TSTP Solution File: GEG002^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : GEG002^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 19:56:51 EDT 2024

% Result   : Theorem 0.96s 0.56s
% Output   : CNFRefutation 0.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   98 (  29 unt;  24 typ;   0 def)
%            Number of atoms       :  368 (  19 equ;   0 cnn)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives : 1187 ( 121   ~; 120   |;  83   &; 810   @)
%                                         (   0 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;   8 con; 0-2 aty)
%            Number of variables   :  176 (  38   ^ 112   !;  26   ?; 176   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    reg: $tType ).

thf(decl_22,type,
    c: reg > reg > $o ).

thf(decl_23,type,
    dc: reg > reg > $o ).

thf(decl_24,type,
    p: reg > reg > $o ).

thf(decl_26,type,
    o: reg > reg > $o ).

thf(decl_28,type,
    ec: reg > reg > $o ).

thf(decl_29,type,
    pp: reg > reg > $o ).

thf(decl_30,type,
    tpp: reg > reg > $o ).

thf(decl_31,type,
    ntpp: reg > reg > $o ).

thf(decl_32,type,
    catalunya: reg ).

thf(decl_33,type,
    france: reg ).

thf(decl_34,type,
    spain: reg ).

thf(decl_35,type,
    paris: reg ).

thf(decl_36,type,
    esk1_0: reg ).

thf(decl_37,type,
    esk2_0: reg ).

thf(decl_38,type,
    esk3_1: reg > reg ).

thf(decl_39,type,
    esk4_1: reg > reg ).

thf(decl_40,type,
    esk5_1: reg > reg ).

thf(decl_41,type,
    esk6_1: reg > reg ).

thf(decl_42,type,
    esk7_1: reg > reg ).

thf(decl_43,type,
    esk8_1: reg > reg ).

thf(decl_44,type,
    esk9_0: reg ).

thf(decl_45,type,
    esk10_1: reg > reg ).

thf(decl_46,type,
    esk11_1: reg > reg ).

thf(o,axiom,
    ( o
    = ( ^ [X1: reg,X2: reg] :
        ? [X3: reg] :
          ( ( p @ X3 @ X1 )
          & ( p @ X3 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).

thf(p,axiom,
    ( p
    = ( ^ [X1: reg,X2: reg] :
        ! [X3: reg] :
          ( ( c @ X3 @ X1 )
         => ( c @ X3 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',p) ).

thf(ec,axiom,
    ( ec
    = ( ^ [X1: reg,X2: reg] :
          ( ( c @ X1 @ X2 )
          & ~ ( o @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).

thf(pp,axiom,
    ( pp
    = ( ^ [X1: reg,X2: reg] :
          ( ( p @ X1 @ X2 )
          & ~ ( p @ X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',pp) ).

thf(ntpp,axiom,
    ( ntpp
    = ( ^ [X1: reg,X2: reg] :
          ( ( pp @ X1 @ X2 )
          & ~ ? [X3: reg] :
                ( ( ec @ X3 @ X1 )
                & ( ec @ X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).

thf(tpp,axiom,
    ( tpp
    = ( ^ [X1: reg,X2: reg] :
          ( ( pp @ X1 @ X2 )
          & ? [X3: reg] :
              ( ( ec @ X3 @ X1 )
              & ( ec @ X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).

thf(dc,axiom,
    ( dc
    = ( ^ [X1: reg,X2: reg] :
          ~ ( c @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',dc) ).

thf(ax3,axiom,
    ntpp @ paris @ france,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(con,conjecture,
    ( ( dc @ catalunya @ paris )
    & ( dc @ spain @ paris ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(ax2,axiom,
    ec @ spain @ france,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(ax1,axiom,
    tpp @ catalunya @ spain,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(c_symmetric,axiom,
    ! [X1: reg,X2: reg] :
      ( ( c @ X1 @ X2 )
     => ( c @ X2 @ X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).

