TSTP Solution File: SWW371+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWW371+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 10:03:21 EDT 2024

% Result   : ContradictoryAxioms 61.82s 9.68s
% Output   : CNFRefutation 61.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   83 (  67 unt;   0 def)
%            Number of atoms       :  107 (  84 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   56 (  32   ~;  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    :   21 (  21 usr;   9 con; 0-3 aty)
%            Number of variables   :  136 (  16 sgn  76   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
    ! [X17,X5] :
      ( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.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.BjI7pI98Hc/E---3.1_5304.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X17,X5] : hAPP(c_Set_OCollect(X5),X17) = X17,
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_Collect__def) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X17,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_Collect__neg__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X323,X70,X15,X5] : hAPP(hAPP(c_COMBK(X5,X15),X70),X323) = X70,
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',help_c__COMBK__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.BjI7pI98Hc/E---3.1_5304.p',fact_UNIV__def) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_Zero__neq__Suc) ).

fof(fact_double__complement,axiom,
    ! [X10,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)),X10)) = X10,
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_double__complement) ).

fof(help_c__fNot__1,axiom,
    ! [X17] :
      ( ~ hBOOL(hAPP(c_fNot,X17))
      | ~ hBOOL(X17) ),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',help_c__fNot__1) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_Compl__UNIV__eq) ).

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.BjI7pI98Hc/E---3.1_5304.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.BjI7pI98Hc/E---3.1_5304.p',fact_Pls__def) ).

fof(help_c__COMBB__1,axiom,
    ! [X33,X16,X17,X89,X5,X15] : hAPP(hAPP(hAPP(c_COMBB(X15,X5,X89),X17),X16),X33) = hAPP(X17,hAPP(X16,X33)),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',help_c__COMBB__1) ).

fof(fact_add__0__iff,axiom,
    ! [X6,X13,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X13),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.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.BjI7pI98Hc/E---3.1_5304.p',fact_add__Suc__right) ).

fof(fact_converse__converse,axiom,
    ! [X171,X5,X15] : hAPP(c_Relation_Oconverse(X15,X5),hAPP(c_Relation_Oconverse(X5,X15),X171)) = X171,
    file('/export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p',fact_converse__converse) ).

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.BjI7pI98Hc/E---3.1_5304.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.BjI7pI98Hc/E---3.1_5304.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.BjI7pI98Hc/E---3.1_5304.p',fact_n__not__Suc__n) ).

fof(c_0_19,plain,
    ! [X17,X5] :
      ( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(c_0_20,plain,
    ! [X11186] : c_Orderings_Obot__class_Obot(tc_fun(X11186,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11186),hAPP(c_COMBK(tc_HOL_Obool,X11186),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_21,plain,
    ! [X11164,X11165] : hAPP(c_Set_OCollect(X11165),X11164) = X11164,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_22,plain,
    ! [X11166,X11167] : hAPP(c_Set_OCollect(X11167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11167),c_fNot),X11166)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11167,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11167),X11166)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_23,plain,
    ! [X11174,X11175,X11176,X11177,X11179] :
      ( ( hAPP(c_Set_OCollect(X11175),X11174) != c_Orderings_Obot__class_Obot(tc_fun(X11175,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X11174,X11176)) )
      & ( hBOOL(hAPP(X11177,esk300_1(X11177)))
        | hAPP(c_Set_OCollect(X11179),X11177) = c_Orderings_Obot__class_Obot(tc_fun(X11179,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_19])])])])])]) ).

fof(c_0_24,plain,
    ! [X17589,X17590,X17591,X17592] : hAPP(hAPP(c_COMBK(X17592,X17591),X17590),X17589) = X17590,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(c_0_25,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_20]) ).

cnf(c_0_26,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_27,plain,
    ! [X11190] : c_Orderings_Otop__class_Otop(tc_fun(X11190,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11190),hAPP(c_COMBK(tc_HOL_Obool,X11190),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(c_0_28,plain,
    ! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
    inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(c_0_29,plain,
    ! [X1604,X1605] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1605,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1605,tc_HOL_Obool)),X1604)) = X1604,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_30,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_22]) ).

fof(c_0_31,plain,
    ! [X17] :
      ( ~ hBOOL(hAPP(c_fNot,X17))
      | ~ hBOOL(X17) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_32,plain,
    ( hBOOL(hAPP(X1,esk300_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_23]) ).

cnf(c_0_33,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,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_25,c_0_26]) ).

fof(c_0_35,plain,
    ! [X6716] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6716,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6716,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6716,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).

cnf(c_0_36,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_27]) ).

fof(c_0_37,plain,
    ! [X2696] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2696),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).

cnf(c_0_38,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_39,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

fof(c_0_40,plain,
    ! [X17593,X17594,X17595,X17596,X17597,X17598] : hAPP(hAPP(hAPP(c_COMBB(X17598,X17597,X17596),X17595),X17594),X17593) = hAPP(X17595,hAPP(X17594,X17593)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_41,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_29]) ).

