Propositional preprocessing time : 0.000
% 83.86/13.20 # Propositional encoding time : 0.121
% 83.86/13.20 # Propositional solver time : 0.048
% 83.86/13.20 # Success case prop preproc time : 0.000
% 83.86/13.20 # Success case prop encoding time : 0.000
% 83.86/13.20 # Success case prop solver time : 0.000
% 83.86/13.20 # Current number of processed clauses : 5968
% 83.86/13.20 # Positive orientable unit clauses : 838
% 83.86/13.20 # Positive unorientable unit clauses: 59
% 83.86/13.20 # Negative unit clauses : 1103
% 83.86/13.20 # Non-unit-clauses : 3968
% 83.86/13.20 # Current number of unprocessed clauses: 405187
% 83.86/13.20 # ...number of literals in the above : 1174708
% 83.86/13.20 # Current number of archived formulas : 0
% 83.86/13.20 # Current number of archived clauses : 3003
% 83.86/13.20 # Clause-clause subsumption calls (NU) : 1649806
% 83.86/13.20 # Rec. Clause-clause subsumption calls : 972058
% 83.86/13.20 # Non-unit clause-clause subsumptions : 6821
% 83.86/13.20 # Unit Clause-clause subsumption calls : 104999
% 83.86/13.20 # Rewrite failures with RHS unbound : 193
% 83.86/13.20 # BW rewrite match attempts : 16758
% 83.86/13.20 # BW rewrite match successes : 946
% 83.86/13.20 # Condensation attempts : 0
% 83.86/13.20 # Condensation successes : 0
% 83.86/13.20 # Termbank termtop insertions : 13613664
% 83.86/13.20
% 83.86/13.20 # -------------------------------------------------
% 83.86/13.20 # User time : 10.312 s
% 83.86/13.20 # System time : 0.368 s
% 83.86/13.20 # Total time : 10.680 s
% 83.86/13.20 # Maximum resident set size: 18328 pages
% 83.86/13.20
% 83.86/13.20 # -------------------------------------------------
% 83.86/13.20 # User time : 10.513 s
% 83.86/13.20 # System time : 0.383 s
% 83.86/13.20 # Total time : 10.895 s
% 83.86/13.20 # Maximum resident set size: 9560 pages
% 83.86/13.20 % E---3.1 exiting
% 83.86/13.20 % E---3.1 exiting
%------------------------------------------------------------------------------