thf(c_0_12,plain,
    ( o
    = ( ^ [Z0: reg,Z1: reg] :
        ? [X3: reg] :
          ( ! [X9: reg] :
              ( ( c @ X9 @ X3 )
             => ( c @ X9 @ Z0 ) )
          & ! [X10: reg] :
              ( ( c @ X10 @ X3 )
             => ( c @ X10 @ Z1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[o]) ).

thf(c_0_13,plain,
    ( p
    = ( ^ [Z0: reg,Z1: reg] :
        ! [X3: reg] :
          ( ( c @ X3 @ Z0 )
         => ( c @ X3 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[p]) ).

thf(c_0_14,plain,
    ( ec
    = ( ^ [Z0: reg,Z1: reg] :
          ( ( c @ Z0 @ Z1 )
          & ~ ? [X16: reg] :
                ( ! [X17: reg] :
                    ( ( c @ X17 @ X16 )
                   => ( c @ X17 @ Z0 ) )
                & ! [X18: reg] :
                    ( ( c @ X18 @ X16 )
                   => ( c @ X18 @ Z1 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ec]) ).

thf(c_0_15,plain,
    ( o
    = ( ^ [Z0: reg,Z1: reg] :
        ? [X3: reg] :
          ( ! [X9: reg] :
              ( ( c @ X9 @ X3 )
             => ( c @ X9 @ Z0 ) )
          & ! [X10: reg] :
              ( ( c @ X10 @ X3 )
             => ( c @ X10 @ Z1 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_16,plain,
    ( pp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X19: reg] :
              ( ( c @ X19 @ Z0 )
             => ( c @ X19 @ Z1 ) )
          & ~ ! [X20: reg] :
                ( ( c @ X20 @ Z1 )
               => ( c @ X20 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[pp]) ).

thf(c_0_17,plain,
    ( ntpp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X29: reg] :
              ( ( c @ X29 @ Z0 )
             => ( c @ X29 @ Z1 ) )
          & ~ ! [X30: reg] :
                ( ( c @ X30 @ Z1 )
               => ( c @ X30 @ Z0 ) )
          & ~ ? [X3: reg] :
                ( ( c @ X3 @ Z0 )
                & ~ ? [X31: reg] :
                      ( ! [X32: reg] :
                          ( ( c @ X32 @ X31 )
                         => ( c @ X32 @ X3 ) )
                      & ! [X33: reg] :
                          ( ( c @ X33 @ X31 )
                         => ( c @ X33 @ Z0 ) ) )
                & ( c @ X3 @ Z1 )
                & ~ ? [X34: reg] :
                      ( ! [X35: reg] :
                          ( ( c @ X35 @ X34 )
                         => ( c @ X35 @ X3 ) )
                      & ! [X36: reg] :
                          ( ( c @ X36 @ X34 )
                         => ( c @ X36 @ Z1 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ntpp]) ).

thf(c_0_18,plain,
    ( ec
    = ( ^ [Z0: reg,Z1: reg] :
          ( ( c @ Z0 @ Z1 )
          & ~ ? [X16: reg] :
                ( ! [X17: reg] :
                    ( ( c @ X17 @ X16 )
                   => ( c @ X17 @ Z0 ) )
                & ! [X18: reg] :
                    ( ( c @ X18 @ X16 )
                   => ( c @ X18 @ Z1 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_19,plain,
    ( pp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X19: reg] :
              ( ( c @ X19 @ Z0 )
             => ( c @ X19 @ Z1 ) )
          & ~ ! [X20: reg] :
                ( ( c @ X20 @ Z1 )
               => ( c @ X20 @ Z0 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_16,c_0_13]) ).

thf(c_0_20,plain,
    ( ntpp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X29: reg] :
              ( ( c @ X29 @ Z0 )
             => ( c @ X29 @ Z1 ) )
          & ~ ! [X30: reg] :
                ( ( c @ X30 @ Z1 )
               => ( c @ X30 @ Z0 ) )
          & ~ ? [X3: reg] :
                ( ( c @ X3 @ Z0 )
                & ~ ? [X31: reg] :
                      ( ! [X32: reg] :
                          ( ( c @ X32 @ X31 )
                         => ( c @ X32 @ X3 ) )
                      & ! [X33: reg] :
                          ( ( c @ X33 @ X31 )
                         => ( c @ X33 @ Z0 ) ) )
                & ( c @ X3 @ Z1 )
                & ~ ? [X34: reg] :
                      ( ! [X35: reg] :
                          ( ( c @ X35 @ X34 )
                         => ( c @ X35 @ X3 ) )
                      & ! [X36: reg] :
                          ( ( c @ X36 @ X34 )
                         => ( c @ X36 @ Z1 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

