TSTP Solution File: SWW304+1 by E-SAT---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.2.0
% Problem  : SWW304+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d SAT

% Computer : n013.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 18:14:07 EDT 2024

% Result   : ContradictoryAxioms 71.18s 10.78s
% Output   : CNFRefutation 71.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   88 (  68 unt;   0 def)
%            Number of atoms       :  110 (  88 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   53 (  31   ~;  17   |;   1   &)
%                                         (   2 <=>;   2  =>;   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   :  146 (  20 sgn  80   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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.5YB4vQJiZE/E---3.1_14094.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_Collect__def) ).

fof(fact_bot__apply,axiom,
    ! [X22,X17,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17,X5)),X22) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_bot__apply) ).

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/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_Collect__empty__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X314,X48,X5,X58] : hAPP(hAPP(c_COMBK(X58,X5),X48),X314) = X48,
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',help_c__COMBK__1) ).

fof(arity_HOL__Obool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_HOL_Obool),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',arity_HOL__Obool__Orderings_Obot) ).

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/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_Collect__neg__eq) ).

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.5YB4vQJiZE/E---3.1_14094.p',fact_Zero__not__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/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_double__complement) ).

fof(help_c__fNot__1,axiom,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.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.5YB4vQJiZE/E---3.1_14094.p',fact_UNIV__def) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X57,X72] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = X72
     => X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.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/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.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.5YB4vQJiZE/E---3.1_14094.p',fact_Pls__def) ).

fof(help_c__COMBB__1,axiom,
    ! [X31,X26,X23,X116,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X116),X23),X26),X31) = hAPP(X23,hAPP(X26,X31)),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.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/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_Compl__empty__eq) ).

fof(fact_add__Suc__right,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_add__Suc__right) ).

fof(fact_converse__converse,axiom,
    ! [X171,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(c_Relation_Oconverse(X5,X17),X171)) = X171,
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_converse__converse) ).

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.5YB4vQJiZE/E---3.1_14094.p',fact_Nat_Oadd__0__right) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X57] : X57 != hAPP(c_Nat_OSuc,X57),
    file('/export/starexec/sandbox/tmp/tmp.5YB4vQJiZE/E---3.1_14094.p',fact_n__not__Suc__n) ).

fof(c_0_20,plain,
    ! [X11076] : c_Orderings_Obot__class_Obot(tc_fun(X11076,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11076),hAPP(c_COMBK(tc_HOL_Obool,X11076),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_21,plain,
    ! [X11062,X11063] : hAPP(c_Set_OCollect(X11063),X11062) = X11062,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_22,plain,
    ! [X363,X364,X365] :
      ( ~ class_Orderings_Obot(X365)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X364,X365)),X363) = c_Orderings_Obot__class_Obot(X365) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])])]) ).

fof(c_0_23,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_24,plain,
    ! [X17623,X17624,X17625,X17626] : hAPP(hAPP(c_COMBK(X17626,X17625),X17624),X17623) = X17624,
    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]) ).

cnf(c_0_27,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).

fof(c_0_29,plain,
    ! [X11041,X11042] : hAPP(c_Set_OCollect(X11042),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11042),c_fNot),X11041)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11042,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11042),X11041)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_30,plain,
    ! [X11064,X11065,X11066,X11067,X11069] :
      ( ( hAPP(c_Set_OCollect(X11065),X11064) != c_Orderings_Obot__class_Obot(tc_fun(X11065,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X11064,X11066)) )
      & ( hBOOL(hAPP(X11067,esk287_1(X11067)))
        | hAPP(c_Set_OCollect(X11069),X11067) = c_Orderings_Obot__class_Obot(tc_fun(X11069,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_23])])])])])]) ).

cnf(c_0_31,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

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_25,c_0_26]) ).

cnf(c_0_33,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_34,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_35,plain,
    ! [X2680,X2681] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2681,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2681,tc_HOL_Obool)),X2680)) = X2680,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_36,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_29]) ).

fof(c_0_37,plain,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_fNot,X23))
      | ~ hBOOL(X23) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_38,plain,
    ( hBOOL(hAPP(X1,esk287_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_30]) ).

cnf(c_0_39,plain,
    c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

fof(c_0_40,plain,
    ! [X11058] : c_Orderings_Otop__class_Otop(tc_fun(X11058,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11058),hAPP(c_COMBK(tc_HOL_Obool,X11058),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(c_0_41,plain,
    ! [X862,X863] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X863),X862) != X863
      | X862 = 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_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,
    ! [X532] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X532),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).