cnf(c_0_42,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_30,c_0_26]),c_0_26]) ).

fof(c_0_43,plain,
    ! [X17615] :
      ( ~ hBOOL(hAPP(c_fNot,X17615))
      | ~ hBOOL(X17615) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).

cnf(c_0_44,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk300_1(X1))) ),
    inference(rw,[status(thm)],[c_0_32,c_0_26]) ).

cnf(c_0_45,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_46,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,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_36,c_0_26]) ).

fof(c_0_48,plain,
    ! [X2640,X2641,X2642] :
      ( ( X2641 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2642),X2641),X2640)
        | X2640 = c_Groups_Ozero__class_Ozero(X2642)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2642) )
      & ( X2640 != c_Groups_Ozero__class_Ozero(X2642)
        | X2641 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2642),X2641),X2640)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2642) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).

fof(c_0_49,plain,
    ! [X2253,X2254] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2254),hAPP(c_Nat_OSuc,X2253)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2254),X2253)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_50,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_51,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_52,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_53,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_41,c_0_42]),c_0_42]) ).

fof(c_0_54,plain,
    ! [X16672,X16673,X16674] : hAPP(c_Relation_Oconverse(X16674,X16673),hAPP(c_Relation_Oconverse(X16673,X16674),X16672)) = X16672,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

cnf(c_0_55,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_56,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_45]),c_0_33]) ).

cnf(c_0_57,plain,
    hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_46,c_0_42]) ).

cnf(c_0_58,plain,
    hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
    inference(spm,[status(thm)],[c_0_33,c_0_47]) ).

cnf(c_0_59,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_48]) ).

cnf(c_0_60,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_49]) ).

cnf(c_0_61,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_62,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_50,c_0_51]) ).

fof(c_0_63,plain,
    ! [X2708] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2708),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2708,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(c_0_64,plain,
    ! [X99] : X99 != hAPP(c_Nat_OSuc,X99),
    inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_65,plain,
    hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).

cnf(c_0_66,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_67,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_68,plain,
    hAPP(c_fNot,c_fTrue) = c_fFalse,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_45]),c_0_58]) ).

cnf(c_0_69,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_59,c_0_60]),c_0_51]),c_0_61])]),c_0_62]) ).

cnf(c_0_70,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_63]) ).

fof(c_0_71,plain,
    ! [X1870] : X1870 != hAPP(c_Nat_OSuc,X1870),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).

cnf(c_0_72,plain,
    hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_73,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_67,c_0_56]) ).

cnf(c_0_74,plain,
    hAPP(c_fNot,c_fFalse) = c_fTrue,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_68]) ).

cnf(c_0_75,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_69,c_0_60]) ).

cnf(c_0_76,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_70,c_0_51]) ).

cnf(c_0_77,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_78,plain,
    ( c_fFalse = X1
    | c_fTrue = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).

cnf(c_0_79,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_80,plain,
    hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78])]) ).

