%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SWW097+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 20:08:32 EDT 2023

% Result   : Theorem 39.34s 5.37s
% Output   : CNFRefutation 39.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   66
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  440 ( 120 unt;   0 def)
%            Number of atoms       : 1019 ( 411 equ)
%            Maximal formula atoms :   75 (   2 avg)
%            Number of connectives :  981 ( 402   ~; 516   |;  49   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   7 con; 0-3 aty)
%            Number of variables   :  361 (  76 sgn;  75   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(def_false2,axiom,
    ? [X5] :
      ( false2 = phi(f7(X5))
      & ~ ? [X10] : forallprefers(f7(X10),f7(X5)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_false2) ).

fof(def_f7,axiom,
    ! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_f7) ).

fof(prop_false,axiom,
    ! [X1] :
      ( prop(X1) = false
    <=> ~ bool(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',prop_false) ).

fof(lazy_impl_axiom2,axiom,
    ! [X4] : lazy_impl(false,X4) = true,
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_impl_axiom2) ).

fof(def_phi,axiom,
    ! [X1] :
      ( ( d(X1)
        & phi(X1) = X1 )
      | ( ~ d(X1)
        & phi(X1) = err ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_phi) ).

fof(prop_true,axiom,
    ! [X1] :
      ( prop(X1) = true
    <=> bool(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',prop_true) ).

fof(lazy_impl_axiom3,axiom,
    ! [X4] : lazy_impl(true,X4) = phi(X4),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_impl_axiom3) ).

fof(def_forallprefers,axiom,
    ! [X1,X2] :
      ( forallprefers(X1,X2)
    <=> ( ( ~ d(X1)
          & d(X2) )
        | ( d(X1)
          & d(X2)
          & ~ bool(X1)
          & bool(X2) )
        | ( X1 = false
          & X2 = true ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_forallprefers) ).

fof(lazy_impl_axiom1,axiom,
    ! [X3,X4] :
      ( ~ bool(X3)
     => lazy_impl(X3,X4) = phi(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_impl_axiom1) ).

fof(def_bool,axiom,
    ! [X1] :
      ( bool(X1)
    <=> ( X1 = false
        | X1 = true ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_bool) ).

fof(false_true_err_in_d,axiom,
    ( d(true)
    & d(false)
    & d(err) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',false_true_err_in_d) ).

fof(def_lazy_and2,axiom,
    ! [X5,X6] :
    ? [X7] :
      ( lazy_and2(X5,X6) = phi(f2(X5,X6,X7))
      & ~ ? [X8] : forallprefers(f2(X5,X6,X8),f2(X5,X6,X7)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_lazy_and2) ).

fof(def_f2,axiom,
    ! [X5,X6,X7] : f2(X5,X6,X7) = lazy_impl(prop(X7),impl(lazy_impl(X5,impl(X6,X7)),X7)),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_f2) ).

fof(impl_axiom4,axiom,
    ! [X4] :
      ( bool(X4)
     => impl(true,X4) = X4 ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',impl_axiom4) ).

fof(distinct_false_true_err,axiom,
    ( true != false
    & true != err
    & false != err ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',distinct_false_true_err) ).

fof(lazy_and1_lazy_and2,conjecture,
    ! [X5,X6] : lazy_and1(X5,X6) = lazy_and2(X5,X6),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_and1_lazy_and2) ).

fof(impl_axiom1,axiom,
    ! [X3,X4] :
      ( ~ bool(X3)
     => impl(X3,X4) = phi(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',impl_axiom1) ).

fof(lazy_and1_axiom1,axiom,
    ! [X3,X4] :
      ( ~ bool(X3)
     => lazy_and1(X3,X4) = phi(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_and1_axiom1) ).

fof(def_and2,axiom,
    ! [X5,X6] :
    ? [X7] :
      ( and2(X5,X6) = phi(f1(X5,X6,X7))
      & ~ ? [X8] : forallprefers(f1(X5,X6,X8),f1(X5,X6,X7)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_and2) ).

fof(def_f1,axiom,
    ! [X5,X6,X7] : f1(X5,X6,X7) = lazy_impl(prop(X7),impl(impl(X5,impl(X6,X7)),X7)),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',def_f1) ).

fof(impl_axiom3,axiom,
    ! [X4] :
      ( bool(X4)
     => impl(false,X4) = true ),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',impl_axiom3) ).

fof(lazy_and1_axiom2,axiom,
    ! [X4] : lazy_and1(false,X4) = false,
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_and1_axiom2) ).

fof(lazy_and1_axiom3,axiom,
    ! [X4] : lazy_and1(true,X4) = phi(X4),
    file('/export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p',lazy_and1_axiom3) ).

fof(c_0_23,plain,
    ! [X83] :
      ( false2 = phi(f7(esk7_0))
      & ~ forallprefers(f7(X83),f7(esk7_0)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_false2])])])]) ).

fof(c_0_24,plain,
    ! [X81] : f7(X81) = lazy_impl(prop(X81),X81),
    inference(variable_rename,[status(thm)],[def_f7]) ).

fof(c_0_25,plain,
    ! [X1] :
      ( prop(X1) = false
    <=> ~ bool(X1) ),
    inference(fof_simplification,[status(thm)],[prop_false]) ).

cnf(c_0_26,plain,
    ~ forallprefers(f7(X1),f7(esk7_0)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_27,plain,
    f7(X1) = lazy_impl(prop(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_28,plain,
    ! [X18] :
      ( ( prop(X18) != false
        | ~ bool(X18) )
      & ( bool(X18)
        | prop(X18) = false ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).

fof(c_0_29,plain,
    ! [X27] : lazy_impl(false,X27) = true,
    inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).

fof(c_0_30,plain,
    ! [X1] :
      ( ( d(X1)
        & phi(X1) = X1 )
      | ( ~ d(X1)
        & phi(X1) = err ) ),
    inference(fof_simplification,[status(thm)],[def_phi]) ).

cnf(c_0_31,plain,
    ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).

cnf(c_0_32,plain,
    ( bool(X1)
    | prop(X1) = false ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,plain,
    lazy_impl(false,X1) = true,
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_34,plain,
    ! [X17] :
      ( ( prop(X17) != true
        | bool(X17) )
      & ( ~ bool(X17)
        | prop(X17) = true ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[prop_true])]) ).

fof(c_0_35,plain,
    ! [X16] :
      ( ( ~ d(X16)
        | d(X16) )
      & ( phi(X16) = err
        | d(X16) )
      & ( ~ d(X16)
        | phi(X16) = X16 )
      & ( phi(X16) = err
        | phi(X16) = X16 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).

fof(c_0_36,plain,
    ! [X28] : lazy_impl(true,X28) = phi(X28),
    inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).

fof(c_0_37,plain,
    ! [X1,X2] :
      ( forallprefers(X1,X2)
    <=> ( ( ~ d(X1)
          & d(X2) )
        | ( d(X1)
          & d(X2)
          & ~ bool(X1)
          & bool(X2) )
        | ( X1 = false
          & X2 = true ) ) ),
    inference(fof_simplification,[status(thm)],[def_forallprefers]) ).

fof(c_0_38,plain,
    ! [X3,X4] :
      ( ~ bool(X3)
     => lazy_impl(X3,X4) = phi(X3) ),
    inference(fof_simplification,[status(thm)],[lazy_impl_axiom1]) ).

cnf(c_0_39,plain,
    ( bool(esk7_0)
    | ~ forallprefers(lazy_impl(prop(X1),X1),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_40,plain,
    ( prop(X1) = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_41,plain,
    ( phi(X1) = X1
    | ~ d(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    lazy_impl(true,X1) = phi(X1),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

fof(c_0_43,plain,
    ! [X12,X13] :
      ( ( X12 = false
        | d(X12)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | d(X12)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | d(X13)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | d(X13)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | ~ bool(X12)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | ~ bool(X12)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | bool(X13)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | bool(X13)
        | ~ d(X12)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | d(X12)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | d(X12)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | d(X13)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | d(X13)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | ~ bool(X12)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | ~ bool(X12)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X12 = false
        | bool(X13)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( X13 = true
        | bool(X13)
        | d(X13)
        | ~ forallprefers(X12,X13) )
      & ( d(X12)
        | ~ d(X13)
        | forallprefers(X12,X13) )
      & ( ~ d(X12)
        | ~ d(X13)
        | bool(X12)
        | ~ bool(X13)
        | forallprefers(X12,X13) )
      & ( X12 != false
        | X13 != true
        | forallprefers(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).

fof(c_0_44,plain,
    ! [X11] :
      ( ( ~ bool(X11)
        | X11 = false
        | X11 = true )
      & ( X11 != false
        | bool(X11) )
      & ( X11 != true
        | bool(X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_bool])])]) ).

fof(c_0_45,plain,
    ! [X25,X26] :
      ( bool(X25)
      | lazy_impl(X25,X26) = phi(X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).

cnf(c_0_46,plain,
    false2 = phi(f7(esk7_0)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_47,plain,
    ( phi(X1) = err
    | phi(X1) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_48,plain,
    ( bool(esk7_0)
    | ~ forallprefers(lazy_impl(true,X1),true)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_49,plain,
    ( lazy_impl(true,X1) = X1
    | ~ d(X1) ),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_50,plain,
    ( forallprefers(X1,X2)
    | X1 != false
    | X2 != true ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_51,plain,
    ( bool(X1)
    | X1 != false ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_52,plain,
    ( bool(X1)
    | lazy_impl(X1,X2) = phi(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_53,plain,
    false2 = lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_42]),c_0_27]) ).

cnf(c_0_54,plain,
    ( lazy_impl(true,X1) = X1
    | lazy_impl(true,X1) = err ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_42]),c_0_42]) ).

cnf(c_0_55,plain,
    ( bool(esk7_0)
    | ~ forallprefers(X1,true)
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_56,plain,
    forallprefers(false,true),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])]) ).

cnf(c_0_57,plain,
    d(false),
    inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).

cnf(c_0_58,plain,
    bool(false),
    inference(er,[status(thm)],[c_0_51]) ).

cnf(c_0_59,plain,
    ( lazy_impl(X1,X2) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[c_0_52,c_0_42]) ).

cnf(c_0_60,plain,
    ( lazy_impl(prop(esk7_0),esk7_0) = false2
    | false2 = err ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_53]) ).

