TSTP Solution File: SWW306+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SWW306+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 20:09:03 EDT 2023

% Result   : ContradictoryAxioms 96.45s 15.72s
% Output   : CNFRefutation 96.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   88 (  72 unt;   0 def)
%            Number of atoms       :  112 (  89 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   54 (  30   ~;  18   |;   2   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;   9 con; 0-3 aty)
%            Number of variables   :  153 (  17 sgn;  84   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
    ! [X23,X5] :
      ( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Collect__empty__eq) ).

fof(fact_empty__def,axiom,
    ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Collect__def) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X23,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X23)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Collect__neg__eq) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [X23,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(c_Set_OCollect(X17),X23)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X17,tc_HOL_Obool,X5),X23),X2)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_vimage__Collect__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X311,X310,X5,X39] : hAPP(hAPP(c_COMBK(X39,X5),X310),X311) = X310,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',help_c__COMBK__1) ).

fof(fact_double__complement,axiom,
    ! [X19,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)),X19)) = X19,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_double__complement) ).

fof(fact_vimage__id,axiom,
    ! [X19,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X19) = X19,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_vimage__id) ).

fof(help_c__fNot__1,axiom,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',help_c__fNot__1) ).

fof(fact_UNIV__def,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_UNIV__def) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Zero__not__Suc) ).

fof(fact_transfer__nat__int__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Pls__def) ).

fof(fact_Compl__empty__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Compl__empty__eq) ).

fof(fact_add__0__iff,axiom,
    ! [X6,X22,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_add__0__iff) ).

fof(fact_add__Suc__right,axiom,
    ! [X99,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),hAPP(c_Nat_OSuc,X99)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X99)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_add__Suc__right) ).

fof(fact_id__def,axiom,
    ! [X208,X39] : hAPP(c_Fun_Oid(X39),X208) = X208,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_id__def) ).

fof(help_c__COMBB__1,axiom,
    ! [X32,X26,X23,X48,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X48),X23),X26),X32) = hAPP(X23,hAPP(X26,X32)),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',help_c__COMBB__1) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X100,
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_Nat_Oadd__0__right) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X99] : X99 != hAPP(c_Nat_OSuc,X99),
    file('/export/starexec/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p',fact_n__not__Suc__n) ).

fof(c_0_21,plain,
    ! [X23,X5] :
      ( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(c_0_22,plain,
    ! [X611] : c_Orderings_Obot__class_Obot(tc_fun(X611,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X611),hAPP(c_COMBK(tc_HOL_Obool,X611),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_23,plain,
    ! [X459,X460] : hAPP(c_Set_OCollect(X460),X459) = X459,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_24,plain,
    ! [X8189,X8190] : hAPP(c_Set_OCollect(X8190),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8190),c_fNot),X8189)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8190,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8190),X8189)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_25,plain,
    ! [X2487,X2488,X2489,X2490] : hAPP(c_Set_Ovimage(X2490,X2489,X2488),hAPP(c_Set_OCollect(X2489),X2487)) = hAPP(c_Set_OCollect(X2490),hAPP(hAPP(c_COMBB(X2489,tc_HOL_Obool,X2490),X2487),X2488)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(c_0_26,plain,
    ! [X583,X584,X585,X586,X588] :
      ( ( hAPP(c_Set_OCollect(X584),X583) != c_Orderings_Obot__class_Obot(tc_fun(X584,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X583,X585)) )
      & ( hBOOL(hAPP(X586,esk12_1(X586)))
        | hAPP(c_Set_OCollect(X588),X586) = c_Orderings_Obot__class_Obot(tc_fun(X588,tc_HOL_Obool)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).

fof(c_0_27,plain,
    ! [X17627,X17628,X17629,X17630] : hAPP(hAPP(c_COMBK(X17630,X17629),X17628),X17627) = X17628,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(c_0_28,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_30,plain,
    ! [X8150,X8151] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8151,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8151,tc_HOL_Obool)),X8150)) = X8150,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_31,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_24]) ).

fof(c_0_32,plain,
    ! [X10924,X10925] : hAPP(c_Set_Ovimage(X10925,X10925,c_Fun_Oid(X10925)),X10924) = X10924,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

cnf(c_0_33,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_25]) ).

fof(c_0_34,plain,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_35,plain,
    ( hBOOL(hAPP(X1,esk12_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_26]) ).

cnf(c_0_36,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_38,plain,
    ! [X2031] : c_Orderings_Otop__class_Otop(tc_fun(X2031,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2031),hAPP(c_COMBK(tc_HOL_Obool,X2031),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(c_0_39,plain,
    ! [X3730] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3730),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

cnf(c_0_40,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).

cnf(c_0_41,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

cnf(c_0_42,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_30]) ).

cnf(c_0_43,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_31,c_0_29]),c_0_29]) ).

cnf(c_0_44,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_45,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_33,c_0_29]),c_0_29]) ).

fof(c_0_46,plain,
    ! [X17653] :
      ( ~ hBOOL(hAPP(c_fNot,X17653))
      | ~ hBOOL(X17653) ),
    inference(variable_rename,[status(thm)],[c_0_34]) ).