cnf(c_0_81,plain,
    hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_82,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_78]),c_0_77]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW371+1 : TPTP v8.1.2. Released v5.2.0.
% 0.14/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 13:20:16 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 1.24/1.45  Running first-order model finding
% 1.24/1.45  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.BjI7pI98Hc/E---3.1_5304.p
% 61.82/9.68  # Version: 3.1.0
% 61.82/9.68  # Preprocessing class: FMLMSLSMSSSNFFN.
% 61.82/9.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 61.82/9.68  # Starting new_bool_3 with 300s (1) cores
% 61.82/9.68  # Starting new_bool_1 with 300s (1) cores
% 61.82/9.68  # Starting sh5l with 300s (1) cores
% 61.82/9.68  # SAT001_MinMin_p005000_rr_RG with pid 5576 completed with status 0
% 61.82/9.68  # Result found by SAT001_MinMin_p005000_rr_RG
% 61.82/9.68  # Preprocessing class: FMLMSLSMSSSNFFN.
% 61.82/9.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 61.82/9.68  # No SInE strategy applied
% 61.82/9.68  # Search class: FGHSM-SMLM33-DFFFFFNN
% 61.82/9.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr with 811s (1) cores
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr_RG with 151s (1) cores
% 61.82/9.68  # Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 61.82/9.68  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 61.82/9.68  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 61.82/9.68  # SAT001_MinMin_p005000_rr with pid 5699 completed with status 0
% 61.82/9.68  # Result found by SAT001_MinMin_p005000_rr
% 61.82/9.68  # Preprocessing class: FMLMSLSMSSSNFFN.
% 61.82/9.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 61.82/9.68  # No SInE strategy applied
% 61.82/9.68  # Search class: FGHSM-SMLM33-DFFFFFNN
% 61.82/9.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 61.82/9.68  # Starting SAT001_MinMin_p005000_rr with 811s (1) cores
% 61.82/9.68  # Preprocessing time       : 0.171 s
% 61.82/9.68  # Presaturation interreduction done
% 61.82/9.68  
% 61.82/9.68  # Proof found!
% 61.82/9.68  # SZS status ContradictoryAxioms
% 61.82/9.68  # SZS output start CNFRefutation
% See solution above
% 61.82/9.68  # Parsed axioms                        : 5249
% 61.82/9.68  # Removed by relevancy pruning/SinE    : 0
% 61.82/9.68  # Initial clauses                      : 7536
% 61.82/9.68  # Removed in clause preprocessing      : 228
% 61.82/9.68  # Initial clauses in saturation        : 7308
% 61.82/9.68  # Processed clauses                    : 22311
% 61.82/9.68  # ...of these trivial                  : 435
% 61.82/9.68  # ...subsumed                          : 9350
% 61.82/9.68  # ...remaining for further processing  : 12526
% 61.82/9.68  # Other redundant clauses eliminated   : 1516
% 61.82/9.68  # Clauses deleted for lack of memory   : 0
% 61.82/9.68  # Backward-subsumed                    : 163
% 61.82/9.68  # Backward-rewritten                   : 381
% 61.82/9.68  # Generated clauses                    : 197446
% 61.82/9.68  # ...of the previous two non-redundant : 187047
% 61.82/9.68  # ...aggressively subsumed             : 0
% 61.82/9.68  # Contextual simplify-reflections      : 37
% 61.82/9.68  # Paramodulations                      : 195938
% 61.82/9.68  # Factorizations                       : 6
% 61.82/9.68  # NegExts                              : 0
% 61.82/9.68  # Equation resolutions                 : 1569
% 61.82/9.68  # Disequality decompositions           : 0
% 61.82/9.68  # Total rewrite steps                  : 65661
% 61.82/9.68  # ...of those cached                   : 46935
% 61.82/9.68  # Propositional unsat checks           : 3
% 61.82/9.68  #    Propositional check models        : 2
% 61.82/9.68  #    Propositional check unsatisfiable : 0
% 61.82/9.68  #    Propositional clauses             : 0
% 61.82/9.68  #    Propositional clauses after purity: 0
% 61.82/9.68  #    Propositional unsat core size     : 0
% 61.82/9.68  #    Propositional preprocessing time  : 0.000
% 61.82/9.68  #    Propositional encoding time       : 0.154
% 61.82/9.68  #    Propositional solver time         : 0.059
% 61.82/9.68  #    Success case prop preproc time    : 0.000
% 61.82/9.68  #    Success case prop encoding time   : 0.000
% 61.82/9.68  #    Success case prop solver time     : 0.000
% 61.82/9.68  # Current number of processed clauses  : 5587
% 61.82/9.68  #    Positive orientable unit clauses  : 1685
% 61.82/9.68  #    Positive unorientable unit clauses: 129
% 61.82/9.68  #    Negative unit clauses             : 951
% 61.82/9.68  #    Non-unit-clauses                  : 2822
% 61.82/9.68  # Current number of unprocessed clauses: 169178
% 61.82/9.68  # ...number of literals in the above   : 322941
% 61.82/9.68  # Current number of archived formulas  : 0
% 61.82/9.68  # Current number of archived clauses   : 6487
% 61.82/9.68  # Clause-clause subsumption calls (NU) : 4236414
% 61.82/9.68  # Rec. Clause-clause subsumption calls : 2043816
% 61.82/9.68  # Non-unit clause-clause subsumptions  : 5884
% 61.82/9.68  # Unit Clause-clause subsumption calls : 165652
% 61.82/9.68  # Rewrite failures with RHS unbound    : 738
% 61.82/9.68  # BW rewrite match attempts            : 39229
% 61.82/9.68  # BW rewrite match successes           : 1281
% 61.82/9.68  # Condensation attempts                : 0
% 61.82/9.68  # Condensation successes               : 0
% 61.82/9.68  # Termbank termtop insertions          : 6776986
% 61.82/9.68  # Search garbage collected termcells   : 99257
% 61.82/9.68  
% 61.82/9.68  # -------------------------------------------------
% 61.82/9.68  # User time                : 7.719 s
% 61.82/9.68  # System time              : 0.242 s
% 61.82/9.68  # Total time               : 7.961 s
% 61.82/9.68  # Maximum resident set size: 40584 pages
% 61.82/9.68  
% 61.82/9.68  # -------------------------------------------------
% 61.82/9.68  # User time                : 35.447 s
% 61.82/9.68  # System time              : 1.112 s
% 61.82/9.68  # Total time               : 36.558 s
% 61.82/9.68  # Maximum resident set size: 9524 pages
% 61.82/9.68  % E---3.1 exiting
%------------------------------------------------------------------------------