TSTP Solution File: SWW102+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:16:19 EDT 2023

% Result   : Theorem 0.22s 0.67s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  150 (  36 unt;  39 typ;   0 def)
%            Number of atoms       :  315 ( 136 equ)
%            Maximal formula atoms :   75 (   2 avg)
%            Number of connectives :  332 ( 128   ~; 147   |;  45   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   57 (  32   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   7 con; 0-3 aty)
%            Number of variables   :   81 (   4 sgn;  40   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    bool: $i > $o ).

tff(decl_23,type,
    false: $i ).

tff(decl_24,type,
    true: $i ).

tff(decl_25,type,
    err: $i ).

tff(decl_26,type,
    d: $i > $o ).

tff(decl_27,type,
    forallprefers: ( $i * $i ) > $o ).

tff(decl_28,type,
    existsprefers: ( $i * $i ) > $o ).

tff(decl_29,type,
    phi: $i > $i ).

tff(decl_30,type,
    prop: $i > $i ).

tff(decl_31,type,
    impl: ( $i * $i ) > $i ).

tff(decl_32,type,
    lazy_impl: ( $i * $i ) > $i ).

tff(decl_33,type,
    and1: ( $i * $i ) > $i ).

tff(decl_34,type,
    f1: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    and2: ( $i * $i ) > $i ).

tff(decl_36,type,
    lazy_and1: ( $i * $i ) > $i ).

tff(decl_37,type,
    f2: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    lazy_and2: ( $i * $i ) > $i ).

tff(decl_39,type,
    or1: ( $i * $i ) > $i ).

tff(decl_40,type,
    f3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    or2: ( $i * $i ) > $i ).

tff(decl_42,type,
    exists1: $i > $i ).

tff(decl_43,type,
    apply: ( $i * $i ) > $i ).

tff(decl_44,type,
    f4: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    f5: ( $i * $i ) > $i ).

tff(decl_46,type,
    f6: ( $i * $i ) > $i ).

tff(decl_47,type,
    exists2: $i > $i ).

tff(decl_48,type,
    false1: $i ).

tff(decl_49,type,
    f7: $i > $i ).

tff(decl_50,type,
    false2: $i ).

tff(decl_51,type,
    not1: $i > $i ).

tff(decl_52,type,
    not2: $i > $i ).

tff(decl_53,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk4_1: $i > $i ).

tff(decl_57,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk6_1: $i > $i ).

tff(decl_59,type,
    esk7_0: $i ).

tff(decl_60,type,
    esk8_0: $i ).

fof(not1_not2,conjecture,
    ! [X5] : not1(X5) = not2(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not1_not2) ).

fof(not1_axiom1,axiom,
    ! [X3] :
      ( ~ bool(X3)
     => not1(X3) = phi(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',not1_axiom1) ).

fof(def_false2,axiom,
    ? [X5] :
      ( false2 = phi(f7(X5))
      & ~ ? [X10] : forallprefers(f7(X10),f7(X5)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_false2) ).

fof(def_f7,axiom,
    ! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_f7) ).

fof(def_phi,axiom,
    ! [X1] :
      ( ( d(X1)
        & phi(X1) = X1 )
      | ( ~ d(X1)
        & phi(X1) = err ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_phi) ).

fof(def_not2,axiom,
    ! [X5] : not2(X5) = impl(X5,false2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_not2) ).

fof(lazy_impl_axiom3,axiom,
    ! [X4] : lazy_impl(true,X4) = phi(X4),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).

fof(impl_axiom1,axiom,
    ! [X3,X4] :
      ( ~ bool(X3)
     => impl(X3,X4) = phi(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',impl_axiom1) ).

fof(prop_true,axiom,
    ! [X1] :
      ( prop(X1) = true
    <=> bool(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',prop_true) ).

fof(prop_false,axiom,
    ! [X1] :
      ( prop(X1) = false
    <=> ~ bool(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',prop_false) ).