cnf(c_0_47,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk12_1(X1))) ),
    inference(rw,[status(thm)],[c_0_35,c_0_29]) ).

cnf(c_0_48,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_49,plain,
    ! [X8279] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8279,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8279,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8279,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

cnf(c_0_50,plain,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

fof(c_0_51,plain,
    ! [X3430,X3431,X3432] :
      ( ( X3431 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3432),X3431),X3430)
        | X3430 = c_Groups_Ozero__class_Ozero(X3432)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3432) )
      & ( X3430 != c_Groups_Ozero__class_Ozero(X3432)
        | X3431 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3432),X3431),X3430)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3432) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(c_0_52,plain,
    ! [X3617,X3618] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3618),hAPP(c_Nat_OSuc,X3617)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3618),X3617)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_53,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_54,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_40,c_0_41]) ).

fof(c_0_55,plain,
    ! [X10910,X10911] : hAPP(c_Fun_Oid(X10911),X10910) = X10910,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

cnf(c_0_56,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_42,c_0_43]),c_0_43]) ).

cnf(c_0_57,plain,
    hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
    inference(rw,[status(thm)],[c_0_44,c_0_45]) ).

fof(c_0_58,plain,
    ! [X17631,X17632,X17633,X17634,X17635,X17636] : hAPP(hAPP(hAPP(c_COMBB(X17636,X17635,X17634),X17633),X17632),X17631) = hAPP(X17633,hAPP(X17632,X17631)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_59,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_60,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_48]),c_0_36]) ).

cnf(c_0_61,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_62,plain,
    hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_50,c_0_29]) ).

cnf(c_0_63,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_64,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_65,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

cnf(c_0_66,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_53,c_0_54]) ).

fof(c_0_67,plain,
    ! [X3333] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3333),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3333,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

cnf(c_0_68,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_69,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_56,c_0_57]) ).

cnf(c_0_70,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_71,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_72,plain,
    hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_61,c_0_43]) ).

cnf(c_0_73,plain,
    hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
    inference(spm,[status(thm)],[c_0_36,c_0_62]) ).

cnf(c_0_74,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54]),c_0_65])]),c_0_66]) ).

cnf(c_0_75,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

fof(c_0_76,plain,
    ! [X3159] : X3159 != hAPP(c_Nat_OSuc,X3159),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_77,plain,
    hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).

cnf(c_0_78,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_71,c_0_60]) ).

cnf(c_0_79,plain,
    hAPP(c_fNot,c_fFalse) = c_fTrue,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_72]),c_0_73]),c_0_48]) ).

cnf(c_0_80,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
    inference(spm,[status(thm)],[c_0_74,c_0_64]) ).

cnf(c_0_81,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
    inference(rw,[status(thm)],[c_0_75,c_0_54]) ).

cnf(c_0_82,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_83,plain,
    ( c_fFalse = X1
    | c_fTrue = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).

cnf(c_0_84,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_85,plain,
    hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83])]) ).

