TSTP Solution File: SWW309+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SWW309+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 20:10:59 EDT 2023

% Result   : ContradictoryAxioms 20.21s 4.65s
% Output   : CNFRefutation 20.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   65 (  52 unt;   0 def)
%            Number of atoms       :   86 (  44 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   45 (  24   ~;  14   |;   2   &)
%                                         (   1 <=>;   4  =>;   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    :   24 (  24 usr;   6 con; 0-3 aty)
%            Number of variables   :  107 (  12 sgn;  59   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
    ! [X23,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X23)) = X23,
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_Collect__mem__eq) ).

fof(fact_Collect__def,axiom,
    ! [X10,X5] : hAPP(c_Set_OCollect(X5),X10) = X10,
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_Collect__def) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X115] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),X115)),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_less__irrefl__nat) ).

fof(help_c__COMBC__1,axiom,
    ! [X35,X27,X10,X5,X51,X21] : hAPP(hAPP(hAPP(c_COMBC(X21,X51,X5),X10),X27),X35) = hAPP(hAPP(X10,X35),X27),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',help_c__COMBC__1) ).

fof(fact_number__of__is__id,axiom,
    ! [X117] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X117) = X117,
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_number__of__is__id) ).

fof(fact_nat__number__of__def,axiom,
    ! [X168] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_nat__number__of__def) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X114] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X114) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X114)),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_less__eq__Suc__le__raw) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X139] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X139))
    <=> ? [X140] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X139))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X140)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_one__is__num__one,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_one__is__num__one) ).

fof(fact_card__infinite,axiom,
    ! [X23,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X23))
     => hAPP(c_Finite__Set_Ocard(X5),X23) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_card__infinite) ).

fof(fact_rangeI,axiom,
    ! [X21,X20,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),hAPP(c_Set_Oimage(X21,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X21,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_rangeI) ).

fof(fact_card__UNIV__bool,axiom,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_card__UNIV__bool) ).

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/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.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/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_Pls__def) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X116] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X116),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_Zero__not__Suc) ).

fof(fact_semiring__norm_I115_J,axiom,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_semiring__norm_I115_J) ).

fof(fact_finite__imageI,axiom,
    ! [X52,X21,X136,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X136))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X21),hAPP(c_Set_Oimage(X5,X21,X52),X136))) ),
    file('/export/starexec/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p',fact_finite__imageI) ).

fof(c_0_17,plain,
    ! [X1540,X1541] : hAPP(c_Set_OCollect(X1541),hAPP(hAPP(c_COMBC(X1541,tc_fun(X1541,tc_HOL_Obool),tc_HOL_Obool),c_member(X1541)),X1540)) = X1540,
    inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).

fof(c_0_18,plain,
    ! [X1521,X1522] : hAPP(c_Set_OCollect(X1522),X1521) = X1521,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_19,plain,
    ! [X115] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),X115)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(c_0_20,plain,
    ! [X599,X600,X601,X602,X603,X604] : hAPP(hAPP(hAPP(c_COMBC(X604,X603,X602),X601),X600),X599) = hAPP(hAPP(X601,X599),X600),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

cnf(c_0_21,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_17]) ).

cnf(c_0_22,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_23,plain,
    ! [X4067] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4067) = X4067,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(c_0_24,plain,
    ! [X3520] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3520) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3520)),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).

fof(c_0_25,plain,
    ! [X1318] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1318),X1318)),
    inference(variable_rename,[status(thm)],[c_0_19]) ).

fof(c_0_26,plain,
    ! [X2858] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2858) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2858)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(c_0_27,plain,
    ! [X1482,X1484,X1485,X1486] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1482))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1484),X1482))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1484),esk33_1(X1482))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk34_2(X1485,X1486)),X1485))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1485)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk34_2(X1485,X1486)),X1486))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1485)) ) ),
    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_finite__nat__set__iff__bounded__le])])])])])]) ).

cnf(c_0_28,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,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_21,c_0_22]) ).

cnf(c_0_30,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).