cnf(c_0_61,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,esk7_0))
    | ~ bool(esk7_0) ),
    inference(spm,[status(thm)],[c_0_31,c_0_40]) ).

cnf(c_0_62,plain,
    bool(esk7_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).

cnf(c_0_63,plain,
    ( lazy_impl(true,lazy_impl(true,esk7_0)) = false2
    | ~ bool(esk7_0) ),
    inference(spm,[status(thm)],[c_0_53,c_0_40]) ).

cnf(c_0_64,plain,
    ( phi(X1) = err
    | d(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_65,plain,
    ( lazy_impl(true,prop(esk7_0)) = false2
    | false2 = err
    | bool(prop(esk7_0)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

fof(c_0_66,plain,
    ! [X49,X50,X52] :
      ( lazy_and2(X49,X50) = phi(f2(X49,X50,esk2_2(X49,X50)))
      & ~ forallprefers(f2(X49,X50,X52),f2(X49,X50,esk2_2(X49,X50))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_lazy_and2])])])]) ).

fof(c_0_67,plain,
    ! [X46,X47,X48] : f2(X46,X47,X48) = lazy_impl(prop(X48),impl(lazy_impl(X46,impl(X47,X48)),X48)),
    inference(variable_rename,[status(thm)],[def_f2]) ).

cnf(c_0_68,plain,
    ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,esk7_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).

cnf(c_0_69,plain,
    lazy_impl(true,lazy_impl(true,esk7_0)) = false2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_62])]) ).

cnf(c_0_70,plain,
    ( lazy_impl(true,X1) = err
    | d(X1) ),
    inference(rw,[status(thm)],[c_0_64,c_0_42]) ).

cnf(c_0_71,plain,
    lazy_impl(true,err) = err,
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_54])]) ).

cnf(c_0_72,plain,
    ( X1 = false
    | X1 = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_73,plain,
    ( prop(esk7_0) = false2
    | false2 = err
    | bool(prop(esk7_0)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_65]) ).

cnf(c_0_74,plain,
    ~ forallprefers(f2(X1,X2,X3),f2(X1,X2,esk2_2(X1,X2))),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_75,plain,
    f2(X1,X2,X3) = lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_76,plain,
    ( false2 = err
    | ~ forallprefers(false2,lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_60]) ).

cnf(c_0_77,plain,
    ( false2 = err
    | d(esk7_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).

cnf(c_0_78,plain,
    ( bool(X1)
    | forallprefers(X1,X2)
    | ~ d(X1)
    | ~ d(X2)
    | ~ bool(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_79,plain,
    ( d(X1)
    | forallprefers(X1,X2)
    | ~ d(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_80,plain,
    ( prop(esk7_0) = false2
    | prop(esk7_0) = true
    | prop(esk7_0) = false
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_81,plain,
    ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),lazy_impl(prop(esk2_2(X1,X2)),impl(lazy_impl(X1,impl(X2,esk2_2(X1,X2))),esk2_2(X1,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_75]) ).

cnf(c_0_82,plain,
    ( false2 = err
    | ~ forallprefers(false2,esk7_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_49]),c_0_77]) ).

cnf(c_0_83,plain,
    ( forallprefers(X1,X2)
    | bool(X1)
    | ~ d(X2)
    | ~ bool(X2) ),
    inference(csr,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_84,plain,
    ( lazy_impl(true,false2) = false2
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_53,c_0_60]) ).

cnf(c_0_85,plain,
    ( prop(esk7_0) = false
    | prop(esk7_0) = true
    | false2 = err
    | false2 != true ),
    inference(ef,[status(thm)],[c_0_80]) ).

cnf(c_0_86,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(prop(esk2_2(false,X2)),impl(true,esk2_2(false,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_33]),c_0_33]) ).

fof(c_0_87,plain,
    ! [X24] :
      ( ~ bool(X24)
      | impl(true,X24) = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom4])]) ).

cnf(c_0_88,plain,
    ( ~ forallprefers(lazy_impl(true,X1),lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_40]) ).

cnf(c_0_89,plain,
    ( false2 = err
    | ~ forallprefers(lazy_impl(prop(X1),X1),false2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_60]) ).

cnf(c_0_90,plain,
    ( false2 = err
    | bool(false2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_62])]),c_0_77]) ).

cnf(c_0_91,plain,
    ( false2 = err
    | d(false2) ),
    inference(spm,[status(thm)],[c_0_70,c_0_84]) ).

cnf(c_0_92,plain,
    ( prop(X1) != false
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_93,plain,
    ( prop(esk7_0) = false
    | prop(esk7_0) = true
    | false2 = err ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_80]),c_0_62])]),c_0_85]) ).

cnf(c_0_94,plain,
    ( bool(esk2_2(false,X1))
    | ~ forallprefers(lazy_impl(prop(X2),impl(true,X2)),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_32]),c_0_33]) ).

cnf(c_0_95,plain,
    ( impl(true,X1) = X1
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_96,plain,
    ~ forallprefers(lazy_impl(true,prop(X1)),lazy_impl(prop(esk7_0),esk7_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_59]),c_0_88]) ).

cnf(c_0_97,plain,
    ( false2 = err
    | bool(lazy_impl(prop(X1),X1)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_83]),c_0_90]),c_0_91]) ).

cnf(c_0_98,plain,
    ( prop(esk7_0) = true
    | false2 = err ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_62])]) ).

cnf(c_0_99,plain,
    ( bool(esk2_2(false,X1))
    | ~ forallprefers(lazy_impl(prop(X2),X2),true)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_100,plain,
    ~ forallprefers(lazy_impl(true,prop(X1)),lazy_impl(true,esk7_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_40]),c_0_62])]) ).

cnf(c_0_101,plain,
    ( false2 = err
    | bool(lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_102,plain,
    ( bool(esk2_2(false,X1))
    | ~ forallprefers(lazy_impl(true,X2),true)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_99,c_0_40]) ).

cnf(c_0_103,plain,
    ( ~ forallprefers(prop(X1),lazy_impl(true,esk7_0))
    | ~ d(prop(X1)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_49]) ).

cnf(c_0_104,plain,
    ( lazy_impl(true,esk7_0) = false2
    | ~ d(lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_69]) ).

cnf(c_0_105,plain,
    ( lazy_impl(true,esk7_0) = true
    | lazy_impl(true,esk7_0) = false
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_72,c_0_101]) ).

cnf(c_0_106,plain,
    ( bool(esk2_2(false,X1))
    | ~ forallprefers(X2,true)
    | ~ d(X2)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_102,c_0_49]) ).

cnf(c_0_107,plain,
    ( bool(X1)
    | ~ forallprefers(false,lazy_impl(true,esk7_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_32]),c_0_57])]) ).

cnf(c_0_108,plain,
    ( lazy_impl(true,esk7_0) = true
    | false2 = err
    | false2 = false ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_57])]) ).

cnf(c_0_109,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(true,impl(true,esk2_2(false,X2))))
    | ~ bool(esk2_2(false,X2)) ),
    inference(spm,[status(thm)],[c_0_86,c_0_40]) ).

cnf(c_0_110,plain,
    bool(esk2_2(false,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_56]),c_0_57]),c_0_58])]) ).

cnf(c_0_111,plain,
    ( d(lazy_impl(prop(X1),X1))
    | ~ d(lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_79]) ).

cnf(c_0_112,plain,
    ( false2 = false
    | false2 = err
    | bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_56])]) ).

cnf(c_0_113,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(true,impl(true,esk2_2(false,X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).

cnf(c_0_114,plain,
    ( d(esk7_0)
    | ~ forallprefers(lazy_impl(prop(X1),X1),err) ),
    inference(spm,[status(thm)],[c_0_68,c_0_70]) ).

cnf(c_0_115,plain,
    d(err),
    inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).

cnf(c_0_116,plain,
    ( d(lazy_impl(prop(X1),X1))
    | ~ d(esk7_0) ),
    inference(spm,[status(thm)],[c_0_111,c_0_49]) ).

cnf(c_0_117,plain,
    ( lazy_impl(true,esk7_0) = err
    | lazy_impl(true,esk7_0) = false2 ),
    inference(spm,[status(thm)],[c_0_69,c_0_54]) ).

cnf(c_0_118,plain,
    ( false2 = err
    | false2 = false
    | X1 = true
    | X1 = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_112]) ).

cnf(c_0_119,plain,
    false != err,
    inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).

cnf(c_0_120,plain,
    true != err,
    inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).

cnf(c_0_121,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(true,esk2_2(false,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_95]),c_0_110])]) ).

cnf(c_0_122,plain,
    ( lazy_impl(prop(esk7_0),esk7_0) = false2
    | ~ d(lazy_impl(prop(esk7_0),esk7_0)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_53]) ).

cnf(c_0_123,plain,
    d(lazy_impl(prop(X1),X1)),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_79]),c_0_115])]),c_0_116]) ).

cnf(c_0_124,plain,
    ( lazy_impl(true,esk7_0) = err
    | false2 != err ),
    inference(ef,[status(thm)],[c_0_117]) ).

cnf(c_0_125,plain,
    ( false2 = false
    | false2 = err ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_118]),c_0_71]),c_0_119]),c_0_120]) ).

cnf(c_0_126,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,esk2_2(false,X2)))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_121,c_0_95]) ).

cnf(c_0_127,plain,
    lazy_impl(prop(esk7_0),esk7_0) = false2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]) ).

cnf(c_0_128,plain,
    ( lazy_impl(true,esk7_0) = err
    | false2 = false ),
    inference(spm,[status(thm)],[c_0_124,c_0_125]) ).

cnf(c_0_129,plain,
    ~ forallprefers(false2,lazy_impl(true,esk2_2(false,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_62])]) ).

cnf(c_0_130,plain,
    ( false2 = false
    | d(lazy_impl(prop(X1),X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_128]),c_0_115])]) ).

cnf(c_0_131,plain,
    ( ~ forallprefers(false2,esk2_2(false,X1))
    | ~ d(esk2_2(false,X1)) ),
    inference(spm,[status(thm)],[c_0_129,c_0_49]) ).

cnf(c_0_132,plain,
    ( esk2_2(false,X1) = true
    | esk2_2(false,X1) = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_110]) ).