thf(c_0_21,plain,
    ( tpp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X21: reg] :
              ( ( c @ X21 @ Z0 )
             => ( c @ X21 @ Z1 ) )
          & ~ ! [X22: reg] :
                ( ( c @ X22 @ Z1 )
               => ( c @ X22 @ Z0 ) )
          & ? [X3: reg] :
              ( ( c @ X3 @ Z0 )
              & ~ ? [X23: reg] :
                    ( ! [X24: reg] :
                        ( ( c @ X24 @ X23 )
                       => ( c @ X24 @ X3 ) )
                    & ! [X25: reg] :
                        ( ( c @ X25 @ X23 )
                       => ( c @ X25 @ Z0 ) ) )
              & ( c @ X3 @ Z1 )
              & ~ ? [X26: reg] :
                    ( ! [X27: reg] :
                        ( ( c @ X27 @ X26 )
                       => ( c @ X27 @ X3 ) )
                    & ! [X28: reg] :
                        ( ( c @ X28 @ X26 )
                       => ( c @ X28 @ Z1 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[tpp]) ).

thf(c_0_22,plain,
    ( dc
    = ( ^ [Z0: reg,Z1: reg] :
          ~ ( c @ Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[dc]) ).

thf(c_0_23,plain,
    ( ! [X49: reg] :
        ( ( c @ X49 @ paris )
       => ( c @ X49 @ france ) )
    & ~ ! [X50: reg] :
          ( ( c @ X50 @ france )
         => ( c @ X50 @ paris ) )
    & ~ ? [X51: reg] :
          ( ( c @ X51 @ paris )
          & ~ ? [X52: reg] :
                ( ! [X53: reg] :
                    ( ( c @ X53 @ X52 )
                   => ( c @ X53 @ X51 ) )
                & ! [X54: reg] :
                    ( ( c @ X54 @ X52 )
                   => ( c @ X54 @ paris ) ) )
          & ( c @ X51 @ france )
          & ~ ? [X55: reg] :
                ( ! [X56: reg] :
                    ( ( c @ X56 @ X55 )
                   => ( c @ X56 @ X51 ) )
                & ! [X57: reg] :
                    ( ( c @ X57 @ X55 )
                   => ( c @ X57 @ france ) ) ) ) ),
    inference(apply_def,[status(thm)],[ax3,c_0_20]) ).

thf(c_0_24,plain,
    ( tpp
    = ( ^ [Z0: reg,Z1: reg] :
          ( ! [X21: reg] :
              ( ( c @ X21 @ Z0 )
             => ( c @ X21 @ Z1 ) )
          & ~ ! [X22: reg] :
                ( ( c @ X22 @ Z1 )
               => ( c @ X22 @ Z0 ) )
          & ? [X3: reg] :
              ( ( c @ X3 @ Z0 )
              & ~ ? [X23: reg] :
                    ( ! [X24: reg] :
                        ( ( c @ X24 @ X23 )
                       => ( c @ X24 @ X3 ) )
                    & ! [X25: reg] :
                        ( ( c @ X25 @ X23 )
                       => ( c @ X25 @ Z0 ) ) )
              & ( c @ X3 @ Z1 )
              & ~ ? [X26: reg] :
                    ( ! [X27: reg] :
                        ( ( c @ X27 @ X26 )
                       => ( c @ X27 @ X3 ) )
                    & ! [X28: reg] :
                        ( ( c @ X28 @ X26 )
                       => ( c @ X28 @ Z1 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_18]),c_0_19]) ).

thf(c_0_25,negated_conjecture,
    ~ ( ~ ( c @ catalunya @ paris )
      & ~ ( c @ spain @ paris ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[con]),c_0_22])]) ).

