TSTP Solution File: NLP266_4 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 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 : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 00:58:22 EDT 2024

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   71 (   9 unt;  19 typ;   0 def)
%            Number of atoms       :  302 (   0 equ)
%            Maximal formula atoms :   57 (   5 avg)
%            Number of connectives :  446 ( 196   ~; 194   |;  34   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   9 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   39 (  13   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :  169 (   0 sgn 158   !;  11   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    '$ki_world': $tType ).

tff(decl_22,type,
    '$ki_local_world': '$ki_world' ).

tff(decl_23,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

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

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

tff(decl_26,type,
    number: ( '$ki_world' * $i * $i ) > $o ).

tff(decl_27,type,
    string: ( '$ki_world' * $i ) > $o ).

tff(decl_28,type,
    in: ( '$ki_world' * $i * $i * $i ) > $o ).

tff(decl_29,type,
    do: ( '$ki_world' * $i * $i * $i ) > $o ).

tff(decl_30,type,
    entry_box: ( '$ki_world' * $i ) > $o ).

tff(decl_31,type,
    userid: ( '$ki_world' * $i * $i ) > $o ).

tff(decl_32,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(decl_33,type,
    esk1_0: '$ki_world' ).

tff(decl_34,type,
    esk2_4: ( $i * $i * $i * $i ) > '$ki_world' ).

tff(decl_35,type,
    esk3_4: ( $i * $i * $i * $i ) > '$ki_world' ).

tff(decl_36,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk5_4: ( '$ki_world' * $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk7_1: '$ki_world' > $i ).

tff(decl_40,type,
    esk8_0: $i ).

tff(verify,conjecture,
    ! [X1: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X1)
     => ? [X5] :
          ( '$ki_exists_in_world_$i'(X1,X5)
          & ? [X7] :
              ( '$ki_exists_in_world_$i'(X1,X7)
              & ? [X9] :
                  ( '$ki_exists_in_world_$i'(X1,X9)
                  & ? [X8] :
                      ( '$ki_exists_in_world_$i'(X1,X8)
                      & ! [X6: '$ki_world'] :
                          ( '$ki_accessible'(X1,X6)
                         => ( userid(X6,u,X5)
                            & entry_box(X6,X7)
                            & number(X6,X7,one) ) )
                      & ! [X6: '$ki_world'] :
                          ( '$ki_accessible'(X1,X6)
                         => ! [X10] :
                              ( '$ki_exists_in_world_$i'(X6,X10)
                             => ( do(X6,X8,X9,X10)
                               => in(X6,X5,X7,X10) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(ax3,axiom,
    ! [X1: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X1)
     => ! [X8] :
          ( '$ki_exists_in_world_$i'(X1,X8)
         => ! [X5] :
              ( '$ki_exists_in_world_$i'(X1,X5)
             => ! [X7] :
                  ( '$ki_exists_in_world_$i'(X1,X7)
                 => ( ( string(X1,X5)
                      & entry_box(X1,X7) )
                   => ? [X9] :
                        ( '$ki_exists_in_world_$i'(X1,X9)
                        & ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X1,X6)
                           => ! [X10] :
                                ( '$ki_exists_in_world_$i'(X6,X10)
                               => ( do(X6,X8,X9,X10)
                                 => in(X6,X5,X7,X10) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff('$ki_exists_in_world_$i_const',axiom,
    ! [X1: '$ki_world',X4] : '$ki_exists_in_world_$i'(X1,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(ax1,axiom,
    ! [X1: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X1)
     => ? [X5] :
          ( '$ki_exists_in_world_$i'(X1,X5)
          & ! [X6: '$ki_world'] :
              ( '$ki_accessible'(X1,X6)
             => ( userid(X6,u,X5)
                & string(X6,X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(ax2,axiom,
    ? [X7] :
      ( '$ki_exists_in_world_$i'('$ki_local_world',X7)
      & ! [X1: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X1)
         => ( entry_box(X1,X7)
            & number(X1,X7,one) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(mrel_transitive,axiom,
    ! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
      ( ( '$ki_accessible'(X1,X2)
        & '$ki_accessible'(X2,X3) )
     => '$ki_accessible'(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).