cnf(c_0_133,plain,
    ( ~ forallprefers(lazy_impl(true,X1),lazy_impl(true,esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_68,c_0_40]) ).

cnf(c_0_134,plain,
    ( lazy_impl(prop(esk7_0),esk7_0) = false2
    | false2 = false ),
    inference(spm,[status(thm)],[c_0_122,c_0_130]) ).

cnf(c_0_135,plain,
    ( esk2_2(false,X1) = true
    | ~ forallprefers(false2,false) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_57])]) ).

cnf(c_0_136,plain,
    ( false2 = false
    | ~ forallprefers(err,lazy_impl(true,esk7_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_128]),c_0_62])]) ).

cnf(c_0_137,plain,
    ( lazy_impl(true,esk7_0) = false2
    | false2 = false ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_40]),c_0_62])]) ).

cnf(c_0_138,plain,
    ( esk2_2(false,X1) = true
    | bool(false2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_83]),c_0_57]),c_0_58])]) ).

cnf(c_0_139,plain,
    d(true),
    inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).

cnf(c_0_140,plain,
    ( bool(X1)
    | X1 != true ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_141,plain,
    ( lazy_impl(true,esk7_0) = false2
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_54,c_0_69]) ).

cnf(c_0_142,plain,
    ( false2 = false
    | ~ forallprefers(err,false2) ),
    inference(spm,[status(thm)],[c_0_136,c_0_137]) ).

cnf(c_0_143,plain,
    d(false2),
    inference(spm,[status(thm)],[c_0_123,c_0_127]) ).

cnf(c_0_144,plain,
    ( bool(false2)
    | ~ forallprefers(false2,true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_138]),c_0_139])]) ).

cnf(c_0_145,plain,
    bool(true),
    inference(er,[status(thm)],[c_0_140]) ).

cnf(c_0_146,plain,
    ( false2 = esk7_0
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_54,c_0_141]) ).

cnf(c_0_147,plain,
    ( false2 = false
    | bool(err)
    | ~ bool(false2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_83]),c_0_143])]) ).

cnf(c_0_148,plain,
    bool(false2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_83]),c_0_139]),c_0_145])]) ).

cnf(c_0_149,plain,
    ( false2 = err
    | esk7_0 != err ),
    inference(ef,[status(thm)],[c_0_146]) ).

cnf(c_0_150,plain,
    ( false2 = false
    | bool(err) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])]) ).

fof(c_0_151,negated_conjecture,
    ~ ! [X5,X6] : lazy_and1(X5,X6) = lazy_and2(X5,X6),
    inference(assume_negation,[status(cth)],[lazy_and1_lazy_and2]) ).

cnf(c_0_152,plain,
    ( lazy_impl(true,esk7_0) = esk7_0
    | false2 = err ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_146]),c_0_149]) ).

cnf(c_0_153,plain,
    false2 = false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_150]),c_0_119]),c_0_120]) ).

cnf(c_0_154,plain,
    lazy_impl(true,esk7_0) = false2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_40]),c_0_62])]) ).

fof(c_0_155,plain,
    ! [X3,X4] :
      ( ~ bool(X3)
     => impl(X3,X4) = phi(X3) ),
    inference(fof_simplification,[status(thm)],[impl_axiom1]) ).

cnf(c_0_156,plain,
    ( d(X1)
    | ~ forallprefers(err,lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_88,c_0_70]) ).

fof(c_0_157,negated_conjecture,
    lazy_and1(esk8_0,esk9_0) != lazy_and2(esk8_0,esk9_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])])]) ).

cnf(c_0_158,plain,
    lazy_and2(X1,X2) = phi(f2(X1,X2,esk2_2(X1,X2))),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_159,plain,
    ( bool(esk2_2(X1,X2))
    | ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_32]),c_0_33]) ).

cnf(c_0_160,plain,
    ( lazy_impl(X1,X2) = X1
    | bool(X1)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_59]) ).

cnf(c_0_161,plain,
    esk7_0 = false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_119]),c_0_154]),c_0_153]) ).

fof(c_0_162,plain,
    ! [X19,X20] :
      ( bool(X19)
      | impl(X19,X20) = phi(X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])]) ).

cnf(c_0_163,plain,
    ( d(X1)
    | ~ forallprefers(err,false2)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_156,c_0_127]) ).

cnf(c_0_164,negated_conjecture,
    lazy_and1(esk8_0,esk9_0) != lazy_and2(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_157]) ).

cnf(c_0_165,plain,
    lazy_and2(X1,X2) = lazy_impl(true,f2(X1,X2,esk2_2(X1,X2))),
    inference(rw,[status(thm)],[c_0_158,c_0_42]) ).

cnf(c_0_166,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ forallprefers(lazy_impl(prop(X3),impl(X1,X3)),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_159,c_0_160]) ).

cnf(c_0_167,plain,
    prop(false) = true,
    inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_153]),c_0_119]),c_0_161]) ).

cnf(c_0_168,plain,
    ( bool(X1)
    | impl(X1,X2) = phi(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_162]) ).

cnf(c_0_169,plain,
    ( d(X1)
    | bool(err)
    | ~ bool(false2)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_83]),c_0_143])]) ).

cnf(c_0_170,negated_conjecture,
    lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_75]) ).

cnf(c_0_171,plain,
    ( lazy_impl(X1,X2) = lazy_impl(X1,X3)
    | bool(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_59]) ).

cnf(c_0_172,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ forallprefers(lazy_impl(true,impl(X1,false)),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_166,c_0_167]) ).

cnf(c_0_173,plain,
    ( impl(X1,X2) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[c_0_168,c_0_42]) ).

cnf(c_0_174,plain,
    ( bool(lazy_impl(true,X1))
    | ~ d(lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_88,c_0_83]) ).

cnf(c_0_175,plain,
    ( false2 = err
    | d(X1)
    | bool(err)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_146]),c_0_62])]) ).

cnf(c_0_176,negated_conjecture,
    ( bool(esk8_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,X1),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[c_0_170,c_0_171]) ).

cnf(c_0_177,plain,
    ( lazy_impl(X1,X2) = err
    | lazy_impl(X1,X2) = X1
    | bool(X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_59]) ).

cnf(c_0_178,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ forallprefers(lazy_impl(true,lazy_impl(true,X1)),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_172,c_0_173]) ).

cnf(c_0_179,plain,
    ( bool(lazy_impl(true,X1))
    | ~ bool(false2)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_123])]),c_0_127]) ).

cnf(c_0_180,plain,
    ( false2 = err
    | d(X1)
    | ~ bool(X1) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_175]),c_0_119]),c_0_120]) ).

cnf(c_0_181,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(esk8_0,esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[c_0_176,c_0_177]) ).

cnf(c_0_182,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ forallprefers(lazy_impl(true,X1),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_178,c_0_49]) ).

cnf(c_0_183,plain,
    ( bool(lazy_impl(true,X1))
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_148])]) ).

cnf(c_0_184,plain,
    ~ forallprefers(lazy_impl(true,prop(X1)),false2),
    inference(rw,[status(thm)],[c_0_96,c_0_127]) ).

cnf(c_0_185,plain,
    ( false2 = err
    | d(esk2_2(false,X1)) ),
    inference(spm,[status(thm)],[c_0_180,c_0_110]) ).

cnf(c_0_186,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,esk8_0))) != lazy_and1(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[c_0_181,c_0_173]) ).

cnf(c_0_187,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ forallprefers(X1,true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_182,c_0_49]) ).

fof(c_0_188,plain,
    ! [X3,X4] :
      ( ~ bool(X3)
     => lazy_and1(X3,X4) = phi(X3) ),
    inference(fof_simplification,[status(thm)],[lazy_and1_axiom1]) ).

cnf(c_0_189,plain,
    ( lazy_impl(true,X1) = true
    | lazy_impl(true,X1) = false
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_72,c_0_183]) ).

cnf(c_0_190,plain,
    ( bool(lazy_impl(true,prop(X1)))
    | ~ bool(false2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_83]),c_0_143])]) ).

cnf(c_0_191,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),esk2_2(false,X2))
    | ~ d(esk2_2(false,X2)) ),
    inference(spm,[status(thm)],[c_0_121,c_0_49]) ).

cnf(c_0_192,plain,
    d(esk2_2(false,X1)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_153]),c_0_119]) ).

cnf(c_0_193,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_impl(true,lazy_impl(true,lazy_impl(true,esk8_0))) != lazy_and1(esk8_0,esk9_0)
    | ~ bool(esk2_2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_186,c_0_40]) ).

cnf(c_0_194,plain,
    ( bool(esk2_2(X1,X2))
    | bool(X1)
    | ~ d(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_83]),c_0_139]),c_0_145])]) ).

cnf(c_0_195,plain,
    ( lazy_impl(X1,X2) = err
    | d(X1)
    | bool(X1) ),
    inference(spm,[status(thm)],[c_0_70,c_0_59]) ).

fof(c_0_196,plain,
    ! [X42,X43] :
      ( bool(X42)
      | lazy_and1(X42,X43) = phi(X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])]) ).

cnf(c_0_197,plain,
    ( lazy_impl(err,X1) = err
    | bool(err) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_177])]) ).

cnf(c_0_198,plain,
    ~ bool(err),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_189]),c_0_71]),c_0_119]),c_0_120]) ).

cnf(c_0_199,plain,
    ( false2 = err
    | bool(lazy_impl(true,prop(X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_146]),c_0_62])]) ).

cnf(c_0_200,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),esk2_2(false,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_192])]) ).

cnf(c_0_201,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_impl(true,lazy_impl(true,lazy_impl(true,esk8_0))) != lazy_and1(esk8_0,esk9_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_195]) ).

cnf(c_0_202,plain,
    ( bool(X1)
    | lazy_and1(X1,X2) = phi(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_196]) ).

cnf(c_0_203,plain,
    ( bool(lazy_impl(X1,impl(X2,esk2_2(X1,X2))))
    | ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),lazy_impl(prop(esk2_2(X1,X2)),lazy_impl(true,lazy_impl(X1,impl(X2,esk2_2(X1,X2)))))) ),
    inference(spm,[status(thm)],[c_0_81,c_0_173]) ).

cnf(c_0_204,plain,
    lazy_impl(err,X1) = err,
    inference(sr,[status(thm)],[c_0_197,c_0_198]) ).

