TSTP Solution File: SWW376+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW376+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 20:09:15 EDT 2023
% Result : ContradictoryAxioms 41.68s 7.57s
% Output : CNFRefutation 41.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 32
% Syntax : Number of formulae : 146 ( 90 unt; 0 def)
% Number of atoms : 224 ( 131 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 145 ( 67 ~; 57 |; 10 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 10 con; 0-3 aty)
% Number of variables : 288 ( 37 sgn; 146 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_vimage__Collect__eq,axiom,
! [X19,X2,X7,X6] : hAPP(c_Set_Ovimage(X6,X7,X2),hAPP(c_Set_OCollect(X7),X19)) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(X7,tc_HOL_Obool,X6),X19),X2)),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__def,axiom,
! [X19,X6] : hAPP(c_Set_OCollect(X6),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_Collect__def) ).
fof(fact_vimage__id,axiom,
! [X4,X6] : hAPP(c_Set_Ovimage(X6,X6,c_Fun_Oid(X6)),X4) = X4,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_vimage__id) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X19)),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_Collect__neg__eq) ).
fof(help_c__COMBB__1,axiom,
! [X67,X43,X19,X5,X6,X7] : hAPP(hAPP(hAPP(c_COMBB(X7,X6,X5),X19),X43),X67) = hAPP(X19,hAPP(X43,X67)),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__COMBB__1) ).
fof(fact_double__complement,axiom,
! [X4,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X4)) = X4,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_double__complement) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_ext) ).
fof(fact_number__of__is__id,axiom,
! [X137] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X137) = X137,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_number__of__is__id) ).
fof(fact_rev__rev__ident,axiom,
! [X257,X6] : hAPP(c_List_Orev(X6),hAPP(c_List_Orev(X6),X257)) = X257,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_rev__rev__ident) ).
fof(fact_add__Pls,axiom,
! [X137] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X137) = X137,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_add__Pls) ).
fof(fact_vimage__const,axiom,
! [X7,X4,X17,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X17),X4))
=> hAPP(c_Set_Ovimage(X7,X6,hAPP(c_COMBK(X6,X7),X17)),X4) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X17),X4))
=> hAPP(c_Set_Ovimage(X7,X6,hAPP(c_COMBK(X6,X7),X17)),X4) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_vimage__const) ).
fof(fact_Collect__mem__eq,axiom,
! [X4,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X4)) = X4,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_Collect__mem__eq) ).
fof(fact_vimage__Compl,axiom,
! [X4,X2,X7,X6] : hAPP(c_Set_Ovimage(X6,X7,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6,X7,X2),X4)),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_vimage__Compl) ).
fof(help_c__COMBC__1,axiom,
! [X67,X43,X19,X6,X5,X7] : hAPP(hAPP(hAPP(c_COMBC(X7,X5,X6),X19),X43),X67) = hAPP(hAPP(X19,X67),X43),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__COMBC__1) ).
fof(fact_eq__equal,axiom,
! [X6] :
( class_HOL_Oequal(X6)
=> c_fequal = c_HOL_Oequal__class_Oequal(X6) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_eq__equal) ).
fof(help_c__fequal__1,axiom,
! [X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X24),X25))
| X24 = X25 ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__fequal__1) ).
fof(fact_eq__int__code_I3_J,axiom,
! [X217] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X217)))
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X217)) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_eq__int__code_I3_J) ).
fof(arity_Int__Oint__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',arity_Int__Oint__HOL_Oequal) ).
fof(fact_ex__nat,axiom,
! [X19] :
( ? [X192] : hBOOL(hAPP(X19,X192))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X19,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_ex__nat) ).
fof(fact_zle__iff__zadd,axiom,
! [X54,X134] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),X54))
<=> ? [X175] : X54 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X175)) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_zle__iff__zadd) ).
fof(help_c__fequal__2,axiom,
! [X25,X24] :
( X24 != X25
| hBOOL(hAPP(hAPP(c_fequal,X24),X25)) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__fequal__2) ).
fof(help_c__COMBK__1,axiom,
! [X326,X39,X7,X6] : hAPP(hAPP(c_COMBK(X6,X7),X39),X326) = X39,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__COMBK__1) ).
fof(fact_neg__number__of__Bit0,axiom,
! [X134] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X134))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X134))) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_neg__number__of__Bit0) ).
fof(fact_not__neg__0,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_not__neg__0) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_Pls__def) ).
fof(fact_nat__int,axiom,
! [X136] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X136)) = X136,
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_nat__int) ).
