TSTP Solution File: SWW354+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW354+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 10:00:52 EDT 2024
% Result : ContradictoryAxioms 18.83s 4.98s
% Output : CNFRefutation 18.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 145 ( 96 unt; 0 def)
% Number of atoms : 228 ( 116 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 154 ( 71 ~; 58 |; 10 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 9 con; 0-3 aty)
% Number of variables : 317 ( 28 sgn 173 !; 3 ?)
% 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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_Collect__def) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_option_Osimps_I2_J) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_option_Oinject) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_ext) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_Collect__empty__eq) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_number__of__is__id) ).
fof(help_c__fconj__2,axiom,
! [X20,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X20))
| hBOOL(X17) ),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',help_c__fconj__2) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_Collect__mem__eq) ).
fof(help_c__fNot__1,axiom,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',help_c__fNot__1) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',help_c__COMBC__1) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_add__Pls) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_le__refl) ).
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.gvdo17SMBM/E---3.1_23032.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.gvdo17SMBM/E---3.1_23032.p',fact_Compl__partition) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_neg__number__of__Min) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_rangeI) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_Compl__Un) ).
fof(fact_Diff__cancel,axiom,
! [X13,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',fact_Diff__cancel) ).
fof(fact_finite__set,axiom,
! [X250,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X250))),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',fact_finite__set) ).
fof(fact_UNIV__enum,axiom,
! [X5] :
( class_Enum_Oenum(X5)
=> c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5)) ),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',fact_UNIV__enum) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_double__complement) ).
fof(fact_finite__Un,axiom,
! [X4,X67,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X67),X4)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X67))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) ) ),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',fact_finite__Un) ).
fof(fact_Un__UNIV__left,axiom,
! [X79,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X79) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',fact_Un__UNIV__left) ).
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.gvdo17SMBM/E---3.1_23032.p',fact_finite__imageI) ).
fof(arity_HOL__Obool__Enum_Oenum,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.gvdo17SMBM/E---3.1_23032.p',arity_HOL__Obool__Enum_Oenum) ).
fof(c_0_34,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_35,plain,
! [X2595,X2596] : hAPP(c_Set_OCollect(X2596),X2595) = X2595,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_36,plain,
! [X5,X10] :
( X10 != c_Option_Ooption_ONone(X5)
<=> ? [X97] : X10 = hAPP(c_Option_Ooption_OSome(X5),X97) ),
inference(fof_simplification,[status(thm)],[fact_not__None__eq]) ).
fof(c_0_37,plain,
! [X164,X5] : c_Option_Ooption_ONone(X5) != hAPP(c_Option_Ooption_OSome(X5),X164),
inference(fof_simplification,[status(thm)],[fact_option_Osimps_I2_J]) ).
fof(c_0_38,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_39,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_34]) ).
cnf(c_0_40,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_41,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])])]) ).
fof(c_0_42,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(fof_nnf,[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)],[c_0_36])])])])])]) ).
fof(c_0_43,plain,
! [X2769,X2770] : c_Option_Ooption_ONone(X2770) != hAPP(c_Option_Ooption_OSome(X2770),X2769),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
fof(c_0_44,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_45,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,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_39,c_0_40]),c_0_40]) ).
cnf(c_0_47,plain,
( X2 = X3
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,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_42]) ).
cnf(c_0_49,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_52,plain,
! [X387,X388] :
( hAPP(X388,esk5_2(X387,X388)) != hAPP(X387,esk5_2(X387,X388))
| X388 = X387 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_53,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_47,c_0_48])]),c_0_49]) ).
cnf(c_0_54,plain,
hAPP(X1,hAPP(c_Fun_Oid(X2),X3)) = hAPP(X1,X3),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_55,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]) ).
cnf(c_0_56,plain,
( X1 = X2
| hAPP(X1,esk5_2(X2,X1)) != hAPP(X2,esk5_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_53]) ).