fof(c_0_45,plain,
    ! [X17627,X17628,X17629,X17630,X17631,X17632] : hAPP(hAPP(hAPP(c_COMBB(X17632,X17631,X17630),X17629),X17628),X17627) = hAPP(X17629,hAPP(X17628,X17627)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_46,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_35]) ).

cnf(c_0_47,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_36,c_0_26]),c_0_26]) ).

fof(c_0_48,plain,
    ! [X17649] :
      ( ~ hBOOL(hAPP(c_fNot,X17649))
      | ~ hBOOL(X17649) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).

cnf(c_0_49,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk287_1(X1))) ),
    inference(rw,[status(thm)],[c_0_38,c_0_26]) ).

cnf(c_0_50,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(rw,[status(thm)],[c_0_33,c_0_39]) ).

fof(c_0_51,plain,
    ! [X10085] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10085,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10085,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

cnf(c_0_52,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_40]) ).

cnf(c_0_53,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_41]) ).

cnf(c_0_54,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_55,plain,
    ! [X864,X865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X865),hAPP(c_Nat_OSuc,X864)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X865),X864)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_56,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_57,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_58,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_46,c_0_47]),c_0_47]) ).

fof(c_0_59,plain,
    ! [X15796,X15797,X15798] : hAPP(c_Relation_Oconverse(X15798,X15797),hAPP(c_Relation_Oconverse(X15797,X15798),X15796)) = X15796,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

cnf(c_0_60,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_61,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_49]),c_0_50]),c_0_31]) ).

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_51]) ).

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_52,c_0_26]) ).

cnf(c_0_64,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_53,c_0_54]) ).

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_55]) ).

cnf(c_0_66,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_56,c_0_54]) ).

fof(c_0_67,plain,
    ! [X859] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X859),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X859,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(c_0_68,plain,
    ! [X57] : X57 != hAPP(c_Nat_OSuc,X57),
    inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_69,plain,
    hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_57]) ).

cnf(c_0_70,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_71,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_72,plain,
    hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_62,c_0_47]) ).

cnf(c_0_73,plain,
    hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
    inference(spm,[status(thm)],[c_0_31,c_0_63]) ).

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

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

fof(c_0_76,plain,
    ! [X488] : X488 != hAPP(c_Nat_OSuc,X488),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).

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

cnf(c_0_78,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_71,c_0_61]) ).

cnf(c_0_79,plain,
    hAPP(c_fNot,c_fFalse) = c_fTrue,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_72]),c_0_73]),c_0_33]),c_0_39]) ).

cnf(c_0_80,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
    inference(spm,[status(thm)],[c_0_74,c_0_65]) ).