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.8gt2hswYxV/E---3.1_25229.p',fact_neg__number__of__Min) ).
fof(help_c__fNot__2,axiom,
! [X19] :
( ~ ~ hBOOL(X19)
| hBOOL(hAPP(c_fNot,X19)) ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',help_c__fNot__2) ).
fof(fact_com_Osimps_I18_J,axiom,
! [X79] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X79),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_com_Osimps_I18_J) ).
fof(fact_com_Osimps_I6_J,axiom,
! [X9,X10] :
( hAPP(c_Com_Ocom_OBODY,X10) = hAPP(c_Com_Ocom_OBODY,X9)
<=> X10 = X9 ),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_com_Osimps_I6_J) ).
fof(fact_com_Osimps_I41_J,axiom,
! [X52,X30,X307,X9] : hAPP(c_Com_Ocom_OBODY,X9) != c_Com_Ocom_OLocal(X307,X30,X52),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_com_Osimps_I41_J) ).
fof(fact_com_Osimps_I10_J,axiom,
! [X49,X28,X308] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X308,X28,X49),
file('/export/starexec/sandbox/tmp/tmp.8gt2hswYxV/E---3.1_25229.p',fact_com_Osimps_I10_J) ).
fof(c_0_32,plain,
! [X6827,X6828,X6829,X6830] : hAPP(c_Set_Ovimage(X6830,X6829,X6828),hAPP(c_Set_OCollect(X6829),X6827)) = hAPP(c_Set_OCollect(X6830),hAPP(hAPP(c_COMBB(X6829,tc_HOL_Obool,X6830),X6827),X6828)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_33,plain,
! [X3103,X3104] : hAPP(c_Set_OCollect(X3104),X3103) = X3103,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_34,plain,
! [X6853,X6854] : hAPP(c_Set_Ovimage(X6854,X6854,c_Fun_Oid(X6854)),X6853) = X6853,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_35,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_32]) ).
cnf(c_0_36,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X3064,X3065] : hAPP(c_Set_OCollect(X3065),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3065),c_fNot),X3064)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3065,tc_HOL_Obool)),hAPP(c_Set_OCollect(X3065),X3064)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_38,plain,
! [X720,X721,X722,X723,X724,X725] : hAPP(hAPP(hAPP(c_COMBB(X725,X724,X723),X722),X721),X720) = hAPP(X722,hAPP(X721,X720)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_39,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,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_35,c_0_36]),c_0_36]) ).
fof(c_0_41,plain,
! [X4006,X4007] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4007,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4007,tc_HOL_Obool)),X4006)) = X4006,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_42,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_37]) ).
fof(c_0_43,plain,
! [X342,X343] :
( hAPP(X343,esk6_2(X342,X343)) != hAPP(X342,esk6_2(X342,X343))
| X343 = X342 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(c_0_44,plain,
! [X4639] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4639) = X4639,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_45,plain,
! [X6390,X6391] : hAPP(c_List_Orev(X6391),hAPP(c_List_Orev(X6391),X6390)) = X6390,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_46,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,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_41]) ).
cnf(c_0_49,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_42,c_0_36]),c_0_36]) ).
cnf(c_0_50,plain,
( X1 = X2
| hAPP(X1,esk6_2(X2,X1)) != hAPP(X2,esk6_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
hAPP(X1,hAPP(c_Fun_Oid(X2),X3)) = hAPP(X1,X3),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_54,plain,
! [X6856] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X6856) = X6856,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_55,plain,
! [X7,X4,X17,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X17),X4))
=> hAPP(c_Set_Ovimage(X7,X6,hAPP(c_COMBK(X6,X7),X17)),X4) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X17),X4))
=> hAPP(c_Set_Ovimage(X7,X6,hAPP(c_COMBK(X6,X7),X17)),X4) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).
