TSTP Solution File: SWW341+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWW341+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 10:03:15 EDT 2024

% Result   : ContradictoryAxioms 64.41s 9.62s
% Output   : CNFRefutation 64.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   90 (  74 unt;   0 def)
%            Number of atoms       :  114 (  91 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    :   22 (  22 usr;   9 con; 0-3 aty)
%            Number of variables   :  155 (  17 sgn  86   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
    ! [X9,X5] :
      ( hAPP(c_Set_OCollect(X5),X9) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X9,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.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/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X9,X5] : hAPP(c_Set_OCollect(X5),X9) = X9,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_Collect__def) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X9,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X9)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X9)),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_Collect__neg__eq) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [X9,X2,X24,X5] : hAPP(c_Set_Ovimage(X5,X24,X2),hAPP(c_Set_OCollect(X24),X9)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X24,tc_HOL_Obool,X5),X9),X2)),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_vimage__Collect__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X321,X320,X5,X44] : hAPP(hAPP(c_COMBK(X44,X5),X320),X321) = X320,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',help_c__COMBK__1) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_Zero__not__Suc) ).

fof(fact_double__complement,axiom,
    ! [X26,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)),X26)) = X26,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_double__complement) ).

fof(fact_vimage__id,axiom,
    ! [X26,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X26) = X26,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_vimage__id) ).

fof(help_c__fNot__1,axiom,
    ! [X9] :
      ( ~ hBOOL(hAPP(c_fNot,X9))
      | ~ hBOOL(X9) ),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.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/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_UNIV__def) ).

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.KbgMvAMx47/E---3.1_28559.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.KbgMvAMx47/E---3.1_28559.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/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_Compl__empty__eq) ).

fof(fact_add__0__iff,axiom,
    ! [X6,X28,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X28 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_add__0__iff) ).

fof(fact_add__Suc__right,axiom,
    ! [X35,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X35)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X35)),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_add__Suc__right) ).

fof(fact_id__def,axiom,
    ! [X227,X44] : hAPP(c_Fun_Oid(X44),X227) = X227,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_id__def) ).

fof(help_c__COMBB__1,axiom,
    ! [X40,X7,X9,X118,X5,X24] : hAPP(hAPP(hAPP(c_COMBB(X24,X5,X118),X9),X7),X40) = hAPP(X9,hAPP(X7,X40)),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.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/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X72,
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_Nat_Oadd__0__right) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X35] : X35 != hAPP(c_Nat_OSuc,X35),
    file('/export/starexec/sandbox/tmp/tmp.KbgMvAMx47/E---3.1_28559.p',fact_n__not__Suc__n) ).

fof(c_0_21,plain,
    ! [X9,X5] :
      ( hAPP(c_Set_OCollect(X5),X9) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X9,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(c_0_22,plain,
    ! [X11117] : c_Orderings_Obot__class_Obot(tc_fun(X11117,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11117),hAPP(c_COMBK(tc_HOL_Obool,X11117),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_23,plain,
    ! [X11121,X11122] : hAPP(c_Set_OCollect(X11122),X11121) = X11121,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_24,plain,
    ! [X11100,X11101] : hAPP(c_Set_OCollect(X11101),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11101),c_fNot),X11100)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11101,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11101),X11100)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_25,plain,
    ! [X11123,X11124,X11125,X11126] : hAPP(c_Set_Ovimage(X11126,X11125,X11124),hAPP(c_Set_OCollect(X11125),X11123)) = hAPP(c_Set_OCollect(X11126),hAPP(hAPP(c_COMBB(X11125,tc_HOL_Obool,X11126),X11123),X11124)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(c_0_26,plain,
    ! [X11105,X11106,X11107,X11108,X11110] :
      ( ( hAPP(c_Set_OCollect(X11106),X11105) != c_Orderings_Obot__class_Obot(tc_fun(X11106,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X11105,X11107)) )
      & ( hBOOL(hAPP(X11108,esk303_1(X11108)))
        | hAPP(c_Set_OCollect(X11110),X11108) = c_Orderings_Obot__class_Obot(tc_fun(X11110,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_21])])])])])]) ).

fof(c_0_27,plain,
    ! [X17673,X17674,X17675,X17676] : hAPP(hAPP(c_COMBK(X17676,X17675),X17674),X17673) = X17674,
    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,
    ! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
    inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).

fof(c_0_31,plain,
    ! [X4400,X4401] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4401,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4401,tc_HOL_Obool)),X4400)) = X4400,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_32,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_33,plain,
    ! [X11331,X11332] : hAPP(c_Set_Ovimage(X11332,X11332,c_Fun_Oid(X11332)),X11331) = X11331,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

cnf(c_0_34,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_35,plain,
    ! [X9] :
      ( ~ hBOOL(hAPP(c_fNot,X9))
      | ~ hBOOL(X9) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_36,plain,
    ( hBOOL(hAPP(X1,esk303_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_37,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_38,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_39,plain,
    ! [X11127] : c_Orderings_Otop__class_Otop(tc_fun(X11127,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11127),hAPP(c_COMBK(tc_HOL_Obool,X11127),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(c_0_40,plain,
    ! [X2085] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2085),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).

