TSTP Solution File: SWW301+1 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SWW301+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 18:11:33 EDT 2024

% Result   : ContradictoryAxioms 80.22s 12.20s
% Output   : CNFRefutation 80.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   81 (  64 unt;   0 def)
%            Number of atoms       :  100 (  83 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   48 (  29   ~;  15   |;   1   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   9 con; 0-3 aty)
%            Number of variables   :  132 (  16 sgn  72   !;   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.PTlG6x98Yn/E---3.1_25415.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.PTlG6x98Yn/E---3.1_25415.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.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.PTlG6x98Yn/E---3.1_25415.p',fact_Collect__neg__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X304,X303,X5,X44] : hAPP(hAPP(c_COMBK(X44,X5),X303),X304) = X303,
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',help_c__COMBK__1) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_Zero__neq__Suc) ).

fof(fact_double__complement,axiom,
    ! [X18,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)),X18)) = X18,
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_double__complement) ).

fof(help_c__fNot__1,axiom,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.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.PTlG6x98Yn/E---3.1_25415.p',fact_UNIV__def) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X74,X73] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74) = X73
     => X74 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_add__eq__self__zero) ).

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.PTlG6x98Yn/E---3.1_25415.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.PTlG6x98Yn/E---3.1_25415.p',fact_Pls__def) ).

fof(help_c__COMBB__1,axiom,
    ! [X30,X26,X23,X132,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X132),X23),X26),X30) = hAPP(X23,hAPP(X26,X30)),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',help_c__COMBB__1) ).

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.PTlG6x98Yn/E---3.1_25415.p',fact_Compl__empty__eq) ).

fof(fact_add__Suc__right,axiom,
    ! [X74,X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),hAPP(c_Nat_OSuc,X74)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74)),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_add__Suc__right) ).

fof(fact_rev__rev__ident,axiom,
    ! [X225,X44] : hAPP(c_List_Orev(X44),hAPP(c_List_Orev(X44),X225)) = X225,
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_rev__rev__ident) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_Nat_Oadd__0__right) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
    file('/export/starexec/sandbox2/tmp/tmp.PTlG6x98Yn/E---3.1_25415.p',fact_n__not__Suc__n) ).

fof(c_0_18,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_19,plain,
    ! [X10933] : c_Orderings_Obot__class_Obot(tc_fun(X10933,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10933),hAPP(c_COMBK(tc_HOL_Obool,X10933),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_20,plain,
    ! [X10949,X10950] : hAPP(c_Set_OCollect(X10950),X10949) = X10949,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_21,plain,
    ! [X10956,X10957] : hAPP(c_Set_OCollect(X10957),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10957),c_fNot),X10956)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10957,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10957),X10956)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_22,plain,
    ! [X10934,X10935,X10936,X10937,X10939] :
      ( ( hAPP(c_Set_OCollect(X10935),X10934) != c_Orderings_Obot__class_Obot(tc_fun(X10935,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X10934,X10936)) )
      & ( hBOOL(hAPP(X10937,esk294_1(X10937)))
        | hAPP(c_Set_OCollect(X10939),X10937) = c_Orderings_Obot__class_Obot(tc_fun(X10939,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])]) ).

fof(c_0_23,plain,
    ! [X17523,X17524,X17525,X17526] : hAPP(hAPP(c_COMBK(X17526,X17525),X17524),X17523) = X17524,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(c_0_24,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_19]) ).

cnf(c_0_25,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_26,plain,
    ! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
    inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(c_0_27,plain,
    ! [X5760,X5761] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5761,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5761,tc_HOL_Obool)),X5760)) = X5760,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_28,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_21]) ).

fof(c_0_29,plain,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_30,plain,
    ( hBOOL(hAPP(X1,esk294_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_22]) ).

cnf(c_0_31,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,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_24,c_0_25]) ).

fof(c_0_33,plain,
    ! [X10951] : c_Orderings_Otop__class_Otop(tc_fun(X10951,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10951),hAPP(c_COMBK(tc_HOL_Obool,X10951),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(c_0_34,plain,
    ! [X3150,X3151] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3151),X3150) != X3151
      | X3150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).

cnf(c_0_35,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_36,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

fof(c_0_37,plain,
    ! [X3139] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3139),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).

fof(c_0_38,plain,
    ! [X17527,X17528,X17529,X17530,X17531,X17532] : hAPP(hAPP(hAPP(c_COMBB(X17532,X17531,X17530),X17529),X17528),X17527) = hAPP(X17529,hAPP(X17528,X17527)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_39,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_27]) ).

