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E-SAT---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : CSR133^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 07:46:46 AM UTC 2026

% Result   : Theorem 0.08s 0.16s
% Output   : CNFRefutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   46 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :  147 (  18 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  439 (  62   ~;  60   |;  26   &; 289   @)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   41 (   0   ^;  32   !;   9   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_29,type,
    holdsDuring_THFTYPE_IiooI: $i > $o > $o ).

thf(decl_34,type,
    lAnna_THFTYPE_i: $i ).

thf(decl_37,type,
    lBen_THFTYPE_i: $i ).

thf(decl_38,type,
    lBill_THFTYPE_i: $i ).

thf(decl_40,type,
    lBob_THFTYPE_i: $i ).

thf(decl_47,type,
    lSue_THFTYPE_i: $i ).

thf(decl_54,type,
    lYearFn_THFTYPE_IiiI: $i > $i ).

thf(decl_55,type,
    likes_THFTYPE_IiioI: $i > $i > $o ).

thf(decl_59,type,
    n2009_THFTYPE_i: $i ).

thf(decl_61,type,
    parent_THFTYPE_IiioI: $i > $i > $o ).

thf(con,conjecture,
    ? [X36: $i > $i > $o,X37: $i > $i > $o,X2: $i] :
      ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
      @ ( ( X37 @ X2 @ lBill_THFTYPE_i )
        & ( X36 @ X2 @ lAnna_THFTYPE_i )
        & ( X37 != X36 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',con) ).

thf(ax_014,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',ax_014) ).

thf(ax_009,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',ax_009) ).

thf(ax_003,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',ax_003) ).

thf(ax_034,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',ax_034) ).

thf(ax_026,axiom,
    ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
    @ ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) ),
    file('/export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p',ax_026) ).

thf(c_0_6,negated_conjecture,
    ~ ? [X36: $i > $i > $o,X37: $i > $i > $o,X2: $i] :
        ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
        @ ( ( X37 @ X2 @ lBill_THFTYPE_i )
          & ( X36 @ X2 @ lAnna_THFTYPE_i )
          & ( X37 != X36 ) ) ),
    inference(assume_negation,[status(cth)],[con]) ).

thf(c_0_7,negated_conjecture,
    ~ ? [X36: $i > $i > $o,X37: $i > $i > $o,X2: $i] :
        ( ( ~ ( ( X37 @ X2 @ lBill_THFTYPE_i )
              & ( X36 @ X2 @ lAnna_THFTYPE_i )
              & ( X37 != X36 ) )
          | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
        & ( ( ( X37 @ X2 @ lBill_THFTYPE_i )
            & ( X36 @ X2 @ lAnna_THFTYPE_i )
            & ( X37 != X36 ) )
          | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_6])]) ).

thf(c_0_8,axiom,
    ( ( ~ ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax_014]) ).

thf(c_0_9,negated_conjecture,
    ! [X43: $i > $i > $o,X44: $i > $i > $o,X45: $i] :
      ( ( ~ ( X44 @ X45 @ lBill_THFTYPE_i )
        | ~ ( X43 @ X45 @ lAnna_THFTYPE_i )
        | ( X44 = X43 )
        | ( X44 @ X45 @ lBill_THFTYPE_i ) )
      & ( ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false )
        | ( X44 @ X45 @ lBill_THFTYPE_i ) )
      & ( ~ ( X44 @ X45 @ lBill_THFTYPE_i )
        | ~ ( X43 @ X45 @ lAnna_THFTYPE_i )
        | ( X44 = X43 )
        | ( X43 @ X45 @ lAnna_THFTYPE_i ) )
      & ( ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false )
        | ( X43 @ X45 @ lAnna_THFTYPE_i ) )
      & ( ~ ( X44 @ X45 @ lBill_THFTYPE_i )
        | ~ ( X43 @ X45 @ lAnna_THFTYPE_i )
        | ( X44 = X43 )
        | ( X44 != X43 ) )
      & ( ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false )
        | ( X44 != X43 ) )
      & ( ~ ( X44 @ X45 @ lBill_THFTYPE_i )
        | ~ ( X43 @ X45 @ lAnna_THFTYPE_i )
        | ( X44 = X43 )
        | ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
      & ( ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false )
        | ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

thf(c_0_10,plain,
    ( ( ~ ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X36: $i > $i > $o,X37: $i > $i > $o] :
      ( ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true )
      | ( X36 != X37 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_12,plain,
    ( ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
    | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true ),
    inference(er,[status(thm)],[c_0_11]) ).