cnf(c_0_41,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_42,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

cnf(c_0_43,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_31]) ).

cnf(c_0_44,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_32,c_0_29]),c_0_29]) ).

cnf(c_0_45,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_46,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_34,c_0_29]),c_0_29]) ).

fof(c_0_47,plain,
    ! [X17699] :
      ( ~ hBOOL(hAPP(c_fNot,X17699))
      | ~ hBOOL(X17699) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).

cnf(c_0_48,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk303_1(X1))) ),
    inference(rw,[status(thm)],[c_0_36,c_0_29]) ).

cnf(c_0_49,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

fof(c_0_50,plain,
    ! [X8384] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8384,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8384,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8384,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

cnf(c_0_51,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_39]) ).

fof(c_0_52,plain,
    ! [X2478,X2479,X2480] :
      ( ( X2479 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2480),X2479),X2478)
        | X2478 = c_Groups_Ozero__class_Ozero(X2480)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2480) )
      & ( X2478 != c_Groups_Ozero__class_Ozero(X2480)
        | X2479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2480),X2479),X2478)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2480) ) ),
    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_53,plain,
    ! [X1492,X1493] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1493),hAPP(c_Nat_OSuc,X1492)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1493),X1492)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_54,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_55,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

fof(c_0_56,plain,
    ! [X11333,X11334] : hAPP(c_Fun_Oid(X11334),X11333) = X11333,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

cnf(c_0_57,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_43,c_0_44]),c_0_44]) ).

cnf(c_0_58,plain,
    hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_59,plain,
    ! [X17677,X17678,X17679,X17680,X17681,X17682] : hAPP(hAPP(hAPP(c_COMBB(X17682,X17681,X17680),X17679),X17678),X17677) = hAPP(X17679,hAPP(X17678,X17677)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_60,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_61,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_48]),c_0_49]),c_0_37]) ).

cnf(c_0_62,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_50]) ).

cnf(c_0_63,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_51,c_0_29]) ).

cnf(c_0_64,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_52]) ).

cnf(c_0_65,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_53]) ).

cnf(c_0_66,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_67,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_54,c_0_55]) ).

fof(c_0_68,plain,
    ! [X2101] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2101),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2101,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(c_0_69,plain,
    ! [X35] : X35 != hAPP(c_Nat_OSuc,X35),
    inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_70,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_71,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_57,c_0_58]) ).

cnf(c_0_72,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_73,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_74,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_62,c_0_44]) ).

cnf(c_0_75,plain,
    hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
    inference(spm,[status(thm)],[c_0_37,c_0_63]) ).

cnf(c_0_76,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_64,c_0_65]),c_0_55]),c_0_66])]),c_0_67]) ).

cnf(c_0_77,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_68]) ).

fof(c_0_78,plain,
    ! [X1241] : X1241 != hAPP(c_Nat_OSuc,X1241),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_69])]) ).

cnf(c_0_79,plain,
    hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).

cnf(c_0_80,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_73,c_0_61]) ).

cnf(c_0_81,plain,
    hAPP(c_fNot,c_fFalse) = c_fTrue,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_74]),c_0_75]),c_0_49]) ).

cnf(c_0_82,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_76,c_0_65]) ).

cnf(c_0_83,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_77,c_0_55]) ).

cnf(c_0_84,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_85,plain,
    ( c_fFalse = X1
    | c_fTrue = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).

cnf(c_0_86,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_87,plain,
    hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85])]) ).