fof(c_0_58,plain,
! [X4388] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4388) = X4388,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_59,plain,
! [X20,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X20))
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(c_0_60,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(fof_nnf,[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)],[c_0_55])])])])])]) ).
fof(c_0_61,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_62,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]) ).
cnf(c_0_63,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_56,c_0_57]) ).
cnf(c_0_64,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_65,plain,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_66,plain,
! [X2082,X2083] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X2083),X2082))
| hBOOL(X2083) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_59])]) ).
cnf(c_0_67,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_60]) ).
fof(c_0_68,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
fof(c_0_69,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_70,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(fof_nnf,[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_71,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_72,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_62]) ).
fof(c_0_73,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_74,plain,
c_Fun_Oid(X1) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_75,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_76,plain,
! [X2013] :
( ~ hBOOL(hAPP(c_fNot,X2013))
| ~ hBOOL(X2013) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_65])]) ).
cnf(c_0_77,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,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_67,c_0_40]) ).
cnf(c_0_79,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_68]) ).
cnf(c_0_80,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_69]) ).
cnf(c_0_81,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(c_0_82,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_83,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_70]) ).
cnf(c_0_84,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_85,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_72,c_0_40]) ).
fof(c_0_86,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_87,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_73]) ).
fof(c_0_88,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_89,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_63,c_0_74]),c_0_74]),c_0_74]) ).
cnf(c_0_90,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_91,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_92,plain,
( hAPP(c_fconj,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_93,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]) ).
cnf(c_0_94,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_79,c_0_80]),c_0_81]),c_0_80])]) ).
cnf(c_0_95,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_96,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_83,c_0_80]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
fof(c_0_98,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]) ).
fof(c_0_99,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_100,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_86]) ).
cnf(c_0_101,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_87,c_0_40]),c_0_40]) ).
cnf(c_0_102,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_88]) ).
cnf(c_0_103,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_51,c_0_74]) ).
cnf(c_0_104,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_89,c_0_90]) ).
fof(c_0_105,plain,
! [X450,X451] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X451,tc_HOL_Obool)),X450),X450) = c_Orderings_Obot__class_Obot(tc_fun(X451,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
cnf(c_0_106,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_91,c_0_92]) ).
cnf(c_0_107,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
inference(rw,[status(thm)],[c_0_93,c_0_64]) ).
fof(c_0_108,plain,
! [X2885,X2886] : hBOOL(hAPP(c_Finite__Set_Ofinite(X2886),hAPP(c_List_Oset(X2886),X2885))),
inference(variable_rename,[status(thm)],[fact_finite__set]) ).
fof(c_0_109,plain,
! [X5510] :
( ~ class_Enum_Oenum(X5510)
| c_Orderings_Otop__class_Otop(tc_fun(X5510,tc_HOL_Obool)) = hAPP(c_List_Oset(X5510),c_Enum_Oenum__class_Oenum(X5510)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNIV__enum])])]) ).
cnf(c_0_110,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_94,c_0_95]) ).
cnf(c_0_111,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_96,c_0_97]) ).
cnf(c_0_112,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_98]) ).
fof(c_0_113,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]) ).
cnf(c_0_114,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_99]) ).
cnf(c_0_115,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_100,c_0_101]) ).
cnf(c_0_116,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_102,c_0_101]) ).
cnf(c_0_117,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_103,c_0_104]) ).
cnf(c_0_118,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_119,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_106,c_0_107]) ).
fof(c_0_120,plain,
! [X1282,X1283,X1284] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),X1283))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1284,tc_HOL_Obool)),X1283),X1282))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),X1282))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1284,tc_HOL_Obool)),X1283),X1282))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),X1283))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),X1282))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1284,tc_HOL_Obool)),X1283),X1282))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])])]) ).
fof(c_0_121,plain,
! [X2719,X2720] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2720,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2720,tc_HOL_Obool))),X2719) = c_Orderings_Otop__class_Otop(tc_fun(X2720,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).