tff(mrel_reflexive,axiom,
    ! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(c_0_7,negated_conjecture,
    ~ ! [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
       => ? [X5] :
            ( '$ki_exists_in_world_$i'(X1,X5)
            & ? [X7] :
                ( '$ki_exists_in_world_$i'(X1,X7)
                & ? [X9] :
                    ( '$ki_exists_in_world_$i'(X1,X9)
                    & ? [X8] :
                        ( '$ki_exists_in_world_$i'(X1,X8)
                        & ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X1,X6)
                           => ( userid(X6,u,X5)
                              & entry_box(X6,X7)
                              & number(X6,X7,one) ) )
                        & ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X1,X6)
                           => ! [X10] :
                                ( '$ki_exists_in_world_$i'(X6,X10)
                               => ( do(X6,X8,X9,X10)
                                 => in(X6,X5,X7,X10) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[verify]) ).

tff(c_0_8,plain,
    ! [X19: '$ki_world',X20,X21,X22,X24: '$ki_world',X25] :
      ( ( '$ki_exists_in_world_$i'(X19,esk5_4(X19,X20,X21,X22))
        | ~ string(X19,X21)
        | ~ entry_box(X19,X22)
        | ~ '$ki_exists_in_world_$i'(X19,X22)
        | ~ '$ki_exists_in_world_$i'(X19,X21)
        | ~ '$ki_exists_in_world_$i'(X19,X20)
        | ~ '$ki_accessible'('$ki_local_world',X19) )
      & ( ~ '$ki_accessible'(X19,X24)
        | ~ '$ki_exists_in_world_$i'(X24,X25)
        | ~ do(X24,X20,esk5_4(X19,X20,X21,X22),X25)
        | in(X24,X21,X22,X25)
        | ~ string(X19,X21)
        | ~ entry_box(X19,X22)
        | ~ '$ki_exists_in_world_$i'(X19,X22)
        | ~ '$ki_exists_in_world_$i'(X19,X21)
        | ~ '$ki_exists_in_world_$i'(X19,X20)
        | ~ '$ki_accessible'('$ki_local_world',X19) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).

tff(c_0_9,plain,
    ! [X26: '$ki_world',X27] : '$ki_exists_in_world_$i'(X26,X27),
    inference(variable_rename,[status(thm)],['$ki_exists_in_world_$i_const']) ).

tff(c_0_10,negated_conjecture,
    ! [X12,X13,X14,X15] :
      ( '$ki_accessible'('$ki_local_world',esk1_0)
      & ( '$ki_accessible'(esk1_0,esk3_4(X12,X13,X14,X15))
        | '$ki_accessible'(esk1_0,esk2_4(X12,X13,X14,X15))
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( '$ki_exists_in_world_$i'(esk3_4(X12,X13,X14,X15),esk4_4(X12,X13,X14,X15))
        | '$ki_accessible'(esk1_0,esk2_4(X12,X13,X14,X15))
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( do(esk3_4(X12,X13,X14,X15),X15,X14,esk4_4(X12,X13,X14,X15))
        | '$ki_accessible'(esk1_0,esk2_4(X12,X13,X14,X15))
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( ~ in(esk3_4(X12,X13,X14,X15),X12,X13,esk4_4(X12,X13,X14,X15))
        | '$ki_accessible'(esk1_0,esk2_4(X12,X13,X14,X15))
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( '$ki_accessible'(esk1_0,esk3_4(X12,X13,X14,X15))
        | ~ userid(esk2_4(X12,X13,X14,X15),u,X12)
        | ~ entry_box(esk2_4(X12,X13,X14,X15),X13)
        | ~ number(esk2_4(X12,X13,X14,X15),X13,one)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( '$ki_exists_in_world_$i'(esk3_4(X12,X13,X14,X15),esk4_4(X12,X13,X14,X15))
        | ~ userid(esk2_4(X12,X13,X14,X15),u,X12)
        | ~ entry_box(esk2_4(X12,X13,X14,X15),X13)
        | ~ number(esk2_4(X12,X13,X14,X15),X13,one)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( do(esk3_4(X12,X13,X14,X15),X15,X14,esk4_4(X12,X13,X14,X15))
        | ~ userid(esk2_4(X12,X13,X14,X15),u,X12)
        | ~ entry_box(esk2_4(X12,X13,X14,X15),X13)
        | ~ number(esk2_4(X12,X13,X14,X15),X13,one)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) )
      & ( ~ in(esk3_4(X12,X13,X14,X15),X12,X13,esk4_4(X12,X13,X14,X15))
        | ~ userid(esk2_4(X12,X13,X14,X15),u,X12)
        | ~ entry_box(esk2_4(X12,X13,X14,X15),X13)
        | ~ number(esk2_4(X12,X13,X14,X15),X13,one)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X15)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X14)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X13)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X12) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).