cnf(c_0_88,plain,
    hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_89,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_85]),c_0_84]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SWW341+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.09  % Command    : run_E %s %d THM
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit   : 300
% 0.09/0.28  % WCLimit    : 300
% 0.09/0.28  % DateTime   : Fri May  3 13:06:39 EDT 2024
% 0.09/0.28  % CPUTime    : 
% 0.75/0.99  Running first-order model finding
% 0.75/0.99  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.KbgMvAMx47/E---3.1_28559.p
% 64.41/9.62  # Version: 3.1.0
% 64.41/9.62  # Preprocessing class: FMLMSMSMSSSNFFN.
% 64.41/9.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.41/9.62  # Starting new_bool_3 with 300s (1) cores
% 64.41/9.62  # Starting new_bool_1 with 300s (1) cores
% 64.41/9.62  # Starting sh5l with 300s (1) cores
% 64.41/9.62  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 28895 completed with status 0
% 64.41/9.62  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 64.41/9.62  # Preprocessing class: FMLMSMSMSSSNFFN.
% 64.41/9.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.41/9.62  # No SInE strategy applied
% 64.41/9.62  # Search class: FGHSM-SMLM33-DFFFFFNN
% 64.41/9.62  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 64.41/9.62  # Starting SAT001_MinMin_p005000_rr with 811s (1) cores
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 64.41/9.62  # Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 64.41/9.62  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 64.41/9.62  # SAT001_CA_MinMin_p005000_rr with pid 28904 completed with status 0
% 64.41/9.62  # Result found by SAT001_CA_MinMin_p005000_rr
% 64.41/9.62  # Preprocessing class: FMLMSMSMSSSNFFN.
% 64.41/9.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.41/9.62  # No SInE strategy applied
% 64.41/9.62  # Search class: FGHSM-SMLM33-DFFFFFNN
% 64.41/9.62  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 64.41/9.62  # Starting SAT001_MinMin_p005000_rr with 811s (1) cores
% 64.41/9.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 64.41/9.62  # Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 64.41/9.62  # Preprocessing time       : 0.146 s
% 64.41/9.62  # Presaturation interreduction done
% 64.41/9.62  
% 64.41/9.62  # Proof found!
% 64.41/9.62  # SZS status ContradictoryAxioms
% 64.41/9.62  # SZS output start CNFRefutation
% See solution above
% 64.41/9.62  # Parsed axioms                        : 5226
% 64.41/9.62  # Removed by relevancy pruning/SinE    : 0
% 64.41/9.62  # Initial clauses                      : 7609
% 64.41/9.62  # Removed in clause preprocessing      : 237
% 64.41/9.62  # Initial clauses in saturation        : 7372
% 64.41/9.62  # Processed clauses                    : 22509
% 64.41/9.62  # ...of these trivial                  : 461
% 64.41/9.62  # ...subsumed                          : 7814
% 64.41/9.62  # ...remaining for further processing  : 14234
% 64.41/9.62  # Other redundant clauses eliminated   : 1261
% 64.41/9.62  # Clauses deleted for lack of memory   : 0
% 64.41/9.62  # Backward-subsumed                    : 140
% 64.41/9.62  # Backward-rewritten                   : 699
% 64.41/9.62  # Generated clauses                    : 212630
% 64.41/9.62  # ...of the previous two non-redundant : 203042
% 64.41/9.62  # ...aggressively subsumed             : 0
% 64.41/9.62  # Contextual simplify-reflections      : 27
% 64.41/9.62  # Paramodulations                      : 211382
% 64.41/9.62  # Factorizations                       : 2
% 64.41/9.62  # NegExts                              : 0
% 64.41/9.62  # Equation resolutions                 : 1311
% 64.41/9.62  # Disequality decompositions           : 0
% 64.41/9.62  # Total rewrite steps                  : 61446
% 64.41/9.62  # ...of those cached                   : 44147
% 64.41/9.62  # Propositional unsat checks           : 3
% 64.41/9.62  #    Propositional check models        : 2
% 64.41/9.62  #    Propositional check unsatisfiable : 0
% 64.41/9.62  #    Propositional clauses             : 0
% 64.41/9.62  #    Propositional clauses after purity: 0
% 64.41/9.62  #    Propositional unsat core size     : 0
% 64.41/9.62  #    Propositional preprocessing time  : 0.000
% 64.41/9.62  #    Propositional encoding time       : 0.140
% 64.41/9.62  #    Propositional solver time         : 0.048
% 64.41/9.62  #    Success case prop preproc time    : 0.000
% 64.41/9.62  #    Success case prop encoding time   : 0.000
% 64.41/9.62  #    Success case prop solver time     : 0.000
% 64.41/9.62  # Current number of processed clauses  : 6948
% 64.41/9.62  #    Positive orientable unit clauses  : 1697
% 64.41/9.62  #    Positive unorientable unit clauses: 130
% 64.41/9.62  #    Negative unit clauses             : 837
% 64.41/9.62  #    Non-unit-clauses                  : 4284
% 64.41/9.62  # Current number of unprocessed clauses: 181252
% 64.41/9.62  # ...number of literals in the above   : 360094
% 64.41/9.62  # Current number of archived formulas  : 0
% 64.41/9.62  # Current number of archived clauses   : 6839
% 64.41/9.62  # Clause-clause subsumption calls (NU) : 5178445
% 64.41/9.62  # Rec. Clause-clause subsumption calls : 2855372
% 64.41/9.62  # Non-unit clause-clause subsumptions  : 7607
% 64.41/9.62  # Unit Clause-clause subsumption calls : 407628
% 64.41/9.62  # Rewrite failures with RHS unbound    : 460
% 64.41/9.62  # BW rewrite match attempts            : 42541
% 64.41/9.62  # BW rewrite match successes           : 1407
% 64.41/9.62  # Condensation attempts                : 236538
% 64.41/9.62  # Condensation successes               : 1830
% 64.41/9.62  # Termbank termtop insertions          : 7327608
% 64.41/9.62  # Search garbage collected termcells   : 103083
% 64.41/9.62  
% 64.41/9.62  # -------------------------------------------------
% 64.41/9.62  # User time                : 8.139 s
% 64.41/9.62  # System time              : 0.235 s
% 64.41/9.62  # Total time               : 8.374 s
% 64.41/9.62  # Maximum resident set size: 40904 pages
% 64.41/9.62  
% 64.41/9.62  # -------------------------------------------------
% 64.41/9.62  # User time                : 37.110 s
% 64.41/9.62  # System time              : 1.127 s
% 64.41/9.62  # Total time               : 38.238 s
% 64.41/9.62  # Maximum resident set size: 9560 pages
% 64.41/9.62  % E---3.1 exiting
%------------------------------------------------------------------------------