cnf(c_0_205,plain,
    ( lazy_impl(true,prop(X1)) = true
    | lazy_impl(true,prop(X1)) = false
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_72,c_0_199]) ).

cnf(c_0_206,plain,
    ~ forallprefers(lazy_impl(true,impl(true,false)),esk2_2(false,X1)),
    inference(spm,[status(thm)],[c_0_200,c_0_167]) ).

cnf(c_0_207,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_and1(esk8_0,esk9_0) != lazy_impl(true,lazy_impl(true,esk8_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_49]),c_0_195]) ).

cnf(c_0_208,plain,
    ( lazy_and1(X1,X2) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[c_0_202,c_0_42]) ).

cnf(c_0_209,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),lazy_impl(prop(esk2_2(err,X2)),err)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_204]),c_0_71]),c_0_198]) ).

cnf(c_0_210,plain,
    ( lazy_impl(true,prop(X1)) = true
    | prop(X1) = false
    | false2 = err ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_205]),c_0_119]) ).

cnf(c_0_211,plain,
    bool(lazy_impl(true,impl(true,false))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_83]),c_0_192]),c_0_110])]) ).

cnf(c_0_212,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | lazy_impl(true,lazy_impl(true,esk8_0)) != lazy_impl(true,esk8_0) ),
    inference(spm,[status(thm)],[c_0_207,c_0_208]) ).

cnf(c_0_213,plain,
    ~ forallprefers(lazy_impl(prop(X1),err),lazy_impl(prop(esk2_2(err,X2)),err)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_173]),c_0_71]),c_0_198]) ).

cnf(c_0_214,plain,
    ( prop(X1) = false
    | prop(X1) = true
    | false2 = err ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_210]),c_0_120]) ).

fof(c_0_215,plain,
    ! [X38,X39,X41] :
      ( and2(X38,X39) = phi(f1(X38,X39,esk1_2(X38,X39)))
      & ~ forallprefers(f1(X38,X39,X41),f1(X38,X39,esk1_2(X38,X39))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_and2])])])]) ).

fof(c_0_216,plain,
    ! [X35,X36,X37] : f1(X35,X36,X37) = lazy_impl(prop(X37),impl(impl(X35,impl(X36,X37)),X37)),
    inference(variable_rename,[status(thm)],[def_f1]) ).

cnf(c_0_217,plain,
    ~ forallprefers(false,lazy_impl(true,esk2_2(false,X1))),
    inference(rw,[status(thm)],[c_0_129,c_0_153]) ).

cnf(c_0_218,plain,
    ( lazy_impl(true,X1) = true
    | false = X1
    | ~ bool(X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_189]),c_0_119]) ).

cnf(c_0_219,plain,
    ( lazy_impl(true,impl(true,false)) = true
    | lazy_impl(true,impl(true,false)) = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_211]) ).

cnf(c_0_220,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0)
    | ~ d(lazy_impl(true,esk8_0)) ),
    inference(spm,[status(thm)],[c_0_212,c_0_49]) ).

cnf(c_0_221,plain,
    ~ forallprefers(err,lazy_impl(prop(esk2_2(err,X1)),err)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_167]),c_0_71]) ).

cnf(c_0_222,plain,
    ( prop(X1) = true
    | prop(X1) = false ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_214,c_0_153]),c_0_119]) ).

cnf(c_0_223,plain,
    ~ forallprefers(f1(X1,X2,X3),f1(X1,X2,esk1_2(X1,X2))),
    inference(split_conjunct,[status(thm)],[c_0_215]) ).

cnf(c_0_224,plain,
    f1(X1,X2,X3) = lazy_impl(prop(X3),impl(impl(X1,impl(X2,X3)),X3)),
    inference(split_conjunct,[status(thm)],[c_0_216]) ).

cnf(c_0_225,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk2_2(false,X2)),impl(true,esk2_2(false,X2))))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_86,c_0_95]) ).

cnf(c_0_226,plain,
    esk2_2(false,X1) = false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_56]),c_0_110])]) ).

cnf(c_0_227,plain,
    ( lazy_impl(true,impl(true,false)) = true
    | d(impl(true,false)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_219]),c_0_119]) ).

cnf(c_0_228,negated_conjecture,
    ( lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0)))) ),
    inference(spm,[status(thm)],[c_0_170,c_0_49]) ).

cnf(c_0_229,plain,
    ( bool(lazy_impl(X1,impl(X2,X3)))
    | bool(esk2_2(X1,X2))
    | ~ forallprefers(lazy_impl(prop(X3),lazy_impl(true,lazy_impl(X1,impl(X2,X3)))),true) ),
    inference(spm,[status(thm)],[c_0_159,c_0_173]) ).

cnf(c_0_230,negated_conjecture,
    ( lazy_impl(esk8_0,X1) = err
    | bool(esk8_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_49]),c_0_195]) ).

cnf(c_0_231,plain,
    ( prop(esk2_2(err,X1)) = true
    | ~ forallprefers(err,true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_33]) ).

cnf(c_0_232,plain,
    ~ forallprefers(lazy_impl(prop(X3),impl(impl(X1,impl(X2,X3)),X3)),lazy_impl(prop(esk1_2(X1,X2)),impl(impl(X1,impl(X2,esk1_2(X1,X2))),esk1_2(X1,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_224]),c_0_224]) ).

fof(c_0_233,plain,
    ! [X23] :
      ( ~ bool(X23)
      | impl(false,X23) = true ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom3])]) ).

cnf(c_0_234,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,impl(true,false)))
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_167]) ).

cnf(c_0_235,plain,
    lazy_impl(true,false) = false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_153]),c_0_161]) ).

cnf(c_0_236,plain,
    ( bool(impl(true,false))
    | ~ d(impl(true,false)) ),
    inference(spm,[status(thm)],[c_0_211,c_0_49]) ).

cnf(c_0_237,plain,
    d(impl(true,false)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_227]),c_0_120]) ).

cnf(c_0_238,plain,
    ( ~ forallprefers(lazy_impl(true,impl(true,X1)),esk2_2(false,X2))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_200,c_0_40]) ).

cnf(c_0_239,plain,
    ( esk7_0 = true
    | esk7_0 = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_62]) ).

cnf(c_0_240,negated_conjecture,
    ( lazy_impl(true,impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(lazy_impl(true,impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))))
    | ~ bool(esk2_2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_228,c_0_40]) ).

cnf(c_0_241,negated_conjecture,
    ( bool(esk2_2(esk8_0,X1))
    | bool(esk8_0)
    | ~ forallprefers(lazy_impl(prop(X2),err),true) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_71]),c_0_198]) ).

cnf(c_0_242,plain,
    prop(esk2_2(err,X1)) = true,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_243,plain,
    ( bool(esk1_2(X1,X2))
    | ~ forallprefers(lazy_impl(prop(X3),impl(impl(X1,impl(X2,X3)),X3)),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_32]),c_0_33]) ).

cnf(c_0_244,plain,
    ( impl(false,X1) = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_233]) ).

cnf(c_0_245,plain,
    ~ forallprefers(false,lazy_impl(true,impl(true,false))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_167]),c_0_235]),c_0_58])]) ).

cnf(c_0_246,plain,
    bool(impl(true,false)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_237])]) ).

cnf(c_0_247,plain,
    ( d(impl(true,X1))
    | ~ forallprefers(err,esk2_2(false,X2))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_238,c_0_70]) ).

cnf(c_0_248,plain,
    ( lazy_impl(true,lazy_impl(true,false)) = false2
    | esk7_0 = true ),
    inference(spm,[status(thm)],[c_0_69,c_0_239]) ).

cnf(c_0_249,negated_conjecture,
    ( bool(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))))
    | lazy_impl(true,lazy_impl(true,lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(lazy_impl(true,lazy_impl(true,lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))))))
    | ~ bool(esk2_2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_240,c_0_173]) ).

cnf(c_0_250,negated_conjecture,
    ( bool(esk2_2(esk8_0,X1))
    | bool(esk8_0)
    | ~ forallprefers(err,true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_71]) ).

cnf(c_0_251,plain,
    ( bool(esk1_2(false,X1))
    | ~ forallprefers(lazy_impl(prop(X2),impl(true,X2)),true)
    | ~ bool(impl(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_243,c_0_244]) ).

cnf(c_0_252,plain,
    impl(true,false) = false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_218]),c_0_56]),c_0_246])]) ).

cnf(c_0_253,plain,
    ( ~ forallprefers(impl(true,X1),esk2_2(false,X2))
    | ~ d(impl(true,X1))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_238,c_0_49]) ).

cnf(c_0_254,plain,
    ( d(impl(true,X1))
    | ~ forallprefers(err,false)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_247,c_0_226]) ).

cnf(c_0_255,plain,
    ( lazy_impl(true,false) = false2
    | esk7_0 = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_49]),c_0_57])]) ).

cnf(c_0_256,plain,
    ( false2 = err
    | ~ forallprefers(esk7_0,lazy_impl(true,esk7_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_152]),c_0_62])]) ).

cnf(c_0_257,negated_conjecture,
    ( bool(esk8_0)
    | lazy_and1(esk8_0,esk9_0) != err
    | ~ bool(esk2_2(esk8_0,esk9_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_230]),c_0_71]),c_0_71]),c_0_71]),c_0_71]),c_0_115])]),c_0_198]) ).

cnf(c_0_258,negated_conjecture,
    ( bool(esk2_2(esk8_0,X1))
    | bool(esk8_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_259,plain,
    ( bool(esk2_2(err,X1))
    | ~ forallprefers(lazy_impl(prop(X2),err),true) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_204]),c_0_71]),c_0_198]) ).

cnf(c_0_260,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(impl(false,impl(X2,X1)),X1)),lazy_impl(prop(esk1_2(false,X2)),impl(true,esk1_2(false,X2))))
    | ~ bool(impl(X2,esk1_2(false,X2))) ),
    inference(spm,[status(thm)],[c_0_232,c_0_244]) ).

cnf(c_0_261,plain,
    bool(esk1_2(false,true)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_167]),c_0_252]),c_0_235]),c_0_56]),c_0_58])]) ).

cnf(c_0_262,plain,
    ( ~ forallprefers(impl(true,X1),false)
    | ~ d(impl(true,X1))
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_253,c_0_226]) ).