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/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).

fof(lazy_impl_axiom2,axiom,
    ! [X4] : lazy_impl(false,X4) = true,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).

fof(def_bool,axiom,
    ! [X1] :
      ( bool(X1)
    <=> ( X1 = false
        | X1 = true ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',def_bool) ).

fof(false_true_err_in_d,axiom,
    ( d(true)
    & d(false)
    & d(err) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).

fof(not1_axiom2,axiom,
    not1(false) = true,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',not1_axiom2) ).

fof(impl_axiom3,axiom,
    ! [X4] :
      ( bool(X4)
     => impl(false,X4) = true ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).

fof(not1_axiom3,axiom,
    not1(true) = false,
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',not1_axiom3) ).

fof(impl_axiom4,axiom,
    ! [X4] :
      ( bool(X4)
     => impl(true,X4) = X4 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',impl_axiom4) ).

fof(distinct_false_true_err,axiom,
    ( true != false
    & true != err
    & false != err ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).

fof(c_0_19,negated_conjecture,
    ~ ! [X5] : not1(X5) = not2(X5),
    inference(assume_negation,[status(cth)],[not1_not2]) ).

fof(c_0_20,plain,
    ! [X3] :
      ( ~ bool(X3)
     => not1(X3) = phi(X3) ),
    inference(fof_simplification,[status(thm)],[not1_axiom1]) ).

fof(c_0_21,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_22,plain,
    ! [X81] : f7(X81) = lazy_impl(prop(X81),X81),
    inference(variable_rename,[status(thm)],[def_f7]) ).

fof(c_0_23,plain,
    ! [X1] :
      ( ( d(X1)
        & phi(X1) = X1 )
      | ( ~ d(X1)
        & phi(X1) = err ) ),
    inference(fof_simplification,[status(thm)],[def_phi]) ).

fof(c_0_24,negated_conjecture,
    not1(esk8_0) != not2(esk8_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).

fof(c_0_25,plain,
    ! [X85] : not2(X85) = impl(X85,false2),
    inference(variable_rename,[status(thm)],[def_not2]) ).

fof(c_0_26,plain,
    ! [X84] :
      ( bool(X84)
      | not1(X84) = phi(X84) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).

fof(c_0_27,plain,
    ! [X28] : lazy_impl(true,X28) = phi(X28),
    inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).

fof(c_0_28,plain,
    ! [X3,X4] :
      ( ~ bool(X3)
     => impl(X3,X4) = phi(X3) ),
    inference(fof_simplification,[status(thm)],[impl_axiom1]) ).

cnf(c_0_29,plain,
    ~ forallprefers(f7(X1),f7(esk7_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    f7(X1) = lazy_impl(prop(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_31,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_32,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_23])]) ).

cnf(c_0_33,negated_conjecture,
    not1(esk8_0) != not2(esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    not2(X1) = impl(X1,false2),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,plain,
    ( bool(X1)
    | not1(X1) = phi(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,plain,
    lazy_impl(true,X1) = phi(X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_37,plain,
    ! [X19,X20] :
      ( bool(X19)
      | impl(X19,X20) = phi(X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).

cnf(c_0_38,plain,
    ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).

cnf(c_0_39,plain,
    ( prop(X1) = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    ( phi(X1) = X1
    | ~ d(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_41,plain,
    ! [X1] :
      ( prop(X1) = false
    <=> ~ bool(X1) ),
    inference(fof_simplification,[status(thm)],[prop_false]) ).

fof(c_0_42,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]) ).

cnf(c_0_43,negated_conjecture,
    impl(esk8_0,false2) != not1(esk8_0),
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_44,plain,
    ( not1(X1) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_45,plain,
    ( bool(X1)
    | impl(X1,X2) = phi(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,plain,
    false2 = phi(f7(esk7_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_47,plain,
    ( phi(X1) = err
    | phi(X1) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_48,plain,
    ( ~ forallprefers(lazy_impl(true,X1),lazy_impl(prop(esk7_0),esk7_0))
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_49,plain,
    ( lazy_impl(true,X1) = X1
    | ~ d(X1) ),
    inference(rw,[status(thm)],[c_0_40,c_0_36]) ).