tcf(c_0_11,plain,
    ! [X2: '$ki_world',X8,X7,X5,X4,X1: '$ki_world'] :
      ( in(X2,X7,X8,X4)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_exists_in_world_$i'(X2,X4)
      | ~ do(X2,X5,esk5_4(X1,X5,X7,X8),X4)
      | ~ string(X1,X7)
      | ~ entry_box(X1,X8)
      | ~ '$ki_exists_in_world_$i'(X1,X8)
      | ~ '$ki_exists_in_world_$i'(X1,X7)
      | ~ '$ki_exists_in_world_$i'(X1,X5)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

tcf(c_0_12,plain,
    ! [X1: '$ki_world',X4] : '$ki_exists_in_world_$i'(X1,X4),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

tcf(c_0_13,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( do(esk3_4(X4,X5,X7,X8),X8,X7,esk4_4(X4,X5,X7,X8))
      | ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_14,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( ~ in(esk3_4(X4,X5,X7,X8),X4,X5,esk4_4(X4,X5,X7,X8))
      | ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_15,plain,
    ! [X8,X7,X5,X4,X2: '$ki_world',X1: '$ki_world'] :
      ( in(X1,X4,X5,X7)
      | ~ entry_box(X2,X5)
      | ~ do(X1,X8,esk5_4(X2,X8,X4,X5),X7)
      | ~ string(X2,X4)
      | ~ '$ki_accessible'('$ki_local_world',X2)
      | ~ '$ki_accessible'(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_16,negated_conjecture,
    ! [X4,X8,X7,X5] :
      ( do(esk3_4(X4,X5,X7,X8),X8,X7,esk4_4(X4,X5,X7,X8))
      | ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_17,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( '$ki_accessible'(esk1_0,esk3_4(X4,X5,X7,X8))
      | ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tff(c_0_18,plain,
    ! [X30: '$ki_world',X32: '$ki_world'] :
      ( ( '$ki_exists_in_world_$i'(X30,esk7_1(X30))
        | ~ '$ki_accessible'('$ki_local_world',X30) )
      & ( userid(X32,u,esk7_1(X30))
        | ~ '$ki_accessible'(X30,X32)
        | ~ '$ki_accessible'('$ki_local_world',X30) )
      & ( string(X32,esk7_1(X30))
        | ~ '$ki_accessible'(X30,X32)
        | ~ '$ki_accessible'('$ki_local_world',X30) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])])])]) ).