thf(c_0_14,axiom,
    ( ( ~ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax_009]) ).

thf(c_0_15,plain,
    ( ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true )
    | ~ ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_16,plain,
    likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
    inference(sr,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_17,plain,
    ( ( ~ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_14]) ).

thf(c_0_18,axiom,
    ( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax_003]) ).

thf(c_0_19,negated_conjecture,
    ! [X37: $i > $i > $o,X36: $i > $i > $o,X1: $i] :
      ( ( X36 = X37 )
      | ~ ( X36 @ X1 @ lBill_THFTYPE_i )
      | ~ ( X37 @ X1 @ lAnna_THFTYPE_i )
      | ~ ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_20,plain,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

thf(c_0_21,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
    | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_22,plain,
    ( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_18]) ).

thf(c_0_23,negated_conjecture,
    ! [X37: $i > $i > $o,X36: $i > $i > $o,X1: $i] :
      ( ( X36 = X37 )
      | ~ ( X37 @ X1 @ lAnna_THFTYPE_i )
      | ~ ( X36 @ X1 @ lBill_THFTYPE_i ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).

thf(c_0_24,plain,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
    inference(sr,[status(thm)],[c_0_21,c_0_13]) ).

thf(c_0_25,plain,
    ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
    | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_26,negated_conjecture,
    ! [X49: $i,X37: $i > $i > $o,X36: $i > $i > $o,X48: $i,X1: $i] :
      ( ( ( X36 @ X48 @ X49 )
      <=> ( X37 @ X48 @ X49 ) )
      | ~ ( X37 @ X1 @ lAnna_THFTYPE_i )
      | ~ ( X36 @ X1 @ lBill_THFTYPE_i ) ),
    inference(arg_cong,[status(thm)],[c_0_23]) ).

thf(c_0_27,axiom,
    ( ( ~ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax_034]) ).

thf(c_0_28,negated_conjecture,
    ! [X36: $i > $i > $o] :
      ( ( X36 = parent_THFTYPE_IiioI )
      | ~ ( X36 @ lSue_THFTYPE_i @ lBill_THFTYPE_i ) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_29,plain,
    likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
    inference(sr,[status(thm)],[c_0_25,c_0_13]) ).

thf(c_0_30,plain,
    ( ( ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[ax_026])]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i,X3: $i,X37: $i > $i > $o,X36: $i > $i > $o,X2: $i] :
      ( ( X36 @ X1 @ X2 )
      | ~ ( X37 @ X3 @ lAnna_THFTYPE_i )
      | ~ ( X36 @ X3 @ lBill_THFTYPE_i )
      | ~ ( X37 @ X1 @ X2 ) ),
    inference(dynamic_cnf,[status(thm)],[c_0_26]) ).

thf(c_0_32,plain,
    ( ( ~ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_27]) ).

thf(c_0_33,negated_conjecture,
    likes_THFTYPE_IiioI = parent_THFTYPE_IiioI,
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_34,plain,
    ( ( ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $true ) )
    & ( ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i )
      | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_30]) ).

thf(c_0_35,negated_conjecture,
    ! [X36: $i > $i > $o,X3: $i,X2: $i,X1: $i] :
      ( ( lBill_THFTYPE_i = X1 )
      | ~ ( X36 @ X2 @ lAnna_THFTYPE_i )
      | ~ ( X36 @ X3 @ X1 ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_31]) ).

thf(c_0_36,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
    | ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_37,negated_conjecture,
    ! [X52: $i,X53: $i] :
      ( ( likes_THFTYPE_IiioI @ X52 @ X53 )
    <=> ( parent_THFTYPE_IiioI @ X52 @ X53 ) ),
    inference(arg_cong,[status(thm)],[c_0_33]) ).

