TSTP Solution File: SWW376+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------