cnf(c_0_31,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_33,plain,
    ! [X23,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X23))
     => hAPP(c_Finite__Set_Ocard(X5),X23) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

cnf(c_0_34,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk33_1(X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_38,plain,
    ! [X1890,X1891,X1892,X1893] : hBOOL(hAPP(hAPP(c_member(X1893),hAPP(X1892,X1891)),hAPP(c_Set_Oimage(X1890,X1893,X1892),c_Orderings_Otop__class_Otop(tc_fun(X1890,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

cnf(c_0_39,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).

cnf(c_0_40,plain,
    c_Int_OBit1(c_Int_OPls) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_41,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
    inference(rw,[status(thm)],[c_0_32,c_0_31]) ).

cnf(c_0_42,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_43,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

fof(c_0_44,plain,
    ! [X3009,X3010] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3010),X3009))
      | hAPP(c_Finite__Set_Ocard(X3010),X3009) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).

fof(c_0_45,plain,
    ! [X2862] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2862),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

cnf(c_0_46,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk33_1(X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_48,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_49,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).

cnf(c_0_50,plain,
    hAPP(c_Int_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).

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_42,c_0_43]) ).

cnf(c_0_52,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

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_45]) ).

cnf(c_0_54,plain,
    ( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk33_1(X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_55,plain,
    hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
    inference(rw,[status(thm)],[c_0_48,c_0_37]) ).

fof(c_0_56,plain,
    ! [X1920,X1921,X1922,X1923] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1923),X1922))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X1921),hAPP(c_Set_Oimage(X1923,X1921,X1920),X1922))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

cnf(c_0_57,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_40]),c_0_41]),c_0_50]),c_0_51]) ).

cnf(c_0_58,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(c_Int_Onat,c_Int_OPls)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(rw,[status(thm)],[c_0_52,c_0_51]) ).

cnf(c_0_59,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_53,c_0_51]) ).