fof(c_0_56,plain,
! [X3092,X3093] : hAPP(c_Set_OCollect(X3093),hAPP(hAPP(c_COMBC(X3093,tc_fun(X3093,tc_HOL_Obool),tc_HOL_Obool),c_member(X3093)),X3092)) = X3092,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_57,plain,
! [X6759,X6760,X6761,X6762] : hAPP(c_Set_Ovimage(X6762,X6761,X6760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6761,tc_HOL_Obool)),X6759)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6762,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6762,X6761,X6760),X6759)),
inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).
cnf(c_0_58,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_48,c_0_49]),c_0_49]) ).
cnf(c_0_59,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint)
| hAPP(X1,esk6_2(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) != esk6_2(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_62,plain,
! [X6814,X6815,X6816,X6817] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X6817),X6816),X6815))
| hAPP(c_Set_Ovimage(X6814,X6817,hAPP(c_COMBK(X6817,X6814),X6816)),X6815) = c_Orderings_Otop__class_Otop(tc_fun(X6814,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X6817),X6816),X6815))
| hAPP(c_Set_Ovimage(X6814,X6817,hAPP(c_COMBK(X6817,X6814),X6816)),X6815) = c_Orderings_Obot__class_Obot(tc_fun(X6814,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])]) ).
fof(c_0_63,plain,
! [X1251,X1252,X1253,X1254,X1255,X1256] : hAPP(hAPP(hAPP(c_COMBC(X1256,X1255,X1254),X1253),X1252),X1251) = hAPP(hAPP(X1253,X1251),X1252),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_64,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_56]) ).
cnf(c_0_65,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
c_Fun_Oid(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_58,c_0_47]) ).
cnf(c_0_67,plain,
c_Fun_Oid(X1) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,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_59,c_0_61]) ).
cnf(c_0_69,plain,
( hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,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_64,c_0_36]) ).
fof(c_0_72,plain,
! [X3906] :
( ~ class_HOL_Oequal(X3906)
| c_fequal = c_HOL_Oequal__class_Oequal(X3906) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equal])]) ).
cnf(c_0_73,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3)),X4) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_49]),c_0_40]),c_0_40]),c_0_49]) ).
cnf(c_0_74,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot) = hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_75,plain,
( hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(rw,[status(thm)],[c_0_69,c_0_40]) ).
cnf(c_0_76,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_77,plain,
! [X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X24),X25))
| X24 = X25 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(c_0_78,plain,
! [X7538] :
( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X7538)))
| hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X7538)) )
& ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X7538))
| hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X7538))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J])]) ).
cnf(c_0_79,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(X1)
| ~ class_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
class_HOL_Oequal(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]) ).
fof(c_0_81,plain,
! [X4544,X4545,X4547,X4548] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk125_1(X4544)))
| ~ hBOOL(hAPP(X4544,X4545)) )
& ( hBOOL(hAPP(X4544,hAPP(c_Int_Onat,esk125_1(X4544))))
| ~ hBOOL(hAPP(X4544,X4545)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4548))
| ~ hBOOL(hAPP(X4547,hAPP(c_Int_Onat,X4548)))
| hBOOL(hAPP(X4547,esk126_1(X4547))) ) ),
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_ex__nat])])])])])]) ).
fof(c_0_82,plain,
! [X4122,X4123,X4125,X4126,X4127] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4123),X4122))
| X4122 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4123),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk99_2(X4122,X4123))) )
& ( X4125 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4126),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4127))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4126),X4125)) ) ),
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_zle__iff__zadd])])])])]) ).
fof(c_0_83,plain,
! [X1112,X1113] :
( X1113 != X1112
| hBOOL(hAPP(hAPP(c_fequal,X1113),X1112)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(c_0_84,plain,
! [X1442,X1443,X1444,X1445] : hAPP(hAPP(c_COMBK(X1445,X1444),X1443),X1442) = X1443,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_85,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls)),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_73]),c_0_74]) ).