tcf(c_0_19,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( do(esk3_4(X4,X5,X7,X8),X8,X7,esk4_4(X4,X5,X7,X8))
      | '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8))
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_20,negated_conjecture,
    ! [X4,X8,X7,X5] :
      ( ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ in(esk3_4(X4,X5,X7,X8),X4,X5,esk4_4(X4,X5,X7,X8))
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_21,negated_conjecture,
    ! [X5,X9,X8,X7,X4,X1: '$ki_world'] :
      ( in(esk3_4(X4,X5,esk5_4(X1,X7,X8,X9),X7),X8,X9,esk4_4(X4,X5,esk5_4(X1,X7,X8,X9),X7))
      | ~ userid(esk2_4(X4,X5,esk5_4(X1,X7,X8,X9),X7),u,X4)
      | ~ entry_box(esk2_4(X4,X5,esk5_4(X1,X7,X8,X9),X7),X5)
      | ~ entry_box(X1,X9)
      | ~ string(X1,X8)
      | ~ number(esk2_4(X4,X5,esk5_4(X1,X7,X8,X9),X7),X5,one)
      | ~ '$ki_accessible'(X1,esk3_4(X4,X5,esk5_4(X1,X7,X8,X9),X7))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

tcf(c_0_22,negated_conjecture,
    ! [X4,X8,X7,X5] :
      ( '$ki_accessible'(esk1_0,esk3_4(X4,X5,X7,X8))
      | ~ userid(esk2_4(X4,X5,X7,X8),u,X4)
      | ~ entry_box(esk2_4(X4,X5,X7,X8),X5)
      | ~ number(esk2_4(X4,X5,X7,X8),X5,one) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_23,plain,
    ! [X1: '$ki_world',X2: '$ki_world'] :
      ( userid(X1,u,esk7_1(X2))
      | ~ '$ki_accessible'(X2,X1)
      | ~ '$ki_accessible'('$ki_local_world',X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tff(c_0_24,plain,
    ! [X34: '$ki_world'] :
      ( '$ki_exists_in_world_$i'('$ki_local_world',esk8_0)
      & ( entry_box(X34,esk8_0)
        | ~ '$ki_accessible'('$ki_local_world',X34) )
      & ( number(X34,esk8_0,one)
        | ~ '$ki_accessible'('$ki_local_world',X34) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])])])]) ).

tff(c_0_25,plain,
    ! [X36: '$ki_world',X37: '$ki_world',X38: '$ki_world'] :
      ( ~ '$ki_accessible'(X36,X37)
      | ~ '$ki_accessible'(X37,X38)
      | '$ki_accessible'(X36,X38) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mrel_transitive])])]) ).

tcf(c_0_26,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8))
      | ~ in(esk3_4(X4,X5,X7,X8),X4,X5,esk4_4(X4,X5,X7,X8))
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_27,negated_conjecture,
    ! [X4,X5,X7,X8] :
      ( do(esk3_4(X4,X5,X7,X8),X8,X7,esk4_4(X4,X5,X7,X8))
      | '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_28,negated_conjecture,
    ! [X4,X7,X5,X1: '$ki_world'] :
      ( ~ userid(esk2_4(X4,X5,esk5_4(X1,X7,X4,X5),X7),u,X4)
      | ~ entry_box(esk2_4(X4,X5,esk5_4(X1,X7,X4,X5),X7),X5)
      | ~ entry_box(X1,X5)
      | ~ string(X1,X4)
      | ~ number(esk2_4(X4,X5,esk5_4(X1,X7,X4,X5),X7),X5,one)
      | ~ '$ki_accessible'(X1,esk3_4(X4,X5,esk5_4(X1,X7,X4,X5),X7))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

tcf(c_0_29,negated_conjecture,
    ! [X4,X7,X5,X1: '$ki_world'] :
      ( '$ki_accessible'(esk1_0,esk3_4(esk7_1(X1),X4,X5,X7))
      | ~ entry_box(esk2_4(esk7_1(X1),X4,X5,X7),X4)
      | ~ number(esk2_4(esk7_1(X1),X4,X5,X7),X4,one)
      | ~ '$ki_accessible'(X1,esk2_4(esk7_1(X1),X4,X5,X7))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

tcf(c_0_30,plain,
    ! [X1: '$ki_world'] :
      ( number(X1,esk8_0,one)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

tcf(c_0_31,plain,
    ! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
      ( '$ki_accessible'(X1,X3)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_accessible'(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