cnf(c_0_60,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(X1,X2,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_61,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_62,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_63,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_64,plain,
    $false,
    inference(sr,[status(thm)],[c_0_62,c_0_63]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SWW309+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.14  % Command    : run_E %s %d THM
% 0.13/0.36  % Computer : n006.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 2400
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Mon Oct  2 22:49:40 EDT 2023
% 0.13/0.36  % CPUTime    : 
% 1.17/1.34  Running first-order model finding
% 1.17/1.34  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.JhKjWtL5Xv/E---3.1_10189.p
% 20.21/4.65  # Version: 3.1pre001
% 20.21/4.65  # Preprocessing class: FMLMSMSMSSSNFFN.
% 20.21/4.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.21/4.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.21/4.65  # Starting new_bool_3 with 300s (1) cores
% 20.21/4.65  # Starting new_bool_1 with 300s (1) cores
% 20.21/4.65  # Starting sh5l with 300s (1) cores
% 20.21/4.65  # new_bool_3 with pid 10282 completed with status 0
% 20.21/4.65  # Result found by new_bool_3
% 20.21/4.65  # Preprocessing class: FMLMSMSMSSSNFFN.
% 20.21/4.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.21/4.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.21/4.65  # Starting new_bool_3 with 300s (1) cores
% 20.21/4.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 20.21/4.65  # Search class: FGHSM-SMLM33-DFFFFFNN
% 20.21/4.65  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 20.21/4.65  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 20.21/4.65  # SAT001_MinMin_p005000_rr with pid 10286 completed with status 0
% 20.21/4.65  # Result found by SAT001_MinMin_p005000_rr
% 20.21/4.65  # Preprocessing class: FMLMSMSMSSSNFFN.
% 20.21/4.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.21/4.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.21/4.65  # Starting new_bool_3 with 300s (1) cores
% 20.21/4.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 20.21/4.65  # Search class: FGHSM-SMLM33-DFFFFFNN
% 20.21/4.65  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 20.21/4.65  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 20.21/4.65  # Preprocessing time       : 0.046 s
% 20.21/4.65  # Presaturation interreduction done
% 20.21/4.65  
% 20.21/4.65  # Proof found!
% 20.21/4.65  # SZS status ContradictoryAxioms
% 20.21/4.65  # SZS output start CNFRefutation
% See solution above
% 20.21/4.65  # Parsed axioms                        : 5228
% 20.21/4.65  # Removed by relevancy pruning/SinE    : 3186
% 20.21/4.65  # Initial clauses                      : 3166
% 20.21/4.65  # Removed in clause preprocessing      : 86
% 20.21/4.65  # Initial clauses in saturation        : 3080
% 20.21/4.65  # Processed clauses                    : 12133
% 20.21/4.65  # ...of these trivial                  : 493
% 20.21/4.65  # ...subsumed                          : 5486
% 20.21/4.65  # ...remaining for further processing  : 6154
% 20.21/4.65  # Other redundant clauses eliminated   : 651
% 20.21/4.65  # Clauses deleted for lack of memory   : 0
% 20.21/4.65  # Backward-subsumed                    : 143
% 20.21/4.65  # Backward-rewritten                   : 494
% 20.21/4.65  # Generated clauses                    : 107443
% 20.21/4.65  # ...of the previous two non-redundant : 102486
% 20.21/4.65  # ...aggressively subsumed             : 0
% 20.21/4.65  # Contextual simplify-reflections      : 20
% 20.21/4.65  # Paramodulations                      : 106771
% 20.21/4.65  # Factorizations                       : 12
% 20.21/4.65  # NegExts                              : 0
% 20.21/4.65  # Equation resolutions                 : 696
% 20.21/4.65  # Total rewrite steps                  : 27034
% 20.21/4.65  # Propositional unsat checks           : 1
% 20.21/4.65  #    Propositional check models        : 0
% 20.21/4.65  #    Propositional check unsatisfiable : 0
% 20.21/4.65  #    Propositional clauses             : 0
% 20.21/4.65  #    Propositional clauses after purity: 0
% 20.21/4.65  #    Propositional unsat core size     : 0
% 20.21/4.65  #    Propositional preprocessing time  : 0.000
% 20.21/4.65  #    Propositional encoding time       : 0.114
% 20.21/4.65  #    Propositional solver time         : 0.039
% 20.21/4.65  #    Success case prop preproc time    : 0.000
% 20.21/4.65  #    Success case prop encoding time   : 0.000
% 20.21/4.65  #    Success case prop solver time     : 0.000
% 20.21/4.65  # Current number of processed clauses  : 2943
% 20.21/4.65  #    Positive orientable unit clauses  : 684
% 20.21/4.65  #    Positive unorientable unit clauses: 60
% 20.21/4.65  #    Negative unit clauses             : 451
% 20.21/4.65  #    Non-unit-clauses                  : 1748
% 20.21/4.65  # Current number of unprocessed clauses: 82605
% 20.21/4.65  # ...number of literals in the above   : 178785
% 20.21/4.65  # Current number of archived formulas  : 0
% 20.21/4.65  # Current number of archived clauses   : 2970
% 20.21/4.65  # Clause-clause subsumption calls (NU) : 990782
% 20.21/4.65  # Rec. Clause-clause subsumption calls : 556020
% 20.21/4.65  # Non-unit clause-clause subsumptions  : 3160
% 20.21/4.65  # Unit Clause-clause subsumption calls : 40412
% 20.21/4.65  # Rewrite failures with RHS unbound    : 701
% 20.21/4.65  # BW rewrite match attempts            : 12708
% 20.21/4.65  # BW rewrite match successes           : 1092
% 20.21/4.65  # Condensation attempts                : 0
% 20.21/4.65  # Condensation successes               : 0
% 20.21/4.65  # Termbank termtop insertions          : 3117737
% 20.21/4.65  
% 20.21/4.65  # -------------------------------------------------
% 20.21/4.65  # User time                : 2.681 s
% 20.21/4.65  # System time              : 0.100 s
% 20.21/4.65  # Total time               : 2.781 s
% 20.21/4.65  # Maximum resident set size: 18796 pages
% 20.21/4.65  
% 20.21/4.65  # -------------------------------------------------
% 20.21/4.65  # User time                : 2.897 s
% 20.21/4.65  # System time              : 0.112 s
% 20.21/4.65  # Total time               : 3.009 s
% 20.21/4.65  # Maximum resident set size: 9464 pages
% 20.21/4.65  % E---3.1 exiting
%------------------------------------------------------------------------------