cnf(c_0_40,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_28,c_0_25]),c_0_25]) ).

fof(c_0_41,plain,
    ! [X17549] :
      ( ~ hBOOL(hAPP(c_fNot,X17549))
      | ~ hBOOL(X17549) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).

cnf(c_0_42,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk294_1(X1))) ),
    inference(rw,[status(thm)],[c_0_30,c_0_25]) ).

cnf(c_0_43,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

fof(c_0_44,plain,
    ! [X6564] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6564,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6564,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6564,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

cnf(c_0_45,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_33]) ).

cnf(c_0_46,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_47,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

fof(c_0_48,plain,
    ! [X2844,X2845] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),hAPP(c_Nat_OSuc,X2844)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),X2844)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_49,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_50,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_51,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_39,c_0_40]),c_0_40]) ).

fof(c_0_52,plain,
    ! [X15527,X15528] : hAPP(c_List_Orev(X15528),hAPP(c_List_Orev(X15528),X15527)) = X15527,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

cnf(c_0_53,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_43]),c_0_31]) ).

cnf(c_0_55,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_44]) ).

cnf(c_0_56,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_45,c_0_25]) ).

cnf(c_0_57,plain,
    ( X1 = hAPP(c_Int_Onat,c_Int_OPls)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_58,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_48]) ).

cnf(c_0_59,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_49,c_0_47]) ).

fof(c_0_60,plain,
    ! [X3154] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3154),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3154,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(c_0_61,plain,
    ! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
    inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_62,plain,
    hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).

cnf(c_0_63,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_64,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_65,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_55,c_0_40]) ).

cnf(c_0_66,plain,
    hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
    inference(spm,[status(thm)],[c_0_31,c_0_56]) ).

cnf(c_0_67,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_68,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_60]) ).

fof(c_0_69,plain,
    ! [X2804] : X2804 != hAPP(c_Nat_OSuc,X2804),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_61])]) ).

cnf(c_0_70,plain,
    hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_71,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_64,c_0_54]) ).

cnf(c_0_72,plain,
    hAPP(c_fNot,c_fFalse) = c_fTrue,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_65]),c_0_66]),c_0_43]) ).

cnf(c_0_73,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_67,c_0_58]) ).

cnf(c_0_74,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_68,c_0_47]) ).

cnf(c_0_75,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_76,plain,
    ( c_fFalse = X1
    | c_fTrue = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).

cnf(c_0_77,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_78,plain,
    hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76])]) ).