tcf(c_0_32,negated_conjecture,
    ! [X4,X5,X7,X8] :
      ( '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8))
      | ~ in(esk3_4(X4,X5,X7,X8),X4,X5,esk4_4(X4,X5,X7,X8)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_33,negated_conjecture,
    ! [X5,X9,X8,X7,X4,X1: '$ki_world'] :
      ( in(esk3_4(X4,X5,esk5_4(X1,X7,X8,X9),X7),X8,X9,esk4_4(X4,X5,esk5_4(X1,X7,X8,X9),X7))
      | '$ki_accessible'(esk1_0,esk2_4(X4,X5,esk5_4(X1,X7,X8,X9),X7))
      | ~ entry_box(X1,X9)
      | ~ string(X1,X8)
      | ~ '$ki_accessible'(X1,esk3_4(X4,X5,esk5_4(X1,X7,X8,X9),X7))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_27]) ).

tcf(c_0_34,negated_conjecture,
    ! [X8,X7,X5,X4] :
      ( '$ki_accessible'(esk1_0,esk3_4(X4,X5,X7,X8))
      | '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8))
      | ~ '$ki_exists_in_world_$i'(esk1_0,X8)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X7)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X5)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_35,negated_conjecture,
    ! [X5,X4,X2: '$ki_world',X1: '$ki_world'] :
      ( ~ entry_box(esk2_4(esk7_1(X1),X4,esk5_4(X2,X5,esk7_1(X1),X4),X5),X4)
      | ~ entry_box(X2,X4)
      | ~ string(X2,esk7_1(X1))
      | ~ number(esk2_4(esk7_1(X1),X4,esk5_4(X2,X5,esk7_1(X1),X4),X5),X4,one)
      | ~ '$ki_accessible'(X2,esk3_4(esk7_1(X1),X4,esk5_4(X2,X5,esk7_1(X1),X4),X5))
      | ~ '$ki_accessible'(X1,esk2_4(esk7_1(X1),X4,esk5_4(X2,X5,esk7_1(X1),X4),X5))
      | ~ '$ki_accessible'('$ki_local_world',X2)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_23]) ).

tcf(c_0_36,plain,
    ! [X1: '$ki_world'] :
      ( entry_box(X1,esk8_0)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

tcf(c_0_37,negated_conjecture,
    ! [X5,X4,X1: '$ki_world'] :
      ( '$ki_accessible'(esk1_0,esk3_4(esk7_1(X1),esk8_0,X4,X5))
      | ~ entry_box(esk2_4(esk7_1(X1),esk8_0,X4,X5),esk8_0)
      | ~ '$ki_accessible'(X1,esk2_4(esk7_1(X1),esk8_0,X4,X5))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

tcf(c_0_38,negated_conjecture,
    ! [X4,X7,X5,X1: '$ki_world'] :
      ( '$ki_accessible'(esk1_0,esk2_4(X4,X5,esk5_4(X1,X7,X4,X5),X7))
      | ~ entry_box(X1,X5)
      | ~ string(X1,X4)
      | ~ '$ki_accessible'(X1,esk3_4(X4,X5,esk5_4(X1,X7,X4,X5),X7))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

tcf(c_0_39,negated_conjecture,
    ! [X4,X5,X7,X8] :
      ( '$ki_accessible'(esk1_0,esk3_4(X4,X5,X7,X8))
      | '$ki_accessible'(esk1_0,esk2_4(X4,X5,X7,X8)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).

tcf(c_0_40,negated_conjecture,
    '$ki_accessible'('$ki_local_world',esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tcf(c_0_41,negated_conjecture,
    ! [X4,X2: '$ki_world',X1: '$ki_world'] :
      ( ~ entry_box(esk2_4(esk7_1(X1),esk8_0,esk5_4(X2,X4,esk7_1(X1),esk8_0),X4),esk8_0)
      | ~ string(X2,esk7_1(X1))
      | ~ '$ki_accessible'(X2,esk3_4(esk7_1(X1),esk8_0,esk5_4(X2,X4,esk7_1(X1),esk8_0),X4))
      | ~ '$ki_accessible'(X1,esk2_4(esk7_1(X1),esk8_0,esk5_4(X2,X4,esk7_1(X1),esk8_0),X4))
      | ~ '$ki_accessible'('$ki_local_world',X2)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]),c_0_36]) ).