cnf(c_0_122,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_123,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))
| ~ class_Enum_Oenum(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_124,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_110,c_0_111]) ).
cnf(c_0_125,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_112,c_0_97]) ).
fof(c_0_126,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
cnf(c_0_127,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_113]) ).
cnf(c_0_128,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_114,c_0_101]),c_0_101]),c_0_115]),c_0_101]) ).
cnf(c_0_129,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_116,c_0_117]) ).
cnf(c_0_130,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))),
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_131,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(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_121]) ).
cnf(c_0_133,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ class_Enum_Oenum(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_134,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]) ).
cnf(c_0_135,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_124,c_0_125]) ).
cnf(c_0_136,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_126]) ).
cnf(c_0_137,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_127,c_0_101]),c_0_101]) ).
cnf(c_0_138,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(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_128,c_0_129]),c_0_117]),c_0_130]) ).
cnf(c_0_139,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_140,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,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_135,c_0_136]) ).
cnf(c_0_142,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_137,c_0_138]) ).
cnf(c_0_143,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),X1)),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_144,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.80/0.84 % Problem : SWW354+1 : TPTP v8.1.2. Released v5.2.0.
% 0.84/0.85 % Command : run_E %s %d THM
% 0.85/1.06 % Computer : n012.cluster.edu
% 0.85/1.06 % Model : x86_64 x86_64
% 0.85/1.06 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.85/1.06 % Memory : 8042.1875MB
% 0.85/1.06 % OS : Linux 3.10.0-693.el7.x86_64
% 0.85/1.06 % CPULimit : 300
% 0.85/1.06 % WCLimit : 300
% 0.85/1.06 % DateTime : Fri May 3 13:07:55 EDT 2024
% 0.85/1.06 % CPUTime :
% 1.90/2.07 Running first-order theorem proving
% 1.90/2.07 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.gvdo17SMBM/E---3.1_23032.p
% 18.83/4.98 # Version: 3.1.0
% 18.83/4.98 # Preprocessing class: FMLMSMSMSSSNFFN.
% 18.83/4.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.83/4.98 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.83/4.98 # Starting new_bool_3 with 300s (1) cores
% 18.83/4.98 # Starting new_bool_1 with 300s (1) cores
% 18.83/4.98 # Starting sh5l with 300s (1) cores
% 18.83/4.98 # new_bool_3 with pid 23116 completed with status 0
% 18.83/4.98 # Result found by new_bool_3
% 18.83/4.98 # Preprocessing class: FMLMSMSMSSSNFFN.
% 18.83/4.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.83/4.98 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.83/4.98 # Starting new_bool_3 with 300s (1) cores
% 18.83/4.98 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 18.83/4.98 # Search class: FGHSM-SMLM33-DFFFFFNN
% 18.83/4.98 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 18.83/4.98 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 18.83/4.98 # SAT001_MinMin_p005000_rr with pid 23120 completed with status 0
% 18.83/4.98 # Result found by SAT001_MinMin_p005000_rr
% 18.83/4.98 # Preprocessing class: FMLMSMSMSSSNFFN.
% 18.83/4.98 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.83/4.98 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.83/4.98 # Starting new_bool_3 with 300s (1) cores
% 18.83/4.98 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 18.83/4.98 # Search class: FGHSM-SMLM33-DFFFFFNN
% 18.83/4.98 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 18.83/4.98 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 18.83/4.98 # Preprocessing time : 0.046 s
% 18.83/4.98 # Presaturation interreduction done
% 18.83/4.98
% 18.83/4.98 # Proof found!