thf(c_0_26,plain,
    ! [X73: reg,X75: reg,X77: reg,X78: reg,X80: reg,X81: reg] :
      ( ( ~ ( c @ X73 @ paris )
        | ( c @ X73 @ france ) )
      & ( c @ esk9_0 @ france )
      & ~ ( c @ esk9_0 @ paris )
      & ( ~ ( c @ X80 @ ( esk11_1 @ X75 ) )
        | ( c @ X80 @ X75 )
        | ~ ( c @ X75 @ france )
        | ~ ( c @ X77 @ ( esk10_1 @ X75 ) )
        | ( c @ X77 @ X75 )
        | ~ ( c @ X75 @ paris ) )
      & ( ~ ( c @ X81 @ ( esk11_1 @ X75 ) )
        | ( c @ X81 @ france )
        | ~ ( c @ X75 @ france )
        | ~ ( c @ X77 @ ( esk10_1 @ X75 ) )
        | ( c @ X77 @ X75 )
        | ~ ( c @ X75 @ paris ) )
      & ( ~ ( c @ X80 @ ( esk11_1 @ X75 ) )
        | ( c @ X80 @ X75 )
        | ~ ( c @ X75 @ france )
        | ~ ( c @ X78 @ ( esk10_1 @ X75 ) )
        | ( c @ X78 @ paris )
        | ~ ( c @ X75 @ paris ) )
      & ( ~ ( c @ X81 @ ( esk11_1 @ X75 ) )
        | ( c @ X81 @ france )
        | ~ ( c @ X75 @ france )
        | ~ ( c @ X78 @ ( esk10_1 @ X75 ) )
        | ( c @ X78 @ paris )
        | ~ ( c @ X75 @ paris ) ) ),
    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_23])])])])])]) ).

thf(c_0_27,plain,
    ( ( c @ spain @ france )
    & ~ ? [X46: reg] :
          ( ! [X47: reg] :
              ( ( c @ X47 @ X46 )
             => ( c @ X47 @ spain ) )
          & ! [X48: reg] :
              ( ( c @ X48 @ X46 )
             => ( c @ X48 @ france ) ) ) ),
    inference(apply_def,[status(thm)],[ax2,c_0_18]) ).

thf(c_0_28,plain,
    ( ! [X37: reg] :
        ( ( c @ X37 @ catalunya )
       => ( c @ X37 @ spain ) )
    & ~ ! [X38: reg] :
          ( ( c @ X38 @ spain )
         => ( c @ X38 @ catalunya ) )
    & ? [X39: reg] :
        ( ( c @ X39 @ catalunya )
        & ~ ? [X40: reg] :
              ( ! [X41: reg] :
                  ( ( c @ X41 @ X40 )
                 => ( c @ X41 @ X39 ) )
              & ! [X42: reg] :
                  ( ( c @ X42 @ X40 )
                 => ( c @ X42 @ catalunya ) ) )
        & ( c @ X39 @ spain )
        & ~ ? [X43: reg] :
              ( ! [X44: reg] :
                  ( ( c @ X44 @ X43 )
                 => ( c @ X44 @ X39 ) )
              & ! [X45: reg] :
                  ( ( c @ X45 @ X43 )
                 => ( c @ X45 @ spain ) ) ) ) ),
    inference(apply_def,[status(thm)],[ax1,c_0_24]) ).

thf(c_0_29,plain,
    ! [X59: reg,X60: reg] :
      ( ~ ( c @ X59 @ X60 )
      | ( c @ X60 @ X59 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])])]) ).

thf(c_0_30,negated_conjecture,
    ( ( c @ catalunya @ paris )
    | ( c @ spain @ paris ) ),
    inference(fof_nnf,[status(thm)],[c_0_25]) ).