tcf(c_0_42,negated_conjecture,
    ! [X5,X4,X1: '$ki_world'] :
      ( '$ki_accessible'(esk1_0,esk3_4(esk7_1(X1),esk8_0,X4,X5))
      | ~ '$ki_accessible'(X1,esk2_4(esk7_1(X1),esk8_0,X4,X5))
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_31]) ).

tcf(c_0_43,negated_conjecture,
    ! [X7,X5,X4] :
      ( '$ki_accessible'(esk1_0,esk2_4(X4,X5,esk5_4(esk1_0,X7,X4,X5),X7))
      | ~ entry_box(esk1_0,X5)
      | ~ string(esk1_0,X4) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

tcf(c_0_44,negated_conjecture,
    ! [X1: '$ki_world',X4,X2: '$ki_world'] :
      ( ~ string(X1,esk7_1(X2))
      | ~ '$ki_accessible'(X1,esk3_4(esk7_1(X2),esk8_0,esk5_4(X1,X4,esk7_1(X2),esk8_0),X4))
      | ~ '$ki_accessible'(X2,esk2_4(esk7_1(X2),esk8_0,esk5_4(X1,X4,esk7_1(X2),esk8_0),X4))
      | ~ '$ki_accessible'('$ki_local_world',X1)
      | ~ '$ki_accessible'('$ki_local_world',X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_31]) ).

tcf(c_0_45,negated_conjecture,
    ! [X4] :
      ( '$ki_accessible'(esk1_0,esk3_4(esk7_1(esk1_0),esk8_0,esk5_4(esk1_0,X4,esk7_1(esk1_0),esk8_0),X4))
      | ~ entry_box(esk1_0,esk8_0)
      | ~ string(esk1_0,esk7_1(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40])]) ).

tff(c_0_46,plain,
    ! [X35: '$ki_world'] : '$ki_accessible'(X35,X35),
    inference(variable_rename,[status(thm)],[mrel_reflexive]) ).

tcf(c_0_47,negated_conjecture,
    ( ~ entry_box(esk1_0,esk8_0)
    | ~ string(esk1_0,esk7_1(esk1_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40])]),c_0_43]) ).

tcf(c_0_48,plain,
    ! [X1: '$ki_world',X2: '$ki_world'] :
      ( string(X1,esk7_1(X2))
      | ~ '$ki_accessible'(X2,X1)
      | ~ '$ki_accessible'('$ki_local_world',X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_49,plain,
    ! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