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

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

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

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

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

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWW304+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13  % Command    : run_E %s %d SAT
% 0.13/0.34  % Computer : n013.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Jun 19 07:16:54 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 1.05/1.24  Running first-order model finding
% 1.05/1.24  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.5YB4vQJiZE/E---3.1_14094.p
% 71.18/10.78  # Version: 3.2.0
% 71.18/10.78  # Preprocessing class: FMLMSMSMSSSNFFN.
% 71.18/10.78  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.18/10.78  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 71.18/10.78  # Starting new_bool_3 with 300s (1) cores
% 71.18/10.78  # Starting new_bool_1 with 300s (1) cores
% 71.18/10.78  # Starting sh5l with 300s (1) cores
% 71.18/10.78  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 14202 completed with status 0
% 71.18/10.78  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 71.18/10.78  # Preprocessing class: FMLMSMSMSSSNFFN.
% 71.18/10.78  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.18/10.78  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 71.18/10.78  # No SInE strategy applied
% 71.18/10.78  # Search class: FGHSM-SMLM33-DFFFFFNN
% 71.18/10.78  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 71.18/10.78  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 71.18/10.78  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 71.18/10.78  # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 71.18/10.78  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 71.18/10.78  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 135s (1) cores
% 71.18/10.78  # SAT001_MinMin_p005000_rr with pid 14213 completed with status 0
% 71.18/10.78  # Result found by SAT001_MinMin_p005000_rr
% 71.18/10.78  # Preprocessing class: FMLMSMSMSSSNFFN.
% 71.18/10.78  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.18/10.78  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 71.18/10.78  # No SInE strategy applied
% 71.18/10.78  # Search class: FGHSM-SMLM33-DFFFFFNN
% 71.18/10.78  # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 71.18/10.78  # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 71.18/10.78  # Preprocessing time       : 0.160 s
% 71.18/10.78  # Presaturation interreduction done
% 71.18/10.78  
% 71.18/10.78  # Proof found!
% 71.18/10.78  # SZS status ContradictoryAxioms
% 71.18/10.78  # SZS output start CNFRefutation
% See solution above
% 71.18/10.78  # Parsed axioms                        : 5226
% 71.18/10.78  # Removed by relevancy pruning/SinE    : 0
% 71.18/10.78  # Initial clauses                      : 7590
% 71.18/10.78  # Removed in clause preprocessing      : 238
% 71.18/10.78  # Initial clauses in saturation        : 7352
% 71.18/10.78  # Processed clauses                    : 21173
% 71.18/10.78  # ...of these trivial                  : 407
% 71.18/10.78  # ...subsumed                          : 7424
% 71.18/10.78  # ...remaining for further processing  : 13342
% 71.18/10.78  # Other redundant clauses eliminated   : 1515
% 71.18/10.78  # Clauses deleted for lack of memory   : 0
% 71.18/10.78  # Backward-subsumed                    : 136
% 71.18/10.78  # Backward-rewritten                   : 432
% 71.18/10.78  # Generated clauses                    : 196194
% 71.18/10.78  # ...of the previous two non-redundant : 186700
% 71.18/10.78  # ...aggressively subsumed             : 0
% 71.18/10.78  # Contextual simplify-reflections      : 36
% 71.18/10.78  # Paramodulations                      : 194689
% 71.18/10.78  # Factorizations                       : 2
% 71.18/10.78  # NegExts                              : 0
% 71.18/10.78  # Equation resolutions                 : 1568
% 71.18/10.78  # Disequality decompositions           : 0
% 71.18/10.78  # Total rewrite steps                  : 63139
% 71.18/10.78  # ...of those cached                   : 45215
% 71.18/10.78  # Propositional unsat checks           : 3
% 71.18/10.78  #    Propositional check models        : 2
% 71.18/10.78  #    Propositional check unsatisfiable : 0
% 71.18/10.78  #    Propositional clauses             : 0
% 71.18/10.78  #    Propositional clauses after purity: 0
% 71.18/10.78  #    Propositional unsat core size     : 0
% 71.18/10.78  #    Propositional preprocessing time  : 0.000
% 71.18/10.78  #    Propositional encoding time       : 0.139
% 71.18/10.78  #    Propositional solver time         : 0.060
% 71.18/10.78  #    Success case prop preproc time    : 0.000
% 71.18/10.78  #    Success case prop encoding time   : 0.000
% 71.18/10.78  #    Success case prop solver time     : 0.000
% 71.18/10.78  # Current number of processed clauses  : 6371
% 71.18/10.78  #    Positive orientable unit clauses  : 1574
% 71.18/10.78  #    Positive unorientable unit clauses: 127
% 71.18/10.78  #    Negative unit clauses             : 910
% 71.18/10.78  #    Non-unit-clauses                  : 3760
% 71.18/10.78  # Current number of unprocessed clauses: 171622
% 71.18/10.78  # ...number of literals in the above   : 337406
% 71.18/10.78  # Current number of archived formulas  : 0
% 71.18/10.78  # Current number of archived clauses   : 6526
% 71.18/10.78  # Clause-clause subsumption calls (NU) : 3830378
% 71.18/10.78  # Rec. Clause-clause subsumption calls : 1851753
% 71.18/10.78  # Non-unit clause-clause subsumptions  : 4594
% 71.18/10.78  # Unit Clause-clause subsumption calls : 242460
% 71.18/10.78  # Rewrite failures with RHS unbound    : 579
% 71.18/10.78  # BW rewrite match attempts            : 37469
% 71.18/10.78  # BW rewrite match successes           : 1376
% 71.18/10.78  # Condensation attempts                : 0
% 71.18/10.78  # Condensation successes               : 0
% 71.18/10.78  # Termbank termtop insertions          : 6937598
% 71.18/10.78  # Search garbage collected termcells   : 101767
% 71.18/10.78  
% 71.18/10.78  # -------------------------------------------------
% 71.18/10.78  # User time                : 8.778 s
% 71.18/10.78  # System time              : 0.239 s
% 71.18/10.78  # Total time               : 9.017 s
% 71.18/10.78  # Maximum resident set size: 40688 pages
% 71.18/10.78  
% 71.18/10.78  # -------------------------------------------------
% 71.18/10.78  # User time                : 40.879 s
% 71.18/10.78  # System time              : 1.172 s
% 71.18/10.78  # Total time               : 42.051 s
% 71.18/10.78  # Maximum resident set size: 9472 pages
% 71.18/10.78  % E---3.1 exiting
% 71.18/10.79  % E exiting
%------------------------------------------------------------------------------