thf(c_0_38,plain,
    ( ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ~ $true )
    | ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_39,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( lBill_THFTYPE_i = X1 )
      | ~ ( parent_THFTYPE_IiioI @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_24]) ).

thf(c_0_40,plain,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i,
    inference(sr,[status(thm)],[c_0_36,c_0_13]) ).

thf(c_0_41,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( parent_THFTYPE_IiioI @ X1 @ X2 )
      | ~ ( likes_THFTYPE_IiioI @ X1 @ X2 ) ),
    inference(dynamic_cnf,[status(thm)],[c_0_37]) ).

thf(c_0_42,plain,
    ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ),
    inference(sr,[status(thm)],[c_0_38,c_0_13]) ).

thf(c_0_43,negated_conjecture,
    lBen_THFTYPE_i = lBill_THFTYPE_i,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_44,negated_conjecture,
    parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
    inference(spm,[status(thm)],[c_0_41,c_0_16]) ).

thf(c_0_45,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : CSR133^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10  % Computer : n012.cluster.edu
% 0.00/0.10  % Model    : x86_64 x86_64
% 0.00/0.10  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10  % Memory   : 8046.5625MB
% 0.00/0.10  % OS       : Linux 6.8.0-71-generic
% 0.00/0.10  % CPULimit : 300
% 0.00/0.10  % WCLimit  : 300
% 0.00/0.10  % DateTime : Tue Sep 29 17:55:33 UTC 2026
% 0.00/0.10  % CPUTime  : 
% 0.00/0.10  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13  Running higher-order theorem proving
% 0.08/0.14  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.fQ15MD6AqM/E---3.1_461547.p
% 0.08/0.16  % Version: 3.5.1-ho
% 0.08/0.16  % Preprocessing class: HSLSSMSMSSSNSSA.
% 0.08/0.16  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16  % Starting new_ho_10_unif with 1500s (5) cores
% 0.08/0.16  % Starting sh3l with 300s (1) cores
% 0.08/0.16  % Starting new_ho_6 with 300s (1) cores
% 0.08/0.16  % Starting lpo6_lambda_fix with 300s (1) cores
% 0.08/0.16  % sh3l with pid 461561 completed with status 0
% 0.08/0.16  % Result found by sh3l
% 0.08/0.16  % Preprocessing class: HSLSSMSMSSSNSSA.
% 0.08/0.16  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16  % Starting new_ho_10_unif with 1500s (5) cores
% 0.08/0.16  % Starting sh3l with 300s (1) cores
% 0.08/0.16  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.08/0.16  % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.08/0.16  % Search class: HGHSF-FFMM11-SSSFFFBN
% 0.08/0.16  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16  % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.16  % SubtermCWHack with pid 461564 completed with status 10
% 0.08/0.16  % Starting sh3l with 31s (1) cores
% 0.08/0.16  % sh3l with pid 461572 completed with status 0
% 0.08/0.16  % Result found by sh3l
% 0.08/0.16  % Preprocessing class: HSLSSMSMSSSNSSA.
% 0.08/0.16  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16  % Starting new_ho_10_unif with 1500s (5) cores
% 0.08/0.16  % Starting sh3l with 300s (1) cores
% 0.08/0.16  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.08/0.16  % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.08/0.16  % Search class: HGHSF-FFMM11-SSSFFFBN
% 0.08/0.16  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16  % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.16  % SubtermCWHack with pid 461564 completed with status 10
% 0.08/0.16  % Starting sh3l with 31s (1) cores
% 0.08/0.16  % Preprocessing time       : 0.001 s
% 0.08/0.16  % Presaturation interreduction done
% 0.08/0.16  
% 0.08/0.16  % Proof found!
% 0.08/0.16  % SZS status Theorem
% 0.08/0.16  % SZS output start CNFRefutation
% See solution above
% 0.08/0.16  % Parsed axioms                        : 128