cnf(c_0_263,plain,
    ( d(impl(true,X1))
    | ~ bool(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_83]),c_0_57]),c_0_58])]),c_0_198]) ).

cnf(c_0_264,plain,
    ( prop(esk7_0) = false
    | prop(esk7_0) = true
    | false2 = err
    | false2 != false ),
    inference(ef,[status(thm)],[c_0_80]) ).

cnf(c_0_265,plain,
    ( esk7_0 = true
    | false2 = false ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_255]),c_0_57])]) ).

cnf(c_0_266,plain,
    ( false2 = err
    | ~ forallprefers(esk7_0,false2) ),
    inference(spm,[status(thm)],[c_0_256,c_0_141]) ).

cnf(c_0_267,negated_conjecture,
    ( bool(esk8_0)
    | lazy_and1(esk8_0,esk9_0) != err ),
    inference(spm,[status(thm)],[c_0_257,c_0_258]) ).

cnf(c_0_268,negated_conjecture,
    ( lazy_impl(true,esk8_0) = err
    | bool(esk8_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_230]) ).

cnf(c_0_269,plain,
    ( bool(esk2_2(err,X1))
    | ~ forallprefers(err,true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_167]),c_0_71]) ).

cnf(c_0_270,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(impl(false,impl(true,X1)),X1)),lazy_impl(prop(esk1_2(false,true)),impl(true,esk1_2(false,true)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_95]),c_0_261])]) ).

cnf(c_0_271,plain,
    ( ~ forallprefers(impl(true,X1),false)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_262,c_0_263]) ).

cnf(c_0_272,plain,
    ( false2 = err
    | bool(lazy_impl(true,true)) ),
    inference(spm,[status(thm)],[c_0_199,c_0_98]) ).

cnf(c_0_273,plain,
    ( prop(esk7_0) = true
    | prop(esk7_0) = false
    | esk7_0 = true ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_119]) ).

cnf(c_0_274,plain,
    ( esk7_0 = true
    | ~ forallprefers(esk7_0,false) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_265]),c_0_119]) ).

cnf(c_0_275,negated_conjecture,
    bool(esk8_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_208]),c_0_268]) ).

fof(c_0_276,plain,
    ! [X44] : lazy_and1(false,X44) = false,
    inference(variable_rename,[status(thm)],[lazy_and1_axiom2]) ).

fof(c_0_277,plain,
    ! [X45] : lazy_and1(true,X45) = phi(X45),
    inference(variable_rename,[status(thm)],[lazy_and1_axiom3]) ).

cnf(c_0_278,plain,
    bool(esk2_2(err,X1)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_279,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(prop(esk1_2(false,true)),impl(true,esk1_2(false,true))))
    | ~ bool(impl(true,X1)) ),
    inference(spm,[status(thm)],[c_0_270,c_0_244]) ).

cnf(c_0_280,plain,
    ( bool(impl(true,X1))
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_83]),c_0_57]),c_0_58])]) ).

cnf(c_0_281,plain,
    ( lazy_impl(true,true) = true
    | lazy_impl(true,true) = false
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_72,c_0_272]) ).

cnf(c_0_282,plain,
    true != false,
    inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).

cnf(c_0_283,plain,
    ( prop(esk7_0) = true
    | esk7_0 = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_273]),c_0_62])]) ).

cnf(c_0_284,plain,
    ( lazy_impl(true,esk7_0) = false2
    | ~ d(esk7_0) ),
    inference(spm,[status(thm)],[c_0_69,c_0_49]) ).

cnf(c_0_285,plain,
    ( esk7_0 = true
    | d(esk7_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_79]),c_0_57])]) ).

cnf(c_0_286,negated_conjecture,
    ( bool(esk9_0)
    | lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,lazy_impl(true,esk9_0)),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,lazy_impl(true,esk9_0)),esk2_2(esk8_0,esk9_0)))) ),
    inference(spm,[status(thm)],[c_0_228,c_0_173]) ).

cnf(c_0_287,plain,
    ( d(X1)
    | ~ bool(X1) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_153]),c_0_119]) ).

cnf(c_0_288,negated_conjecture,
    ( esk8_0 = true
    | esk8_0 = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_275]) ).

cnf(c_0_289,plain,
    lazy_and1(false,X1) = false,
    inference(split_conjunct,[status(thm)],[c_0_276]) ).

cnf(c_0_290,plain,
    lazy_and1(true,X1) = phi(X1),
    inference(split_conjunct,[status(thm)],[c_0_277]) ).

cnf(c_0_291,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),err),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_40]),c_0_71]),c_0_278])]) ).

cnf(c_0_292,plain,
    ( bool(lazy_impl(X1,impl(X2,X3)))
    | ~ forallprefers(lazy_impl(prop(X3),lazy_impl(true,lazy_impl(X1,impl(X2,X3)))),lazy_impl(prop(esk2_2(X1,X2)),impl(lazy_impl(X1,impl(X2,esk2_2(X1,X2))),esk2_2(X1,X2)))) ),
    inference(spm,[status(thm)],[c_0_81,c_0_173]) ).

cnf(c_0_293,plain,
    ~ forallprefers(false,lazy_impl(prop(esk1_2(false,true)),impl(true,esk1_2(false,true)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_252]),c_0_167]),c_0_235]),c_0_58])]) ).

cnf(c_0_294,plain,
    ( impl(true,X1) = true
    | impl(true,X1) = false
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_72,c_0_280]) ).

cnf(c_0_295,plain,
    ( lazy_impl(true,true) = true
    | false2 = err ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_281]),c_0_139])]),c_0_282]) ).

cnf(c_0_296,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(true,true),lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_283]) ).

cnf(c_0_297,plain,
    ( lazy_impl(true,esk7_0) = false2
    | esk7_0 = true ),
    inference(spm,[status(thm)],[c_0_284,c_0_285]) ).

cnf(c_0_298,negated_conjecture,
    ( d(esk9_0)
    | lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,err),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,err),esk2_2(esk8_0,esk9_0)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_70]),c_0_287]) ).

cnf(c_0_299,negated_conjecture,
    esk8_0 = true,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_288]),c_0_226]),c_0_167]),c_0_226]),c_0_33]),c_0_226]),c_0_252]),c_0_235]),c_0_235]),c_0_289])]) ).

cnf(c_0_300,plain,
    lazy_and1(true,X1) = lazy_impl(true,X1),
    inference(rw,[status(thm)],[c_0_290,c_0_42]) ).

cnf(c_0_301,plain,
    d(lazy_impl(prop(X1),impl(err,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_79]),c_0_115])]) ).

cnf(c_0_302,plain,
    ( d(impl(X1,X2))
    | ~ forallprefers(lazy_impl(prop(X2),err),lazy_impl(prop(esk2_2(true,X1)),impl(lazy_impl(true,impl(X1,esk2_2(true,X1))),esk2_2(true,X1)))) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_70]),c_0_71]),c_0_198]) ).

cnf(c_0_303,plain,
    ~ forallprefers(false,lazy_impl(true,impl(true,esk1_2(false,true)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_40]),c_0_261])]) ).

cnf(c_0_304,plain,
    ( impl(true,X1) = true
    | false = X1
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_95,c_0_294]) ).

cnf(c_0_305,plain,
    lazy_impl(true,true) = true,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_295,c_0_153]),c_0_119]) ).

cnf(c_0_306,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(true,true),false2) ),
    inference(spm,[status(thm)],[c_0_296,c_0_297]) ).

cnf(c_0_307,plain,
    ( ~ forallprefers(lazy_impl(true,prop(X1)),esk7_0)
    | ~ d(esk7_0) ),
    inference(spm,[status(thm)],[c_0_100,c_0_49]) ).

cnf(c_0_308,negated_conjecture,
    ( d(esk9_0)
    | lazy_impl(prop(esk2_2(true,esk9_0)),impl(err,esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_298,c_0_299]),c_0_299]),c_0_71]),c_0_299]),c_0_299]),c_0_300]),c_0_299]),c_0_299]),c_0_71]),c_0_299]),c_0_301])]) ).

cnf(c_0_309,plain,
    ( d(impl(X1,X2))
    | bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(prop(X2),err),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_32]),c_0_33]) ).

cnf(c_0_310,plain,
    esk1_2(false,true) = false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_304]),c_0_305]),c_0_56]),c_0_261])]) ).

cnf(c_0_311,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(true,true),false) ),
    inference(spm,[status(thm)],[c_0_306,c_0_265]) ).

cnf(c_0_312,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(true,prop(X1)),false) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_239]),c_0_57])]) ).

cnf(c_0_313,negated_conjecture,
    ( d(esk9_0)
    | lazy_impl(prop(esk2_2(true,esk9_0)),err) != lazy_impl(true,esk9_0) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_173]),c_0_71]),c_0_198]) ).

cnf(c_0_314,plain,
    ( d(impl(X1,false))
    | bool(esk2_2(true,X1))
    | ~ forallprefers(err,true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_167]),c_0_71]) ).

cnf(c_0_315,plain,
    ( d(impl(X1,X2))
    | bool(esk2_2(true,X1))
    | ~ forallprefers(err,true)
    | ~ bool(X2) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_40]),c_0_71]) ).

cnf(c_0_316,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(impl(false,impl(true,X1)),X1)),false),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_310]),c_0_167]),c_0_252]),c_0_235]),c_0_252]),c_0_58])]) ).

cnf(c_0_317,plain,
    ( esk7_0 = true
    | bool(lazy_impl(true,true)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_83]),c_0_57]),c_0_58])]) ).

cnf(c_0_318,plain,
    ( esk7_0 = true
    | bool(lazy_impl(true,prop(X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_83]),c_0_57]),c_0_58])]) ).

cnf(c_0_319,negated_conjecture,
    lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_299]),c_0_299]),c_0_299]),c_0_299]),c_0_299]),c_0_300]) ).

cnf(c_0_320,negated_conjecture,
    ( d(esk9_0)
    | ~ bool(esk2_2(true,esk9_0)) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_40]),c_0_71]),c_0_70]) ).

cnf(c_0_321,plain,
    ( d(impl(X1,false))
    | bool(esk2_2(true,X1)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_322,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(prop(X2),impl(impl(X1,X2),X2)),true)
    | ~ d(impl(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_159,c_0_49]) ).