tcf(c_0_50,negated_conjecture,
    ~ entry_box(esk1_0,esk8_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]),c_0_49])]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_40])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 22:34:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.46  Running first-order model finding
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48  # Version: 3.1.0
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # sh5l with pid 4177 completed with status 0
% 0.19/0.48  # Result found by sh5l
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.48  # Search class: FGHNS-FFMF33-SFFFFFNN
% 0.19/0.48  # partial match(1): FGHSS-FFMF33-SFFFFFNN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 121s (1) cores
% 0.19/0.48  # SAT001_MinMin_p005000_rr_RG with pid 4185 completed with status 0
% 0.19/0.48  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.48  # Search class: FGHNS-FFMF33-SFFFFFNN
% 0.19/0.48  # partial match(1): FGHSS-FFMF33-SFFFFFNN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 121s (1) cores
% 0.19/0.48  # Preprocessing time       : 0.001 s
% 0.19/0.48  # Presaturation interreduction done
% 0.19/0.48  
% 0.19/0.48  # Proof found!
% 0.19/0.48  # SZS status Theorem
% 0.19/0.48  # SZS output start CNFRefutation
% See solution above
% 0.19/0.48  # Parsed axioms                        : 20
% 0.19/0.48  # Removed by relevancy pruning/SinE    : 12
% 0.19/0.48  # Initial clauses                      : 21
% 0.19/0.48  # Removed in clause preprocessing      : 0
% 0.19/0.48  # Initial clauses in saturation        : 21
% 0.19/0.48  # Processed clauses                    : 57
% 0.19/0.48  # ...of these trivial                  : 5
% 0.19/0.48  # ...subsumed                          : 2
% 0.19/0.48  # ...remaining for further processing  : 50
% 0.19/0.48  # Other redundant clauses eliminated   : 0
% 0.19/0.48  # Clauses deleted for lack of memory   : 0
% 0.19/0.48  # Backward-subsumed                    : 4
% 0.19/0.48  # Backward-rewritten                   : 1
% 0.19/0.48  # Generated clauses                    : 34
% 0.19/0.48  # ...of the previous two non-redundant : 31
% 0.19/0.48  # ...aggressively subsumed             : 0
% 0.19/0.48  # Contextual simplify-reflections      : 6
% 0.19/0.48  # Paramodulations                      : 34
% 0.19/0.48  # Factorizations                       : 0
% 0.19/0.48  # NegExts                              : 0
% 0.19/0.48  # Equation resolutions                 : 0
% 0.19/0.48  # Disequality decompositions           : 0
% 0.19/0.48  # Total rewrite steps                  : 54
% 0.19/0.48  # ...of those cached                   : 38
% 0.19/0.48  # Propositional unsat checks           : 0
% 0.19/0.48  #    Propositional check models        : 0
% 0.19/0.48  #    Propositional check unsatisfiable : 0
% 0.19/0.48  #    Propositional clauses             : 0
% 0.19/0.48  #    Propositional clauses after purity: 0
% 0.19/0.48  #    Propositional unsat core size     : 0
% 0.19/0.48  #    Propositional preprocessing time  : 0.000
% 0.19/0.48  #    Propositional encoding time       : 0.000
% 0.19/0.48  #    Propositional solver time         : 0.000
% 0.19/0.48  #    Success case prop preproc time    : 0.000
% 0.19/0.48  #    Success case prop encoding time   : 0.000
% 0.19/0.48  #    Success case prop solver time     : 0.000
% 0.19/0.48  # Current number of processed clauses  : 30
% 0.19/0.48  #    Positive orientable unit clauses  : 3
% 0.19/0.48  #    Positive unorientable unit clauses: 0
% 0.19/0.48  #    Negative unit clauses             : 1
% 0.19/0.48  #    Non-unit-clauses                  : 26
% 0.19/0.48  # Current number of unprocessed clauses: 10
% 0.19/0.48  # ...number of literals in the above   : 53
% 0.19/0.48  # Current number of archived formulas  : 0
% 0.19/0.48  # Current number of archived clauses   : 20
% 0.19/0.48  # Clause-clause subsumption calls (NU) : 355
% 0.19/0.48  # Rec. Clause-clause subsumption calls : 126
% 0.19/0.48  # Non-unit clause-clause subsumptions  : 11
% 0.19/0.48  # Unit Clause-clause subsumption calls : 1
% 0.19/0.48  # Rewrite failures with RHS unbound    : 0
% 0.19/0.48  # BW rewrite match attempts            : 3
% 0.19/0.48  # BW rewrite match successes           : 1
% 0.19/0.48  # Condensation attempts                : 0
% 0.19/0.48  # Condensation successes               : 0
% 0.19/0.48  # Termbank termtop insertions          : 3653
% 0.19/0.48  # Search garbage collected termcells   : 514
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.008 s
% 0.19/0.48  # System time              : 0.003 s
% 0.19/0.48  # Total time               : 0.011 s
% 0.19/0.48  # Maximum resident set size: 1880 pages
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.010 s
% 0.19/0.48  # System time              : 0.004 s
% 0.19/0.48  # Total time               : 0.014 s
% 0.19/0.48  # Maximum resident set size: 1724 pages
% 0.19/0.48  % E---3.1 exiting
%------------------------------------------------------------------------------