thf(c_0_31,plain,
    ! [X1: reg,X3: reg,X2: reg] :
      ( ( c @ X1 @ france )
      | ( c @ X3 @ paris )
      | ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
      | ~ ( c @ X2 @ france )
      | ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
      | ~ ( c @ X2 @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_32,plain,
    ! [X1: reg] :
      ( ( c @ X1 @ france )
      | ~ ( c @ X1 @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_33,plain,
    ! [X70: reg] :
      ( ( c @ spain @ france )
      & ( ( c @ ( esk8_1 @ X70 ) @ X70 )
        | ( c @ ( esk7_1 @ X70 ) @ X70 ) )
      & ( ~ ( c @ ( esk8_1 @ X70 ) @ france )
        | ( c @ ( esk7_1 @ X70 ) @ X70 ) )
      & ( ( c @ ( esk8_1 @ X70 ) @ X70 )
        | ~ ( c @ ( esk7_1 @ X70 ) @ spain ) )
      & ( ~ ( c @ ( esk8_1 @ X70 ) @ france )
        | ~ ( c @ ( esk7_1 @ X70 ) @ spain ) ) ),
    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_27])])])])])]) ).

thf(c_0_34,plain,
    ! [X61: reg,X64: reg,X67: reg] :
      ( ( ~ ( c @ X61 @ catalunya )
        | ( c @ X61 @ spain ) )
      & ( c @ esk1_0 @ spain )
      & ~ ( c @ esk1_0 @ catalunya )
      & ( c @ esk2_0 @ catalunya )
      & ( ( c @ ( esk4_1 @ X64 ) @ X64 )
        | ( c @ ( esk3_1 @ X64 ) @ X64 ) )
      & ( ~ ( c @ ( esk4_1 @ X64 ) @ catalunya )
        | ( c @ ( esk3_1 @ X64 ) @ X64 ) )
      & ( ( c @ ( esk4_1 @ X64 ) @ X64 )
        | ~ ( c @ ( esk3_1 @ X64 ) @ esk2_0 ) )
      & ( ~ ( c @ ( esk4_1 @ X64 ) @ catalunya )
        | ~ ( c @ ( esk3_1 @ X64 ) @ esk2_0 ) )
      & ( c @ esk2_0 @ spain )
      & ( ( c @ ( esk6_1 @ X67 ) @ X67 )
        | ( c @ ( esk5_1 @ X67 ) @ X67 ) )
      & ( ~ ( c @ ( esk6_1 @ X67 ) @ spain )
        | ( c @ ( esk5_1 @ X67 ) @ X67 ) )
      & ( ( c @ ( esk6_1 @ X67 ) @ X67 )
        | ~ ( c @ ( esk5_1 @ X67 ) @ esk2_0 ) )
      & ( ~ ( c @ ( esk6_1 @ X67 ) @ spain )
        | ~ ( c @ ( esk5_1 @ X67 ) @ esk2_0 ) ) ),
    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_28])])])])])]) ).

thf(c_0_35,plain,
    ! [X1: reg,X2: reg] :
      ( ( c @ X2 @ X1 )
      | ~ ( c @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_36,negated_conjecture,
    ( ( c @ catalunya @ paris )
    | ( c @ spain @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_37,plain,
    ! [X1: reg,X2: reg,X3: reg] :
      ( ( c @ X1 @ france )
      | ( c @ X2 @ paris )
      | ~ ( c @ X2 @ ( esk10_1 @ X3 ) )
      | ~ ( c @ X1 @ ( esk11_1 @ X3 ) )
      | ~ ( c @ X3 @ paris ) ),
    inference(csr,[status(thm)],[c_0_31,c_0_32]) ).

thf(c_0_38,plain,
    ! [X1: reg] :
      ( ( c @ ( esk8_1 @ X1 ) @ X1 )
      | ( c @ ( esk7_1 @ X1 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_39,plain,
    ! [X1: reg] :
      ( ( c @ X1 @ spain )
      | ~ ( c @ X1 @ catalunya ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_40,negated_conjecture,
    ( ( c @ spain @ paris )
    | ( c @ paris @ catalunya ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

thf(c_0_41,plain,
    ! [X1: reg,X3: reg,X2: reg] :
      ( ( c @ X1 @ X2 )
      | ( c @ X3 @ paris )
      | ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
      | ~ ( c @ X2 @ france )
      | ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
      | ~ ( c @ X2 @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_42,plain,
    ! [X2: reg,X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
      | ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ( c @ X2 @ france )
      | ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
      | ~ ( c @ X1 @ paris ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_43,plain,
    ! [X1: reg] :
      ( ( c @ ( esk7_1 @ X1 ) @ X1 )
      | ~ ( c @ ( esk8_1 @ X1 ) @ france ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_44,negated_conjecture,
    c @ paris @ spain,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35]) ).