cnf(c_0_323,plain,
    ( d(impl(X1,X2))
    | bool(esk2_2(true,X1))
    | ~ bool(X2) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_324,plain,
    ~ forallprefers(lazy_impl(true,impl(impl(false,false),false)),false),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_252]),c_0_167]) ).

cnf(c_0_325,plain,
    ( lazy_impl(true,true) = true
    | lazy_impl(true,true) = false
    | esk7_0 = true ),
    inference(spm,[status(thm)],[c_0_72,c_0_317]) ).

cnf(c_0_326,plain,
    ( lazy_impl(true,prop(X1)) = true
    | lazy_impl(true,prop(X1)) = false
    | esk7_0 = true ),
    inference(spm,[status(thm)],[c_0_72,c_0_318]) ).

cnf(c_0_327,negated_conjecture,
    ( lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(impl(esk9_0,esk2_2(true,esk9_0)),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0)
    | ~ d(impl(esk9_0,esk2_2(true,esk9_0))) ),
    inference(spm,[status(thm)],[c_0_319,c_0_49]) ).

cnf(c_0_328,negated_conjecture,
    ( d(impl(esk9_0,false))
    | d(esk9_0) ),
    inference(spm,[status(thm)],[c_0_320,c_0_321]) ).

cnf(c_0_329,plain,
    ( bool(esk2_2(X1,X2))
    | ~ forallprefers(lazy_impl(true,impl(lazy_impl(X1,impl(X2,X3)),X3)),true)
    | ~ bool(X3) ),
    inference(spm,[status(thm)],[c_0_159,c_0_40]) ).

cnf(c_0_330,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(prop(X2),impl(impl(X1,X2),X2)),true)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_322,c_0_323]) ).

cnf(c_0_331,plain,
    ( d(impl(impl(false,false),false))
    | ~ forallprefers(err,false) ),
    inference(spm,[status(thm)],[c_0_324,c_0_70]) ).

cnf(c_0_332,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,X1),X1)),lazy_impl(prop(esk2_2(X2,true)),impl(lazy_impl(X2,impl(true,esk2_2(X2,true))),esk2_2(X2,true))))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_81,c_0_95]) ).

cnf(c_0_333,plain,
    ( lazy_impl(true,true) = true
    | esk7_0 = true ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_325]),c_0_139])]),c_0_282]) ).

cnf(c_0_334,plain,
    ( lazy_impl(true,prop(X1)) = true
    | prop(X1) = false
    | esk7_0 = true ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_326]),c_0_119]) ).

cnf(c_0_335,negated_conjecture,
    ( bool(esk9_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,lazy_impl(true,esk9_0)),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[c_0_170,c_0_173]) ).

cnf(c_0_336,negated_conjecture,
    ( bool(esk9_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,esk9_0),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0)
    | ~ d(lazy_impl(true,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_327,c_0_173]) ).

cnf(c_0_337,negated_conjecture,
    ( d(lazy_impl(true,esk9_0))
    | d(esk9_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_173]),c_0_287]) ).

cnf(c_0_338,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(true,impl(impl(X1,X2),X2)),true)
    | ~ d(impl(X1,X2))
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_329,c_0_49]) ).

cnf(c_0_339,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(true,impl(impl(X1,false),false)),true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_167]),c_0_58])]) ).

cnf(c_0_340,plain,
    ( ~ forallprefers(impl(impl(false,false),false),false)
    | ~ d(impl(impl(false,false),false)) ),
    inference(spm,[status(thm)],[c_0_324,c_0_49]) ).

cnf(c_0_341,plain,
    d(impl(impl(false,false),false)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_83]),c_0_57]),c_0_58])]),c_0_198]) ).

cnf(c_0_342,plain,
    ( ~ forallprefers(lazy_impl(true,X1),false2)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_88,c_0_127]) ).

cnf(c_0_343,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(prop(true),impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_333]),c_0_145])]) ).

cnf(c_0_344,plain,
    ( prop(X1) = false
    | prop(X1) = true
    | esk7_0 = true ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_334]),c_0_120]) ).

cnf(c_0_345,negated_conjecture,
    ( bool(lazy_impl(esk8_0,lazy_impl(true,esk9_0)))
    | bool(esk9_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,lazy_impl(esk8_0,lazy_impl(true,esk9_0))))) != lazy_and1(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[c_0_335,c_0_173]) ).

cnf(c_0_346,negated_conjecture,
    ( d(esk9_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,esk9_0),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_337]),c_0_287]) ).

cnf(c_0_347,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(lazy_impl(true,impl(impl(X1,X2),X2)),true)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_338,c_0_323]) ).

cnf(c_0_348,plain,
    ( d(impl(impl(X1,false),false))
    | bool(esk2_2(true,X1))
    | ~ forallprefers(err,true) ),
    inference(spm,[status(thm)],[c_0_339,c_0_70]) ).

cnf(c_0_349,plain,
    ~ forallprefers(impl(impl(false,false),false),false),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_340,c_0_341])]) ).

cnf(c_0_350,plain,
    ( ~ forallprefers(lazy_impl(true,X1),false)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_342,c_0_153]) ).

cnf(c_0_351,plain,
    ( prop(esk2_2(true,true)) = true
    | esk7_0 = true
    | ~ forallprefers(lazy_impl(prop(true),impl(true,true)),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_344]),c_0_33]) ).

cnf(c_0_352,negated_conjecture,
    ( bool(lazy_impl(esk8_0,esk9_0))
    | bool(esk9_0)
    | lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,lazy_impl(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0)
    | ~ d(esk9_0) ),
    inference(spm,[status(thm)],[c_0_345,c_0_49]) ).

cnf(c_0_353,negated_conjecture,
    ( d(esk9_0)
    | bool(lazy_impl(true,esk9_0))
    | lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),lazy_impl(true,lazy_impl(true,esk9_0)))) != lazy_impl(true,esk9_0) ),
    inference(spm,[status(thm)],[c_0_346,c_0_173]) ).

cnf(c_0_354,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(impl(impl(X1,X2),X2),true)
    | ~ d(impl(impl(X1,X2),X2))
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_347,c_0_49]) ).

cnf(c_0_355,plain,
    ( d(impl(impl(X1,false),false))
    | bool(esk2_2(true,X1)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_348,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_356,plain,
    ~ forallprefers(lazy_impl(true,impl(false,false)),false),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_349,c_0_173]),c_0_350]) ).

cnf(c_0_357,plain,
    ( prop(esk2_2(true,true)) = true
    | esk7_0 = true
    | bool(lazy_impl(prop(true),impl(true,true))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_83]),c_0_139]),c_0_145])]) ).

cnf(c_0_358,plain,
    ( false2 = err
    | ~ forallprefers(lazy_impl(prop(true),impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_295]),c_0_145])]) ).

cnf(c_0_359,negated_conjecture,
    ( bool(lazy_impl(true,esk9_0))
    | lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),lazy_impl(true,lazy_impl(true,esk9_0)))) != lazy_impl(true,esk9_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_352,c_0_299]),c_0_299]),c_0_299]),c_0_299]),c_0_300]),c_0_353]),c_0_183]) ).

cnf(c_0_360,plain,
    ( bool(esk2_2(true,X1))
    | ~ forallprefers(impl(impl(X1,false),false),true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354,c_0_355]),c_0_58])]) ).

cnf(c_0_361,plain,
    ( d(impl(false,false))
    | ~ forallprefers(err,false) ),
    inference(spm,[status(thm)],[c_0_356,c_0_70]) ).

cnf(c_0_362,plain,
    ( lazy_impl(prop(true),impl(true,true)) = true
    | lazy_impl(prop(true),impl(true,true)) = false
    | prop(esk2_2(true,true)) = true
    | esk7_0 = true ),
    inference(spm,[status(thm)],[c_0_72,c_0_357]) ).

cnf(c_0_363,plain,
    ( false2 = err
    | ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358,c_0_40]),c_0_145])]) ).

cnf(c_0_364,negated_conjecture,
    ( bool(lazy_impl(true,esk9_0))
    | lazy_impl(prop(esk2_2(true,esk9_0)),lazy_impl(true,lazy_impl(true,esk9_0))) != lazy_impl(true,esk9_0)
    | ~ d(lazy_impl(prop(esk2_2(true,esk9_0)),lazy_impl(true,lazy_impl(true,esk9_0)))) ),
    inference(spm,[status(thm)],[c_0_359,c_0_49]) ).

cnf(c_0_365,plain,
    ( bool(esk2_2(true,X1))
    | bool(X1)
    | ~ forallprefers(impl(lazy_impl(true,X1),false),true) ),
    inference(spm,[status(thm)],[c_0_360,c_0_173]) ).

cnf(c_0_366,plain,
    ( ~ forallprefers(impl(false,false),false)
    | ~ d(impl(false,false)) ),
    inference(spm,[status(thm)],[c_0_356,c_0_49]) ).

cnf(c_0_367,plain,
    d(impl(false,false)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_361,c_0_83]),c_0_57]),c_0_58])]),c_0_198]) ).

cnf(c_0_368,plain,
    ( lazy_impl(prop(true),impl(true,true)) = true
    | prop(esk2_2(true,true)) = true
    | esk7_0 = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_362]),c_0_56])]) ).

cnf(c_0_369,plain,
    ( prop(esk2_2(true,true)) = true
    | false2 = err
    | ~ forallprefers(lazy_impl(true,impl(true,true)),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_363,c_0_214]),c_0_33]) ).

cnf(c_0_370,negated_conjecture,
    ( bool(lazy_impl(true,esk9_0))
    | lazy_impl(true,lazy_impl(true,lazy_impl(true,esk9_0))) != lazy_impl(true,esk9_0)
    | ~ d(lazy_impl(true,lazy_impl(true,lazy_impl(true,esk9_0))))
    | ~ bool(esk2_2(true,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_364,c_0_40]) ).

cnf(c_0_371,plain,
    ( bool(esk2_2(true,X1))
    | bool(X1)
    | ~ forallprefers(impl(X1,false),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_365,c_0_49]) ).

cnf(c_0_372,plain,
    ( bool(esk2_2(X1,false))
    | ~ forallprefers(lazy_impl(prop(X2),impl(lazy_impl(X1,true),X2)),true)
    | ~ bool(X2) ),
    inference(spm,[status(thm)],[c_0_159,c_0_244]) ).