cnf(c_0_86,plain,
( hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_87,plain,
! [X4621] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X4621))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4621))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4621)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X4621)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).
fof(c_0_88,plain,
! [X1110,X1111] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X1111),X1110))
| X1111 = X1110 ),
inference(variable_rename,[status(thm)],[c_0_77]) ).
cnf(c_0_89,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_90,plain,
c_HOL_Oequal__class_Oequal(tc_Int_Oint) = c_fequal,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_91,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_not__neg__0]) ).
cnf(c_0_92,plain,
( hBOOL(hAPP(X2,esk126_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_93,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_94,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_95,plain,
! [X4142] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4142)) = X4142,
inference(variable_rename,[status(thm)],[fact_nat__int]) ).
cnf(c_0_96,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_98,plain,
( hAPP(c_COMBK(tc_HOL_Obool,X1),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_61]) ).
cnf(c_0_99,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_100,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_101,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_102,plain,
( hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90]) ).
cnf(c_0_103,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_104,plain,
( hBOOL(hAPP(X1,esk126_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2))) ),
inference(rw,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))),
inference(er,[status(thm)],[c_0_94]) ).
cnf(c_0_106,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_107,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk125_1(X1))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_108,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(er,[status(thm)],[c_0_96]) ).
cnf(c_0_109,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = X3
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_110,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
inference(rw,[status(thm)],[c_0_99,c_0_51]) ).
fof(c_0_111,plain,
! [X19] :
( hBOOL(X19)
| hBOOL(hAPP(c_fNot,X19)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
cnf(c_0_112,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_51]),c_0_51]) ).
cnf(c_0_113,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),X1)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_114,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(rw,[status(thm)],[c_0_103,c_0_93]) ).
cnf(c_0_115,plain,
( hBOOL(hAPP(X1,esk126_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_61]),c_0_106]) ).
cnf(c_0_116,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),hAPP(c_Int_Onat,esk125_1(hAPP(c_fequal,X1))))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_Nat__Numeral_Oneg,c_Int_OMin),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
fof(c_0_118,plain,
! [X3086] :
( hBOOL(X3086)
| hBOOL(hAPP(c_fNot,X3086)) ),
inference(variable_rename,[status(thm)],[c_0_111]) ).
cnf(c_0_119,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),X1))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_120,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),esk126_1(hAPP(c_fequal,X1)))),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,plain,
( hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) = X1
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_109,c_0_117]) ).
cnf(c_0_122,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_123,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,esk126_1(hAPP(c_fequal,c_Int_OPls)))),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_124,plain,
( hAPP(c_fNot,X1) = hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,plain,
esk126_1(hAPP(c_fequal,X1)) = X1,
inference(spm,[status(thm)],[c_0_101,c_0_120]) ).
cnf(c_0_126,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_66]),c_0_46]) ).
cnf(c_0_127,plain,
hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) = hAPP(c_Nat__Numeral_Oneg,c_Int_OMin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
fof(c_0_128,plain,
! [X1708] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1708),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I18_J]) ).
cnf(c_0_129,plain,
( hAPP(c_fNot,X1) = hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)
| hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) = X1 ),
inference(spm,[status(thm)],[c_0_121,c_0_124]) ).
cnf(c_0_130,plain,
hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
fof(c_0_131,plain,
! [X676,X677] :
( ( hAPP(c_Com_Ocom_OBODY,X677) != hAPP(c_Com_Ocom_OBODY,X676)
| X677 = X676 )
& ( X677 != X676
| hAPP(c_Com_Ocom_OBODY,X677) = hAPP(c_Com_Ocom_OBODY,X676) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])]) ).
cnf(c_0_132,plain,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_133,plain,
( hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) = X1
| hAPP(c_Nat__Numeral_Oneg,c_Int_OPls) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_129]),c_0_130]) ).