% 0.08/0.16  % Removed by relevancy pruning/SinE    : 106
% 0.08/0.16  % Initial clauses                      : 52
% 0.08/0.16  % Removed in clause preprocessing      : 4
% 0.08/0.16  % Initial clauses in saturation        : 48
% 0.08/0.16  % Processed clauses                    : 130
% 0.08/0.16  % ...of these trivial                  : 16
% 0.08/0.16  % ...subsumed                          : 33
% 0.08/0.16  % ...remaining for further processing  : 81
% 0.08/0.16  % Other redundant clauses eliminated   : 1
% 0.08/0.16  % Clauses deleted for lack of memory   : 0
% 0.08/0.16  % Backward-subsumed                    : 0
% 0.08/0.16  % Backward-rewritten                   : 17
% 0.08/0.16  % Generated clauses                    : 133
% 0.08/0.16  % ...of the previous two non-redundant : 90
% 0.08/0.16  % ...aggressively subsumed             : 0
% 0.08/0.16  % Contextual simplify-reflections      : 0
% 0.08/0.16  % Paramodulations                      : 97
% 0.08/0.16  % Factorizations                       : 0
% 0.08/0.16  % NegExts                              : 0
% 0.08/0.16  % Equation resolutions                 : 1
% 0.08/0.16  % Disequality decompositions           : 0
% 0.08/0.16  % Total rewrite steps                  : 99
% 0.08/0.16  % ...of those cached                   : 81
% 0.08/0.16  % Propositional unsat checks           : 0
% 0.08/0.16  %    Propositional check models        : 0
% 0.08/0.16  %    Propositional check unsatisfiable : 0
% 0.08/0.16  %    Propositional clauses             : 0
% 0.08/0.16  %    Propositional clauses after purity: 0
% 0.08/0.16  %    Propositional unsat core size     : 0
% 0.08/0.16  %    Propositional preprocessing time  : 0.000
% 0.08/0.16  %    Propositional encoding time       : 0.000
% 0.08/0.16  %    Propositional solver time         : 0.000
% 0.08/0.16  %    Success case prop preproc time    : 0.000
% 0.08/0.16  %    Success case prop encoding time   : 0.000
% 0.08/0.16  %    Success case prop solver time     : 0.000
% 0.08/0.16  % Current number of processed clauses  : 42
% 0.08/0.16  %    Positive orientable unit clauses  : 14
% 0.08/0.16  %    Positive unorientable unit clauses: 0
% 0.08/0.16  %    Negative unit clauses             : 4
% 0.08/0.16  %    Non-unit-clauses                  : 24
% 0.08/0.16  % Current number of unprocessed clauses: 20
% 0.08/0.16  % ...number of literals in the above   : 54
% 0.08/0.16  % Current number of archived formulas  : 0
% 0.08/0.16  % Current number of archived clauses   : 38
% 0.08/0.16  % Clause-clause subsumption calls (NU) : 189
% 0.08/0.16  % Rec. Clause-clause subsumption calls : 176
% 0.08/0.16  % Non-unit clause-clause subsumptions  : 28
% 0.08/0.16  % Unit Clause-clause subsumption calls : 4
% 0.08/0.16  % Rewrite failures with RHS unbound    : 0
% 0.08/0.16  % BW rewrite match attempts            : 4
% 0.08/0.16  % BW rewrite match successes           : 3
% 0.08/0.16  % Condensation attempts                : 0
% 0.08/0.16  % Condensation successes               : 0
% 0.08/0.16  % Termbank termtop insertions          : 7031
% 0.08/0.16  % Search garbage collected termcells   : 511
% 0.08/0.16  
% 0.08/0.16  % -------------------------------------------------
% 0.08/0.16  % User time                : 0.006 s
% 0.08/0.16  % System time              : 0.005 s
% 0.08/0.16  % Total time               : 0.011 s
% 0.08/0.16  % Maximum resident set size: 3740 pages
% 0.08/0.16  
% 0.08/0.16  % -------------------------------------------------
% 0.08/0.16  % User time                : 0.007 s
% 0.08/0.16  % System time              : 0.008 s
% 0.08/0.16  % Total time               : 0.016 s
% 0.08/0.16  % Maximum resident set size: 4864 pages
% 0.08/0.16  % E exiting
%------------------------------------------------------------------------------