thf(c_0_45,plain,
    ! [X1: reg,X2: reg,X3: reg] :
      ( ( c @ X1 @ paris )
      | ( c @ X2 @ X3 )
      | ~ ( c @ X1 @ ( esk10_1 @ X3 ) )
      | ~ ( c @ X2 @ ( esk11_1 @ X3 ) )
      | ~ ( c @ X3 @ paris ) ),
    inference(csr,[status(thm)],[c_0_41,c_0_32]) ).

thf(c_0_46,plain,
    ! [X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk11_1 @ X1 ) ) @ ( esk11_1 @ X1 ) )
      | ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
      | ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ~ ( c @ X1 @ paris ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_43]) ).

thf(c_0_47,negated_conjecture,
    c @ spain @ paris,
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

thf(c_0_48,plain,
    ! [X1: reg] :
      ( ( c @ ( esk8_1 @ X1 ) @ X1 )
      | ~ ( c @ ( esk7_1 @ X1 ) @ spain ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_49,plain,
    ! [X1: reg] :
      ( ~ ( c @ ( esk8_1 @ X1 ) @ france )
      | ~ ( c @ ( esk7_1 @ X1 ) @ spain ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_50,plain,
    ! [X2: reg,X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
      | ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ( c @ X2 @ X1 )
      | ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
      | ~ ( c @ X1 @ paris ) ),
    inference(spm,[status(thm)],[c_0_45,c_0_38]) ).

thf(c_0_51,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
    | ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
    | ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

thf(c_0_52,plain,
    ! [X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
      | ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ~ ( c @ ( esk7_1 @ ( esk11_1 @ X1 ) ) @ spain )
      | ~ ( c @ X1 @ paris ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_48]),c_0_49]) ).

thf(c_0_53,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
    | ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain )
    | ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47])]) ).

thf(c_0_54,plain,
    ! [X1: reg,X3: reg,X2: reg] :
      ( ( c @ X1 @ france )
      | ( c @ X3 @ X2 )
      | ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
      | ~ ( c @ X2 @ france )
      | ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
      | ~ ( c @ X2 @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_55,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
    | ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_47])]) ).

thf(c_0_56,plain,
    ! [X1: reg,X3: reg,X2: reg] :
      ( ( c @ X1 @ X2 )
      | ( c @ X3 @ X2 )
      | ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
      | ~ ( c @ X2 @ france )
      | ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
      | ~ ( c @ X2 @ paris ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_57,plain,
    ! [X1: reg,X2: reg,X3: reg] :
      ( ( c @ X1 @ france )
      | ( c @ X2 @ X3 )
      | ~ ( c @ X2 @ ( esk10_1 @ X3 ) )
      | ~ ( c @ X1 @ ( esk11_1 @ X3 ) )
      | ~ ( c @ X3 @ paris ) ),
    inference(csr,[status(thm)],[c_0_54,c_0_32]) ).

thf(c_0_58,negated_conjecture,
    c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_55]),c_0_43]) ).

thf(c_0_59,plain,
    ! [X1: reg,X3: reg,X2: reg] :
      ( ( c @ X1 @ X2 )
      | ( c @ X3 @ X2 )
      | ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
      | ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
      | ~ ( c @ X2 @ paris ) ),
    inference(csr,[status(thm)],[c_0_56,c_0_32]) ).

thf(c_0_60,negated_conjecture,
    ! [X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
      | ( c @ X1 @ france )
      | ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_47])]) ).

thf(c_0_61,negated_conjecture,
    ! [X1: reg] :
      ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
      | ( c @ X1 @ spain )
      | ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_58]),c_0_47])]) ).