fof(c_0_50,plain,
    ! [X18] :
      ( ( prop(X18) != false
        | ~ bool(X18) )
      & ( bool(X18)
        | prop(X18) = false ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).

fof(c_0_51,plain,
    ! [X27] : lazy_impl(false,X27) = true,
    inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).

fof(c_0_52,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_42])])]) ).

fof(c_0_53,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])])]) ).

cnf(c_0_54,negated_conjecture,
    ( bool(esk8_0)
    | impl(esk8_0,false2) != lazy_impl(true,esk8_0) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_55,plain,
    ( impl(X1,X2) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[c_0_45,c_0_36]) ).

cnf(c_0_56,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_36]),c_0_30]) ).

cnf(c_0_57,plain,
    ( lazy_impl(true,X1) = X1
    | lazy_impl(true,X1) = err ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_36]),c_0_36]) ).

cnf(c_0_58,plain,
    ( ~ forallprefers(X1,lazy_impl(prop(esk7_0),esk7_0))
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,plain,
    ( bool(X1)
    | prop(X1) = false ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    lazy_impl(false,X1) = true,
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_61,plain,
    ( forallprefers(X1,X2)
    | X1 != false
    | X2 != true ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_62,plain,
    ( bool(X1)
    | X1 != false ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_63,plain,
    ( X1 = false
    | X1 = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_64,negated_conjecture,
    bool(esk8_0),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_65,plain,
    ( lazy_impl(prop(esk7_0),esk7_0) = false2
    | false2 = err ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_56]) ).

cnf(c_0_66,plain,
    ( bool(esk7_0)
    | ~ forallprefers(X1,true)
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).

cnf(c_0_67,plain,
    forallprefers(false,true),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_61])]) ).

cnf(c_0_68,plain,
    d(false),
    inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).

cnf(c_0_69,plain,
    bool(false),
    inference(er,[status(thm)],[c_0_62]) ).

cnf(c_0_70,negated_conjecture,
    ( esk8_0 = true
    | esk8_0 = false ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_71,plain,
    not1(false) = true,
    inference(split_conjunct,[status(thm)],[not1_axiom2]) ).

fof(c_0_72,plain,
    ! [X23] :
      ( ~ bool(X23)
      | impl(false,X23) = true ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom3])]) ).

cnf(c_0_73,plain,
    ( lazy_impl(true,esk7_0) = false2
    | false2 = err
    | ~ bool(esk7_0) ),
    inference(spm,[status(thm)],[c_0_65,c_0_39]) ).

cnf(c_0_74,plain,
    bool(esk7_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).

cnf(c_0_75,negated_conjecture,
    ( esk8_0 = true
    | impl(false,false2) != true ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_70]),c_0_71]) ).

cnf(c_0_76,plain,
    ( impl(false,X1) = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_77,plain,
    ( lazy_impl(true,esk7_0) = false2
    | false2 = err ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).

cnf(c_0_78,negated_conjecture,
    ( esk8_0 = true
    | ~ bool(false2) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_79,plain,
    ( false2 = esk7_0
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_57,c_0_77]) ).

cnf(c_0_80,plain,
    ( ~ forallprefers(lazy_impl(true,X1),lazy_impl(true,esk7_0))
    | ~ bool(esk7_0)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_39]) ).

cnf(c_0_81,plain,
    ( lazy_impl(true,lazy_impl(true,esk7_0)) = false2
    | ~ bool(esk7_0) ),
    inference(spm,[status(thm)],[c_0_56,c_0_39]) ).

cnf(c_0_82,negated_conjecture,
    ( false2 = err
    | esk8_0 = true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_74])]) ).

cnf(c_0_83,plain,
    not1(true) = false,
    inference(split_conjunct,[status(thm)],[not1_axiom3]) ).

fof(c_0_84,plain,
    ! [X24] :
      ( ~ bool(X24)
      | impl(true,X24) = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom4])]) ).