cnf(c_0_86,plain,
    hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_87,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_82]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.16/1.19  % Problem    : SWW306+1 : TPTP v8.1.2. Released v5.2.0.
% 1.16/1.20  % Command    : run_E %s %d THM
% 1.21/1.41  % Computer : n004.cluster.edu
% 1.21/1.41  % Model    : x86_64 x86_64
% 1.21/1.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.21/1.41  % Memory   : 8042.1875MB
% 1.21/1.41  % OS       : Linux 3.10.0-693.el7.x86_64
% 1.21/1.41  % CPULimit   : 2400
% 1.21/1.41  % WCLimit    : 300
% 1.21/1.41  % DateTime   : Mon Oct  2 22:21:16 EDT 2023
% 1.21/1.41  % CPUTime    : 
% 2.31/2.61  Running first-order theorem proving
% 2.31/2.61  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.VnPOUmXcq9/E---3.1_26771.p
% 96.45/15.72  # Version: 3.1pre001
% 96.45/15.72  # Preprocessing class: FMLMSMSMSSSNFFN.
% 96.45/15.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 96.45/15.72  # Starting new_bool_3 with 300s (1) cores
% 96.45/15.72  # Starting new_bool_1 with 300s (1) cores
% 96.45/15.72  # Starting sh5l with 300s (1) cores
% 96.45/15.72  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26870 completed with status 0
% 96.45/15.72  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 96.45/15.72  # Preprocessing class: FMLMSMSMSSSNFFN.
% 96.45/15.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 96.45/15.72  # No SInE strategy applied
% 96.45/15.72  # Search class: FGHSM-SMLM33-DFFFFFNN
% 96.45/15.72  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 96.45/15.72  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 96.45/15.72  # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 96.45/15.72  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 135s (1) cores
% 96.45/15.72  # SAT001_CA_MinMin_p005000_rr with pid 26895 completed with status 0
% 96.45/15.72  # Result found by SAT001_CA_MinMin_p005000_rr
% 96.45/15.72  # Preprocessing class: FMLMSMSMSSSNFFN.
% 96.45/15.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 96.45/15.72  # No SInE strategy applied
% 96.45/15.72  # Search class: FGHSM-SMLM33-DFFFFFNN
% 96.45/15.72  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 96.45/15.72  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 96.45/15.72  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 96.45/15.72  # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 96.45/15.72  # Preprocessing time       : 0.175 s
% 96.45/15.72  # Presaturation interreduction done
% 96.45/15.72  
% 96.45/15.72  # Proof found!
% 96.45/15.72  # SZS status ContradictoryAxioms
% 96.45/15.72  # SZS output start CNFRefutation
% See solution above
% 96.45/15.72  # Parsed axioms                        : 5230
% 96.45/15.72  # Removed by relevancy pruning/SinE    : 0
% 96.45/15.72  # Initial clauses                      : 7574
% 96.45/15.72  # Removed in clause preprocessing      : 230
% 96.45/15.72  # Initial clauses in saturation        : 7344
% 96.45/15.72  # Processed clauses                    : 20589
% 96.45/15.72  # ...of these trivial                  : 440
% 96.45/15.72  # ...subsumed                          : 7023
% 96.45/15.72  # ...remaining for further processing  : 13126
% 96.45/15.72  # Other redundant clauses eliminated   : 1139
% 96.45/15.72  # Clauses deleted for lack of memory   : 0
% 96.45/15.72  # Backward-subsumed                    : 119
% 96.45/15.72  # Backward-rewritten                   : 554
% 96.45/15.72  # Generated clauses                    : 206770
% 96.45/15.72  # ...of the previous two non-redundant : 198077
% 96.45/15.72  # ...aggressively subsumed             : 0
% 96.45/15.72  # Contextual simplify-reflections      : 28
% 96.45/15.72  # Paramodulations                      : 205648
% 96.45/15.72  # Factorizations                       : 2
% 96.45/15.72  # NegExts                              : 0
% 96.45/15.72  # Equation resolutions                 : 1185
% 96.45/15.72  # Total rewrite steps                  : 57105
% 96.45/15.72  # Propositional unsat checks           : 3
% 96.45/15.72  #    Propositional check models        : 2
% 96.45/15.72  #    Propositional check unsatisfiable : 0
% 96.45/15.72  #    Propositional clauses             : 0
% 96.45/15.72  #    Propositional clauses after purity: 0
% 96.45/15.72  #    Propositional unsat core size     : 0
% 96.45/15.72  #    Propositional preprocessing time  : 0.000
% 96.45/15.72  #    Propositional encoding time       : 0.199
% 96.45/15.72  #    Propositional solver time         : 0.093
% 96.45/15.72  #    Success case prop preproc time    : 0.000
% 96.45/15.72  #    Success case prop encoding time   : 0.000
% 96.45/15.72  #    Success case prop solver time     : 0.000
% 96.45/15.72  # Current number of processed clauses  : 6008
% 96.45/15.72  #    Positive orientable unit clauses  : 1630
% 96.45/15.72  #    Positive unorientable unit clauses: 128
% 96.45/15.72  #    Negative unit clauses             : 778
% 96.45/15.72  #    Non-unit-clauses                  : 3472
% 96.45/15.72  # Current number of unprocessed clauses: 178134
% 96.45/15.72  # ...number of literals in the above   : 332535
% 96.45/15.72  # Current number of archived formulas  : 0
% 96.45/15.72  # Current number of archived clauses   : 6667
% 96.45/15.72  # Clause-clause subsumption calls (NU) : 5090363
% 96.45/15.72  # Rec. Clause-clause subsumption calls : 2364957
% 96.45/15.72  # Non-unit clause-clause subsumptions  : 6387
% 96.45/15.72  # Unit Clause-clause subsumption calls : 235767
% 96.45/15.72  # Rewrite failures with RHS unbound    : 448
% 96.45/15.72  # BW rewrite match attempts            : 37840
% 96.45/15.72  # BW rewrite match successes           : 1355
% 96.45/15.72  # Condensation attempts                : 228469
% 96.45/15.72  # Condensation successes               : 1537
% 96.45/15.72  # Termbank termtop insertions          : 7037745
% 96.45/15.72  
% 96.45/15.72  # -------------------------------------------------
% 96.45/15.72  # User time                : 12.197 s
% 96.45/15.72  # System time              : 0.339 s
% 96.45/15.72  # Total time               : 12.536 s
% 96.45/15.72  # Maximum resident set size: 40032 pages
% 96.45/15.72  
% 96.45/15.72  # -------------------------------------------------
% 96.45/15.72  # User time                : 54.802 s
% 96.45/15.72  # System time              : 1.574 s
% 96.45/15.72  # Total time               : 56.376 s
% 96.45/15.72  # Maximum resident set size: 9464 pages
% 96.45/15.72  % E---3.1 exiting
% 96.45/15.72  % E---3.1 exiting
%------------------------------------------------------------------------------