cnf(c_0_134,plain,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_135,plain,
( hAPP(c_Com_Ocom_OBODY,X1) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)
| hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) != c_Com_Ocom_OSKIP ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_136,plain,
( X1 = X2
| hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) != c_Com_Ocom_OSKIP ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_135]) ).
cnf(c_0_137,plain,
( hAPP(c_Nat__Numeral_Oneg,c_Int_OPls) = c_Com_Ocom_OSKIP
| X1 = X2 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_133])]) ).
fof(c_0_138,plain,
! [X1830,X1831,X1832,X1833] : hAPP(c_Com_Ocom_OBODY,X1833) != c_Com_Ocom_OLocal(X1832,X1831,X1830),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J]) ).
cnf(c_0_139,plain,
hAPP(c_Nat__Numeral_Oneg,c_Int_OPls) = c_Com_Ocom_OSKIP,
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_137])]) ).
fof(c_0_140,plain,
! [X1727,X1728,X1729] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1729,X1728,X1727),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J]) ).
cnf(c_0_141,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_142,plain,
( hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) = X1
| c_Com_Ocom_OSKIP = X1 ),
inference(rw,[status(thm)],[c_0_133,c_0_139]) ).
cnf(c_0_143,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_144,plain,
hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Nat__Numeral_Oneg,c_Int_OMin),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_145,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_142]),c_0_132]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.83/0.87 % Problem : SWW376+1 : TPTP v8.1.2. Released v5.2.0.
% 0.83/0.88 % Command : run_E %s %d THM
% 0.90/1.09 % Computer : n016.cluster.edu
% 0.90/1.09 % Model : x86_64 x86_64
% 0.90/1.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.90/1.09 % Memory : 8042.1875MB
% 0.90/1.09 % OS : Linux 3.10.0-693.el7.x86_64
% 0.90/1.09 % CPULimit : 2400
% 0.90/1.09 % WCLimit : 300
% 0.90/1.09 % DateTime : Mon Oct 2 23:05:22 EDT 2023
% 0.90/1.09 % CPUTime :
% 1.75/1.93 Running first-order theorem proving
% 1.75/1.93 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.8gt2hswYxV/E---3.1_25229.p
% 41.68/7.57 # Version: 3.1pre001
% 41.68/7.57 # Preprocessing class: FMLMSLSMSSSNFFN.
% 41.68/7.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.68/7.57 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 41.68/7.57 # Starting new_bool_3 with 300s (1) cores
% 41.68/7.57 # Starting new_bool_1 with 300s (1) cores
% 41.68/7.57 # Starting sh5l with 300s (1) cores
% 41.68/7.57 # new_bool_3 with pid 25308 completed with status 0
% 41.68/7.57 # Result found by new_bool_3
% 41.68/7.57 # Preprocessing class: FMLMSLSMSSSNFFN.
% 41.68/7.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.68/7.57 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 41.68/7.57 # Starting new_bool_3 with 300s (1) cores
% 41.68/7.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 41.68/7.57 # Search class: FGHSM-SMLM33-DFFFFFNN
% 41.68/7.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 41.68/7.57 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 41.68/7.57 # SAT001_MinMin_p005000_rr with pid 25312 completed with status 0
% 41.68/7.57 # Result found by SAT001_MinMin_p005000_rr
% 41.68/7.57 # Preprocessing class: FMLMSLSMSSSNFFN.
% 41.68/7.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.68/7.57 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 41.68/7.57 # Starting new_bool_3 with 300s (1) cores
% 41.68/7.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 41.68/7.57 # Search class: FGHSM-SMLM33-DFFFFFNN
% 41.68/7.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 41.68/7.57 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 41.68/7.57 # Preprocessing time : 0.054 s
% 41.68/7.57 # Presaturation interreduction done
% 41.68/7.57
% 41.68/7.57 # Proof found!