cnf(c_0_85,plain,
    ( ~ forallprefers(lazy_impl(true,X1),lazy_impl(true,esk7_0))
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_74])]) ).

cnf(c_0_86,plain,
    lazy_impl(true,lazy_impl(true,esk7_0)) = false2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_74])]) ).

cnf(c_0_87,negated_conjecture,
    ( false2 = err
    | impl(true,false2) != false ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_82]),c_0_83]) ).

cnf(c_0_88,plain,
    ( impl(true,X1) = X1
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_89,plain,
    ( ~ forallprefers(false2,lazy_impl(true,esk7_0))
    | ~ bool(lazy_impl(true,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_90,negated_conjecture,
    ( false2 = err
    | false2 != false
    | ~ bool(false2) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_91,plain,
    ( false2 = err
    | esk7_0 != err ),
    inference(ef,[status(thm)],[c_0_79]) ).

cnf(c_0_92,plain,
    ( ~ forallprefers(false2,esk7_0)
    | ~ d(esk7_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_49]),c_0_74])]) ).

cnf(c_0_93,plain,
    ( esk7_0 = true
    | esk7_0 = false ),
    inference(spm,[status(thm)],[c_0_63,c_0_74]) ).

cnf(c_0_94,negated_conjecture,
    ( false2 = err
    | esk7_0 != false ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_79]),c_0_74])]),c_0_91]) ).

cnf(c_0_95,plain,
    ( esk7_0 = true
    | ~ forallprefers(false2,false) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_68])]) ).

cnf(c_0_96,negated_conjecture,
    ( esk7_0 = true
    | false2 = err ),
    inference(spm,[status(thm)],[c_0_94,c_0_93]) ).

cnf(c_0_97,plain,
    ( bool(X1)
    | forallprefers(X1,X2)
    | ~ d(X1)
    | ~ d(X2)
    | ~ bool(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_98,plain,
    ( d(X1)
    | forallprefers(X1,X2)
    | ~ d(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_99,plain,
    ( ~ forallprefers(X1,lazy_impl(true,esk7_0))
    | ~ d(X1)
    | ~ bool(esk7_0)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_39]) ).

cnf(c_0_100,negated_conjecture,
    ( esk7_0 = true
    | ~ forallprefers(err,false) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_101,plain,
    ( forallprefers(X1,X2)
    | bool(X1)
    | ~ d(X2)
    | ~ bool(X2) ),
    inference(csr,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_102,plain,
    ( ~ forallprefers(X1,lazy_impl(true,esk7_0))
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_74])]) ).

cnf(c_0_103,negated_conjecture,
    ( esk7_0 = true
    | bool(err) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_68]),c_0_69])]) ).

cnf(c_0_104,plain,
    false != err,
    inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).

cnf(c_0_105,plain,
    true != err,
    inference(split_conjunct,[status(thm)],[distinct_false_true_err]) ).

cnf(c_0_106,plain,
    ( ~ forallprefers(X1,esk7_0)
    | ~ d(esk7_0)
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[c_0_102,c_0_49]) ).

cnf(c_0_107,negated_conjecture,
    esk7_0 = true,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_103]),c_0_104]),c_0_105]) ).

cnf(c_0_108,plain,
    d(true),
    inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).

cnf(c_0_109,plain,
    ( ~ forallprefers(X1,true)
    | ~ d(X1)
    | ~ bool(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107]),c_0_107]),c_0_108])]) ).

cnf(c_0_110,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_67]),c_0_68]),c_0_69])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 20:44:56 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.63  start to proof: theBenchmark
% 0.22/0.67  % Version  : CSE_E---1.5
% 0.22/0.67  % Problem  : theBenchmark.p
% 0.22/0.67  % Proof found
% 0.22/0.67  % SZS status Theorem for theBenchmark.p
% 0.22/0.67  % SZS output start Proof
% See solution above
% 0.22/0.68  % Total time : 0.027000 s
% 0.22/0.68  % SZS output end Proof
% 0.22/0.68  % Total time : 0.031000 s
%------------------------------------------------------------------------------