% 18.83/4.98 # SZS status ContradictoryAxioms
% 18.83/4.98 # SZS output start CNFRefutation
% See solution above
% 18.83/4.98 # Parsed axioms : 5245
% 18.83/4.98 # Removed by relevancy pruning/SinE : 3192
% 18.83/4.98 # Initial clauses : 3006
% 18.83/4.98 # Removed in clause preprocessing : 89
% 18.83/4.98 # Initial clauses in saturation : 2917
% 18.83/4.98 # Processed clauses : 11748
% 18.83/4.98 # ...of these trivial : 529
% 18.83/4.98 # ...subsumed : 5208
% 18.83/4.98 # ...remaining for further processing : 6011
% 18.83/4.98 # Other redundant clauses eliminated : 854
% 18.83/4.98 # Clauses deleted for lack of memory : 0
% 18.83/4.98 # Backward-subsumed : 106
% 18.83/4.98 # Backward-rewritten : 361
% 18.83/4.98 # Generated clauses : 106868
% 18.83/4.98 # ...of the previous two non-redundant : 100035
% 18.83/4.98 # ...aggressively subsumed : 0
% 18.83/4.98 # Contextual simplify-reflections : 19
% 18.83/4.98 # Paramodulations : 105995
% 18.83/4.98 # Factorizations : 8
% 18.83/4.98 # NegExts : 0
% 18.83/4.98 # Equation resolutions : 897
% 18.83/4.98 # Disequality decompositions : 0
% 18.83/4.98 # Total rewrite steps : 28722
% 18.83/4.98 # ...of those cached : 21516
% 18.83/4.98 # Propositional unsat checks : 1
% 18.83/4.98 # Propositional check models : 0
% 18.83/4.98 # Propositional check unsatisfiable : 0
% 18.83/4.98 # Propositional clauses : 0
% 18.83/4.98 # Propositional clauses after purity: 0
% 18.83/4.98 # Propositional unsat core size : 0
% 18.83/4.98 # Propositional preprocessing time : 0.000
% 18.83/4.98 # Propositional encoding time : 0.110
% 18.83/4.98 # Propositional solver time : 0.050
% 18.83/4.98 # Success case prop preproc time : 0.000
% 18.83/4.98 # Success case prop encoding time : 0.000
% 18.83/4.98 # Success case prop solver time : 0.000
% 18.83/4.98 # Current number of processed clauses : 3146
% 18.83/4.98 # Positive orientable unit clauses : 762
% 18.83/4.98 # Positive unorientable unit clauses: 57
% 18.83/4.98 # Negative unit clauses : 630
% 18.83/4.98 # Non-unit-clauses : 1697
% 18.83/4.98 # Current number of unprocessed clauses: 83507
% 18.83/4.98 # ...number of literals in the above : 177140
% 18.83/4.98 # Current number of archived formulas : 0
% 18.83/4.98 # Current number of archived clauses : 2632
% 18.83/4.98 # Clause-clause subsumption calls (NU) : 600898
% 18.83/4.98 # Rec. Clause-clause subsumption calls : 373565
% 18.83/4.98 # Non-unit clause-clause subsumptions : 2393
% 18.83/4.98 # Unit Clause-clause subsumption calls : 29476
% 18.83/4.98 # Rewrite failures with RHS unbound : 163
% 18.83/4.98 # BW rewrite match attempts : 15579
% 18.83/4.98 # BW rewrite match successes : 761
% 18.83/4.98 # Condensation attempts : 0
% 18.83/4.98 # Condensation successes : 0
% 18.83/4.98 # Termbank termtop insertions : 3184961
% 18.83/4.98 # Search garbage collected termcells : 68921
% 18.83/4.98
% 18.83/4.98 # -------------------------------------------------
% 18.83/4.98 # User time : 2.498 s
% 18.83/4.98 # System time : 0.095 s
% 18.83/4.98 # Total time : 2.593 s
% 18.83/4.98 # Maximum resident set size: 18428 pages
% 18.83/4.98
% 18.83/4.98 # -------------------------------------------------
% 18.83/4.98 # User time : 2.729 s
% 18.83/4.98 # System time : 0.105 s
% 18.83/4.98 # Total time : 2.834 s
% 18.83/4.98 # Maximum resident set size: 9576 pages
% 18.83/4.98 % E---3.1 exiting
% 18.83/4.98 % E exiting
%------------------------------------------------------------------------------