cnf(c_0_373,plain,
    ~ forallprefers(impl(false,false),false),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_366,c_0_367])]) ).

cnf(c_0_374,plain,
    ( esk7_0 = true
    | ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_40]),c_0_145])]) ).

cnf(c_0_375,plain,
    ( lazy_impl(true,impl(true,true)) = true
    | prop(esk2_2(true,true)) = true
    | esk7_0 = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368,c_0_40]),c_0_145])]) ).

cnf(c_0_376,plain,
    ( prop(esk2_2(true,true)) = true
    | ~ forallprefers(lazy_impl(true,impl(true,true)),true) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_369,c_0_153]),c_0_119]) ).

cnf(c_0_377,plain,
    ( lazy_impl(true,X1) = X1
    | ~ forallprefers(err,lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_88,c_0_54]) ).

cnf(c_0_378,negated_conjecture,
    ( bool(lazy_impl(true,esk9_0))
    | lazy_impl(true,lazy_impl(true,esk9_0)) != lazy_impl(true,esk9_0)
    | ~ d(lazy_impl(true,lazy_impl(true,esk9_0)))
    | ~ bool(esk2_2(true,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_370,c_0_49]) ).

cnf(c_0_379,plain,
    ( bool(esk2_2(true,X1))
    | bool(X1)
    | ~ forallprefers(lazy_impl(true,X1),true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_371,c_0_173]) ).

cnf(c_0_380,plain,
    ( d(X1)
    | bool(esk2_2(true,X1))
    | ~ forallprefers(impl(err,false),true) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_365,c_0_70]),c_0_287]) ).

cnf(c_0_381,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(true,impl(X2,X1)),X1)),lazy_impl(prop(esk2_2(true,X2)),impl(impl(X2,esk2_2(true,X2)),esk2_2(true,X2))))
    | ~ d(impl(X2,esk2_2(true,X2))) ),
    inference(spm,[status(thm)],[c_0_81,c_0_49]) ).

cnf(c_0_382,plain,
    ( bool(esk2_2(X1,false))
    | ~ forallprefers(lazy_impl(true,impl(lazy_impl(X1,true),false)),true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_372,c_0_167]),c_0_58])]) ).

cnf(c_0_383,plain,
    bool(impl(false,false)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_373,c_0_83]),c_0_57]),c_0_58])]) ).

cnf(c_0_384,plain,
    ( lazy_impl(true,impl(true,true)) = true
    | esk7_0 = true
    | ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(spm,[status(thm)],[c_0_374,c_0_375]) ).

cnf(c_0_385,plain,
    bool(lazy_impl(prop(X1),impl(true,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_83]),c_0_192]),c_0_110])]) ).

cnf(c_0_386,plain,
    ( prop(esk2_2(true,true)) = true
    | impl(true,true) = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_376,c_0_294]),c_0_235]),c_0_56]),c_0_145])]) ).

cnf(c_0_387,plain,
    ( lazy_impl(true,X1) = X1
    | ~ forallprefers(err,false2)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[c_0_377,c_0_127]) ).

cnf(c_0_388,negated_conjecture,
    ( bool(lazy_impl(true,esk9_0))
    | ~ d(lazy_impl(true,esk9_0))
    | ~ bool(esk2_2(true,esk9_0)) ),
    inference(spm,[status(thm)],[c_0_378,c_0_49]) ).

cnf(c_0_389,plain,
    ( bool(esk2_2(true,X1))
    | bool(X1)
    | ~ forallprefers(X1,true)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[c_0_379,c_0_49]) ).

cnf(c_0_390,plain,
    ( d(X1)
    | bool(esk2_2(true,X1))
    | ~ forallprefers(err,true) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_380,c_0_173]),c_0_71]),c_0_198]) ).

cnf(c_0_391,plain,
    ( ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(true,impl(false,X1)),X1)),lazy_impl(prop(esk2_2(true,false)),impl(true,esk2_2(true,false))))
    | ~ bool(esk2_2(true,false)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_244]),c_0_139])]) ).

cnf(c_0_392,plain,
    bool(esk2_2(true,false)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_382,c_0_49]),c_0_252]),c_0_235]),c_0_56]),c_0_139])]) ).

cnf(c_0_393,plain,
    ( impl(false,false) = true
    | impl(false,false) = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_383]) ).

cnf(c_0_394,plain,
    ( impl(true,true) = true
    | esk7_0 = true
    | ~ forallprefers(impl(true,true),lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
    | ~ d(impl(true,true)) ),
    inference(spm,[status(thm)],[c_0_384,c_0_49]) ).

cnf(c_0_395,plain,
    ( impl(true,true) = true
    | bool(lazy_impl(true,impl(true,esk2_2(true,true)))) ),
    inference(spm,[status(thm)],[c_0_385,c_0_386]) ).

cnf(c_0_396,plain,
    ( lazy_impl(true,X1) = X1
    | bool(err)
    | ~ bool(false2)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_83]),c_0_143])]) ).

cnf(c_0_397,negated_conjecture,
    ( bool(esk9_0)
    | ~ bool(esk2_2(true,esk9_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_388,c_0_49]),c_0_320]) ).

cnf(c_0_398,plain,
    ( bool(esk2_2(true,X1))
    | bool(X1)
    | ~ d(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_389,c_0_83]),c_0_139]),c_0_145])]) ).

cnf(c_0_399,plain,
    ( d(X1)
    | bool(esk2_2(true,X1)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_390,c_0_83]),c_0_139]),c_0_145])]),c_0_198]) ).

cnf(c_0_400,plain,
    ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(true,impl(false,X1)),X1)),lazy_impl(prop(esk2_2(true,false)),impl(true,esk2_2(true,false)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_391,c_0_392])]) ).

cnf(c_0_401,plain,
    impl(false,false) = true,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_393]),c_0_58])]),c_0_282]) ).

cnf(c_0_402,plain,
    ( impl(true,true) = true
    | ~ forallprefers(impl(true,true),lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
    | ~ d(impl(true,true)) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_394,c_0_161]),c_0_282]) ).

cnf(c_0_403,plain,
    ( lazy_impl(true,impl(true,esk2_2(true,true))) = true
    | lazy_impl(true,impl(true,esk2_2(true,true))) = false
    | impl(true,true) = true ),
    inference(spm,[status(thm)],[c_0_72,c_0_395]) ).

cnf(c_0_404,negated_conjecture,
    ( prop(esk2_2(esk8_0,esk9_0)) = true
    | false2 = err
    | lazy_and1(esk8_0,esk9_0) != true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_214]),c_0_33]),c_0_33]),c_0_139])]) ).

cnf(c_0_405,plain,
    ( lazy_impl(true,X1) = X1
    | bool(err)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_396,c_0_148])]) ).

cnf(c_0_406,negated_conjecture,
    ( bool(esk9_0)
    | ~ d(esk9_0) ),
    inference(spm,[status(thm)],[c_0_397,c_0_398]) ).

cnf(c_0_407,negated_conjecture,
    d(esk9_0),
    inference(spm,[status(thm)],[c_0_320,c_0_399]) ).

cnf(c_0_408,plain,
    ~ forallprefers(false,lazy_impl(prop(esk2_2(true,false)),impl(true,esk2_2(true,false)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_401]),c_0_167]),c_0_305]),c_0_252]),c_0_235]) ).

cnf(c_0_409,plain,
    ( impl(true,true) = true
    | ~ forallprefers(impl(true,true),lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_402,c_0_263]),c_0_145])]) ).

cnf(c_0_410,plain,
    ( lazy_impl(true,impl(true,esk2_2(true,true))) = true
    | impl(true,esk2_2(true,true)) = false
    | impl(true,true) = true ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_403]),c_0_119]) ).

cnf(c_0_411,negated_conjecture,
    ( prop(esk2_2(esk8_0,esk9_0)) = true
    | lazy_and1(esk8_0,esk9_0) != true ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_404,c_0_153]),c_0_119]) ).

cnf(c_0_412,negated_conjecture,
    ( lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0)
    | ~ bool(lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0)))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_405]),c_0_198]) ).

cnf(c_0_413,negated_conjecture,
    bool(esk9_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_406,c_0_407])]) ).

cnf(c_0_414,plain,
    ~ forallprefers(false,lazy_impl(true,impl(true,esk2_2(true,false)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_408,c_0_40]),c_0_392])]) ).

cnf(c_0_415,negated_conjecture,
    ( bool(esk2_2(esk8_0,esk9_0))
    | lazy_and1(esk8_0,esk9_0) != true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_32]),c_0_33]),c_0_33]),c_0_139])]) ).

cnf(c_0_416,plain,
    ( impl(true,esk2_2(true,true)) = false
    | impl(true,true) = true
    | ~ forallprefers(impl(true,true),lazy_impl(true,impl(true,esk2_2(true,true)))) ),
    inference(spm,[status(thm)],[c_0_409,c_0_410]) ).

cnf(c_0_417,plain,
    ( esk7_0 = true
    | ~ forallprefers(impl(true,true),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
    | ~ d(impl(true,true)) ),
    inference(spm,[status(thm)],[c_0_374,c_0_49]) ).

cnf(c_0_418,negated_conjecture,
    ( prop(esk2_2(true,esk9_0)) = true
    | lazy_impl(true,esk9_0) != true ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_411,c_0_299]),c_0_299]),c_0_300]) ).

cnf(c_0_419,negated_conjecture,
    ( lazy_impl(prop(esk2_2(true,esk9_0)),impl(impl(esk9_0,esk2_2(true,esk9_0)),esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0)
    | ~ bool(lazy_impl(prop(esk2_2(true,esk9_0)),impl(impl(esk9_0,esk2_2(true,esk9_0)),esk2_2(true,esk9_0))))
    | ~ bool(impl(esk9_0,esk2_2(true,esk9_0))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_412,c_0_405]),c_0_198]) ).

cnf(c_0_420,negated_conjecture,
    ( esk9_0 = true
    | esk9_0 = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_413]) ).

cnf(c_0_421,plain,
    esk2_2(true,false) = false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_414,c_0_304]),c_0_305]),c_0_56]),c_0_392])]) ).