% 41.68/7.57 # SZS status ContradictoryAxioms
% 41.68/7.57 # SZS output start CNFRefutation
% See solution above
% 41.68/7.57 # Parsed axioms : 5243
% 41.68/7.57 # Removed by relevancy pruning/SinE : 3008
% 41.68/7.57 # Initial clauses : 3398
% 41.68/7.57 # Removed in clause preprocessing : 96
% 41.68/7.57 # Initial clauses in saturation : 3302
% 41.68/7.57 # Processed clauses : 17745
% 41.68/7.57 # ...of these trivial : 569
% 41.68/7.57 # ...subsumed : 9695
% 41.68/7.57 # ...remaining for further processing : 7481
% 41.68/7.57 # Other redundant clauses eliminated : 6259
% 41.68/7.57 # Clauses deleted for lack of memory : 0
% 41.68/7.57 # Backward-subsumed : 228
% 41.68/7.57 # Backward-rewritten : 453
% 41.68/7.57 # Generated clauses : 293472
% 41.68/7.57 # ...of the previous two non-redundant : 275859
% 41.68/7.57 # ...aggressively subsumed : 0
% 41.68/7.57 # Contextual simplify-reflections : 27
% 41.68/7.57 # Paramodulations : 287159
% 41.68/7.57 # Factorizations : 20
% 41.68/7.57 # NegExts : 0
% 41.68/7.57 # Equation resolutions : 6328
% 41.68/7.57 # Total rewrite steps : 72577
% 41.68/7.57 # Propositional unsat checks : 1
% 41.68/7.57 # Propositional check models : 0
% 41.68/7.57 # Propositional check unsatisfiable : 0
% 41.68/7.57 # Propositional clauses : 0
% 41.68/7.57 # Propositional clauses after purity: 0
% 41.68/7.57 # Propositional unsat core size : 0
% 41.68/7.57 # Propositional preprocessing time : 0.000
% 41.68/7.57 # Propositional encoding time : 0.092
% 41.68/7.57 # Propositional solver time : 0.034
% 41.68/7.57 # Success case prop preproc time : 0.000
% 41.68/7.57 # Success case prop encoding time : 0.000
% 41.68/7.57 # Success case prop solver time : 0.000
% 41.68/7.57 # Current number of processed clauses : 4055
% 41.68/7.57 # Positive orientable unit clauses : 847
% 41.68/7.57 # Positive unorientable unit clauses: 61
% 41.68/7.57 # Negative unit clauses : 638
% 41.68/7.57 # Non-unit-clauses : 2509
% 41.68/7.57 # Current number of unprocessed clauses: 249721
% 41.68/7.57 # ...number of literals in the above : 634739
% 41.68/7.57 # Current number of archived formulas : 0
% 41.68/7.57 # Current number of archived clauses : 3168
% 41.68/7.57 # Clause-clause subsumption calls (NU) : 1227133
% 41.68/7.57 # Rec. Clause-clause subsumption calls : 749919
% 41.68/7.57 # Non-unit clause-clause subsumptions : 4378
% 41.68/7.57 # Unit Clause-clause subsumption calls : 68893
% 41.68/7.57 # Rewrite failures with RHS unbound : 221
% 41.68/7.57 # BW rewrite match attempts : 16781
% 41.68/7.57 # BW rewrite match successes : 851
% 41.68/7.57 # Condensation attempts : 0
% 41.68/7.57 # Condensation successes : 0
% 41.68/7.57 # Termbank termtop insertions : 6408123
% 41.68/7.57
% 41.68/7.57 # -------------------------------------------------
% 41.68/7.57 # User time : 5.223 s
% 41.68/7.57 # System time : 0.191 s
% 41.68/7.57 # Total time : 5.414 s
% 41.68/7.57 # Maximum resident set size: 20168 pages
% 41.68/7.57
% 41.68/7.57 # -------------------------------------------------
% 41.68/7.57 # User time : 5.328 s
% 41.68/7.57 # System time : 0.198 s
% 41.68/7.57 # Total time : 5.526 s
% 41.68/7.57 # Maximum resident set size: 9544 pages
% 41.68/7.57 % E---3.1 exiting
% 41.68/7.57 % E---3.1 exiting
%------------------------------------------------------------------------------