cnf(c_0_79,plain,
    hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_80,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_76]),c_0_75]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWW301+1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Jun 19 04:56:39 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 1.14/1.33  Running first-order theorem proving
% 1.14/1.33  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.PTlG6x98Yn/E---3.1_25415.p
% 80.22/12.20  # Version: 3.2.0
% 80.22/12.20  # Preprocessing class: FMLMSMSMSSSNFFN.
% 80.22/12.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 80.22/12.20  # Starting new_bool_3 with 300s (1) cores
% 80.22/12.20  # Starting new_bool_1 with 300s (1) cores
% 80.22/12.20  # Starting sh5l with 300s (1) cores
% 80.22/12.20  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 25494 completed with status 0
% 80.22/12.20  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 80.22/12.20  # Preprocessing class: FMLMSMSMSSSNFFN.
% 80.22/12.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 80.22/12.20  # No SInE strategy applied
% 80.22/12.20  # Search class: FGHSM-SMLM33-DFFFFFNN
% 80.22/12.20  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 80.22/12.20  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 80.22/12.20  # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 80.22/12.20  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 135s (1) cores
% 80.22/12.20  # SAT001_CA_MinMin_p005000_rr with pid 25503 completed with status 0
% 80.22/12.20  # Result found by SAT001_CA_MinMin_p005000_rr
% 80.22/12.20  # Preprocessing class: FMLMSMSMSSSNFFN.
% 80.22/12.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 80.22/12.20  # No SInE strategy applied
% 80.22/12.20  # Search class: FGHSM-SMLM33-DFFFFFNN
% 80.22/12.20  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 80.22/12.20  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 80.22/12.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 80.22/12.20  # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 80.22/12.20  # Preprocessing time       : 0.168 s
% 80.22/12.20  # Presaturation interreduction done
% 80.22/12.20  
% 80.22/12.20  # Proof found!
% 80.22/12.20  # SZS status ContradictoryAxioms
% 80.22/12.20  # SZS output start CNFRefutation
% See solution above
% 80.22/12.20  # Parsed axioms                        : 5224
% 80.22/12.20  # Removed by relevancy pruning/SinE    : 0
% 80.22/12.20  # Initial clauses                      : 7581
% 80.22/12.20  # Removed in clause preprocessing      : 250
% 80.22/12.20  # Initial clauses in saturation        : 7331
% 80.22/12.20  # Processed clauses                    : 21002
% 80.22/12.20  # ...of these trivial                  : 413
% 80.22/12.20  # ...subsumed                          : 7449
% 80.22/12.20  # ...remaining for further processing  : 13140
% 80.22/12.20  # Other redundant clauses eliminated   : 1467
% 80.22/12.20  # Clauses deleted for lack of memory   : 0
% 80.22/12.20  # Backward-subsumed                    : 134
% 80.22/12.20  # Backward-rewritten                   : 402
% 80.22/12.20  # Generated clauses                    : 191526
% 80.22/12.20  # ...of the previous two non-redundant : 182304
% 80.22/12.20  # ...aggressively subsumed             : 0
% 80.22/12.20  # Contextual simplify-reflections      : 32
% 80.22/12.20  # Paramodulations                      : 190076
% 80.22/12.20  # Factorizations                       : 2
% 80.22/12.20  # NegExts                              : 0
% 80.22/12.20  # Equation resolutions                 : 1514
% 80.22/12.20  # Disequality decompositions           : 0
% 80.22/12.20  # Total rewrite steps                  : 62147
% 80.22/12.20  # ...of those cached                   : 44164
% 80.22/12.20  # Propositional unsat checks           : 3
% 80.22/12.20  #    Propositional check models        : 2
% 80.22/12.20  #    Propositional check unsatisfiable : 0
% 80.22/12.20  #    Propositional clauses             : 0
% 80.22/12.20  #    Propositional clauses after purity: 0
% 80.22/12.20  #    Propositional unsat core size     : 0
% 80.22/12.20  #    Propositional preprocessing time  : 0.000
% 80.22/12.20  #    Propositional encoding time       : 0.176
% 80.22/12.20  #    Propositional solver time         : 0.075
% 80.22/12.20  #    Success case prop preproc time    : 0.000
% 80.22/12.20  #    Success case prop encoding time   : 0.000
% 80.22/12.20  #    Success case prop solver time     : 0.000
% 80.22/12.20  # Current number of processed clauses  : 6206
% 80.22/12.20  #    Positive orientable unit clauses  : 1588
% 80.22/12.20  #    Positive unorientable unit clauses: 126
% 80.22/12.20  #    Negative unit clauses             : 981
% 80.22/12.20  #    Non-unit-clauses                  : 3511
% 80.22/12.20  # Current number of unprocessed clauses: 168670
% 80.22/12.20  # ...number of literals in the above   : 326037
% 80.22/12.20  # Current number of archived formulas  : 0
% 80.22/12.20  # Current number of archived clauses   : 6481
% 80.22/12.20  # Clause-clause subsumption calls (NU) : 4035179
% 80.22/12.20  # Rec. Clause-clause subsumption calls : 2003498
% 80.22/12.20  # Non-unit clause-clause subsumptions  : 5634
% 80.22/12.20  # Unit Clause-clause subsumption calls : 206228
% 80.22/12.20  # Rewrite failures with RHS unbound    : 531
% 80.22/12.20  # BW rewrite match attempts            : 37879
% 80.22/12.20  # BW rewrite match successes           : 1341
% 80.22/12.20  # Condensation attempts                : 213334
% 80.22/12.20  # Condensation successes               : 993
% 80.22/12.20  # Termbank termtop insertions          : 6960317
% 80.22/12.20  # Search garbage collected termcells   : 101797
% 80.22/12.20  
% 80.22/12.20  # -------------------------------------------------
% 80.22/12.20  # User time                : 10.184 s
% 80.22/12.20  # System time              : 0.275 s
% 80.22/12.20  # Total time               : 10.459 s
% 80.22/12.20  # Maximum resident set size: 40712 pages
% 80.22/12.20  
% 80.22/12.20  # -------------------------------------------------
% 80.22/12.20  # User time                : 46.267 s
% 80.22/12.20  # System time              : 1.201 s
% 80.22/12.20  # Total time               : 47.468 s
% 80.22/12.20  # Maximum resident set size: 9464 pages
% 80.22/12.20  % E---3.1 exiting
% 80.22/12.20  % E exiting
%------------------------------------------------------------------------------