cnf(c_0_422,negated_conjecture,
    ( bool(esk2_2(true,esk9_0))
    | lazy_impl(true,esk9_0) != true ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_415,c_0_299]),c_0_299]),c_0_300]) ).

cnf(c_0_423,plain,
    ( impl(true,esk2_2(true,true)) = false
    | impl(true,true) = true
    | ~ forallprefers(impl(true,true),true) ),
    inference(spm,[status(thm)],[c_0_416,c_0_410]) ).

cnf(c_0_424,plain,
    ( ~ forallprefers(impl(true,true),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
    | ~ d(impl(true,true)) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_417,c_0_161]),c_0_282]) ).

cnf(c_0_425,negated_conjecture,
    ( prop(esk2_2(true,esk9_0)) = true
    | lazy_impl(true,esk9_0) = err
    | esk9_0 != true ),
    inference(spm,[status(thm)],[c_0_418,c_0_54]) ).

cnf(c_0_426,negated_conjecture,
    esk9_0 = true,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_419,c_0_420]),c_0_421]),c_0_167]),c_0_421]),c_0_401]),c_0_421]),c_0_252]),c_0_235]),c_0_235]),c_0_421]),c_0_167]),c_0_421]),c_0_401]),c_0_421]),c_0_252]),c_0_235]),c_0_58]),c_0_421]),c_0_401]),c_0_145])]) ).

cnf(c_0_427,negated_conjecture,
    ( bool(esk2_2(true,esk9_0))
    | esk9_0 != true
    | ~ d(esk9_0) ),
    inference(spm,[status(thm)],[c_0_422,c_0_49]) ).

cnf(c_0_428,plain,
    ( impl(true,esk2_2(true,true)) = false
    | impl(true,true) = true ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_423,c_0_294]),c_0_56]),c_0_145])]),c_0_282]) ).

cnf(c_0_429,plain,
    ~ forallprefers(impl(true,true),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_263]),c_0_145])]) ).

cnf(c_0_430,negated_conjecture,
    prop(esk2_2(true,true)) = true,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_425,c_0_426]),c_0_426]),c_0_305]),c_0_426])]),c_0_120]) ).

cnf(c_0_431,negated_conjecture,
    bool(esk2_2(true,true)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_427,c_0_407])]),c_0_426]),c_0_426])]) ).

cnf(c_0_432,plain,
    ( impl(true,true) = true
    | ~ forallprefers(impl(true,true),lazy_impl(true,impl(false,esk2_2(true,true)))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_409,c_0_428]),c_0_235]) ).

cnf(c_0_433,plain,
    ( bool(esk2_2(true,true))
    | ~ forallprefers(impl(true,true),true) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_429,c_0_32]),c_0_33]) ).

cnf(c_0_434,negated_conjecture,
    lazy_impl(true,lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) != true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_319,c_0_426]),c_0_426]),c_0_426]),c_0_426]),c_0_426]),c_0_305]),c_0_430]) ).

cnf(c_0_435,negated_conjecture,
    ( esk2_2(true,true) = true
    | esk2_2(true,true) = false ),
    inference(spm,[status(thm)],[c_0_72,c_0_431]) ).

cnf(c_0_436,plain,
    ( impl(true,true) = true
    | ~ forallprefers(impl(true,true),true) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_432,c_0_244]),c_0_305]),c_0_433]) ).

cnf(c_0_437,negated_conjecture,
    esk2_2(true,true) = true,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_434,c_0_435]),c_0_252]),c_0_235]),c_0_401]),c_0_305]),c_0_305])]) ).

cnf(c_0_438,plain,
    impl(true,true) = true,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_436,c_0_294]),c_0_56]),c_0_145])]),c_0_282]) ).

cnf(c_0_439,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_434,c_0_437]),c_0_438]),c_0_305]),c_0_438]),c_0_305]),c_0_305])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SWW097+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n023.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 2400
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon Oct  2 22:30:52 EDT 2023
% 0.09/0.29  % CPUTime    : 
% 0.13/0.39  Running first-order theorem proving
% 0.13/0.39  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ALG24d0zEh/E---3.1_8761.p
% 39.34/5.37  # Version: 3.1pre001
% 39.34/5.37  # Preprocessing class: FSMSSMSSSSSNFFN.
% 39.34/5.37  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.34/5.37  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 39.34/5.37  # Starting new_bool_3 with 300s (1) cores
% 39.34/5.37  # Starting new_bool_1 with 300s (1) cores
% 39.34/5.37  # Starting sh5l with 300s (1) cores
% 39.34/5.37  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8839 completed with status 0
% 39.34/5.37  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 39.34/5.37  # Preprocessing class: FSMSSMSSSSSNFFN.
% 39.34/5.37  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.34/5.37  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 39.34/5.37  # No SInE strategy applied
% 39.34/5.37  # Search class: FGHSS-FFMM21-DFFFFFNN
% 39.34/5.37  # partial match(1): FGHSS-FFMM21-SFFFFFNN
% 39.34/5.37  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 39.34/5.37  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 811s (1) cores
% 39.34/5.37  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 39.34/5.37  # Starting new_bool_3 with 136s (1) cores
% 39.34/5.37  # Starting new_bool_1 with 136s (1) cores
% 39.34/5.37  # Starting sh5l with 136s (1) cores
% 39.34/5.37  # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 8846 completed with status 0
% 39.34/5.37  # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 39.34/5.37  # Preprocessing class: FSMSSMSSSSSNFFN.
% 39.34/5.37  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.34/5.37  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 39.34/5.37  # No SInE strategy applied
% 39.34/5.37  # Search class: FGHSS-FFMM21-DFFFFFNN
% 39.34/5.37  # partial match(1): FGHSS-FFMM21-SFFFFFNN
% 39.34/5.37  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 39.34/5.37  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 811s (1) cores
% 39.34/5.37  # Preprocessing time       : 0.002 s
% 39.34/5.37  # Presaturation interreduction done
% 39.34/5.37  
% 39.34/5.37  # Proof found!
% 39.34/5.37  # SZS status Theorem
% 39.34/5.37  # SZS output start CNFRefutation
% See solution above
% 39.34/5.37  # Parsed axioms                        : 45
% 39.34/5.37  # Removed by relevancy pruning/SinE    : 0
% 39.34/5.37  # Initial clauses                      : 99
% 39.34/5.37  # Removed in clause preprocessing      : 19
% 39.34/5.37  # Initial clauses in saturation        : 80
% 39.34/5.37  # Processed clauses                    : 21653
% 39.34/5.37  # ...of these trivial                  : 1154
% 39.34/5.37  # ...subsumed                          : 15109
% 39.34/5.37  # ...remaining for further processing  : 5390
% 39.34/5.37  # Other redundant clauses eliminated   : 14
% 39.34/5.37  # Clauses deleted for lack of memory   : 0
% 39.34/5.37  # Backward-subsumed                    : 929
% 39.34/5.37  # Backward-rewritten                   : 2167
% 39.34/5.37  # Generated clauses                    : 258463
% 39.34/5.37  # ...of the previous two non-redundant : 138357
% 39.34/5.37  # ...aggressively subsumed             : 0
% 39.34/5.37  # Contextual simplify-reflections      : 371
% 39.34/5.37  # Paramodulations                      : 258282
% 39.34/5.37  # Factorizations                       : 168
% 39.34/5.37  # NegExts                              : 0
% 39.34/5.37  # Equation resolutions                 : 14
% 39.34/5.37  # Total rewrite steps                  : 378220
% 39.34/5.37  # Propositional unsat checks           : 0
% 39.34/5.37  #    Propositional check models        : 0
% 39.34/5.37  #    Propositional check unsatisfiable : 0
% 39.34/5.37  #    Propositional clauses             : 0
% 39.34/5.37  #    Propositional clauses after purity: 0
% 39.34/5.37  #    Propositional unsat core size     : 0
% 39.34/5.37  #    Propositional preprocessing time  : 0.000
% 39.34/5.37  #    Propositional encoding time       : 0.000
% 39.34/5.37  #    Propositional solver time         : 0.000
% 39.34/5.37  #    Success case prop preproc time    : 0.000
% 39.34/5.37  #    Success case prop encoding time   : 0.000
% 39.34/5.37  #    Success case prop solver time     : 0.000
% 39.34/5.37  # Current number of processed clauses  : 2225
% 39.34/5.37  #    Positive orientable unit clauses  : 155
% 39.34/5.37  #    Positive unorientable unit clauses: 0
% 39.34/5.37  #    Negative unit clauses             : 204
% 39.34/5.37  #    Non-unit-clauses                  : 1866
% 39.34/5.37  # Current number of unprocessed clauses: 102481
% 39.34/5.37  # ...number of literals in the above   : 450413
% 39.34/5.37  # Current number of archived formulas  : 0
% 39.34/5.37  # Current number of archived clauses   : 3175
% 39.34/5.37  # Clause-clause subsumption calls (NU) : 936460
% 39.34/5.37  # Rec. Clause-clause subsumption calls : 594056
% 39.34/5.37  # Non-unit clause-clause subsumptions  : 11870
% 39.34/5.37  # Unit Clause-clause subsumption calls : 62750
% 39.34/5.37  # Rewrite failures with RHS unbound    : 0
% 39.34/5.37  # BW rewrite match attempts            : 2177
% 39.34/5.37  # BW rewrite match successes           : 95
% 39.34/5.37  # Condensation attempts                : 0
% 39.34/5.37  # Condensation successes               : 0
% 39.34/5.37  # Termbank termtop insertions          : 6098047
% 39.34/5.37  
% 39.34/5.37  # -------------------------------------------------
% 39.34/5.37  # User time                : 4.830 s
% 39.34/5.37  # System time              : 0.078 s
% 39.34/5.37  # Total time               : 4.908 s
% 39.34/5.37  # Maximum resident set size: 2040 pages
% 39.34/5.37  
% 39.34/5.37  # -------------------------------------------------
% 39.34/5.37  # User time                : 24.366 s
% 39.34/5.37  # System time              : 0.181 s
% 39.34/5.37  # Total time               : 24.547 s
% 39.34/5.37  # Maximum resident set size: 1720 pages
% 39.34/5.37  % E---3.1 exiting
% 39.34/5.37  % E---3.1 exiting
%------------------------------------------------------------------------------