thf(c_0_62,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
    | ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_38]),c_0_43]) ).

thf(c_0_63,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
    | ~ ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_48]),c_0_49]) ).

thf(c_0_64,plain,
    ! [X2: reg,X1: reg] :
      ( ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ( c @ X2 @ france )
      | ~ ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ spain )
      | ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
      | ~ ( c @ X1 @ paris ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_48]) ).

thf(c_0_65,negated_conjecture,
    c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).

thf(c_0_66,plain,
    ! [X2: reg,X1: reg] :
      ( ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
      | ( c @ X2 @ X1 )
      | ~ ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ spain )
      | ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
      | ~ ( c @ X1 @ paris ) ),
    inference(spm,[status(thm)],[c_0_45,c_0_48]) ).

thf(c_0_67,negated_conjecture,
    ! [X1: reg] :
      ( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
      | ( c @ X1 @ france )
      | ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47])]) ).

thf(c_0_68,negated_conjecture,
    ! [X1: reg] :
      ( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
      | ( c @ X1 @ spain )
      | ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_65]),c_0_47])]) ).

thf(c_0_69,negated_conjecture,
    ( ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
    | ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_38]),c_0_43]) ).

thf(c_0_70,negated_conjecture,
    ( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
    | ~ ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_48]),c_0_49]) ).

thf(c_0_71,negated_conjecture,
    c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).

thf(c_0_72,negated_conjecture,
    c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ france,
    inference(spm,[status(thm)],[c_0_32,c_0_71]) ).

thf(c_0_73,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_72]),c_0_65])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GEG002^1 : TPTP v8.2.0. Released v4.1.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n011.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sat May 18 21:56:07 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.17/0.41  Running higher-order theorem proving
% 0.17/0.41  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/benchmark/theBenchmark.p
% 0.96/0.56  # Version: 3.1.0-ho
% 0.96/0.56  # partial match(1): HSSSSMSSSLSNSFN
% 0.96/0.56  # Preprocessing class: HSSSSMSSMLSNSFN.
% 0.96/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.96/0.56  # Starting post_as_ho5 with 300s (1) cores
% 0.96/0.56  # Starting sh4l with 300s (1) cores
% 0.96/0.56  # Starting ho_unfolding_2 with 300s (1) cores
% 0.96/0.56  # post_as_ho5 with pid 618 completed with status 8
% 0.96/0.56  # ho_unfolding_3 with pid 617 completed with status 0
% 0.96/0.56  # Result found by ho_unfolding_3
% 0.96/0.56  # partial match(1): HSSSSMSSSLSNSFN
% 0.96/0.56  # Preprocessing class: HSSSSMSSMLSNSFN.
% 0.96/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.96/0.56  # No SInE strategy applied
% 0.96/0.56  # Search class: HGHNF-FFMM11-SSFSMFNN
% 0.96/0.56  # partial match(3): HGHNF-FFMF11-SHSSMFNN
% 0.96/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.96/0.56  # Starting new_ho_10_cnf2 with 811s (1) cores
% 0.96/0.56  # Starting ho_unfolding_3 with 151s (1) cores
% 0.96/0.56  # Starting new_ho_9 with 136s (1) cores
% 0.96/0.56  # Starting post_as_ho4 with 136s (1) cores
% 0.96/0.56  # Starting post_as_ho1 with 136s (1) cores
% 0.96/0.56  # ho_unfolding_3 with pid 626 completed with status 0
% 0.96/0.56  # Result found by ho_unfolding_3
% 0.96/0.56  # partial match(1): HSSSSMSSSLSNSFN
% 0.96/0.56  # Preprocessing class: HSSSSMSSMLSNSFN.
% 0.96/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.96/0.56  # No SInE strategy applied
% 0.96/0.56  # Search class: HGHNF-FFMM11-SSFSMFNN
% 0.96/0.56  # partial match(3): HGHNF-FFMF11-SHSSMFNN
% 0.96/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.96/0.56  # Starting new_ho_10_cnf2 with 811s (1) cores
% 0.96/0.56  # Starting ho_unfolding_3 with 151s (1) cores
% 0.96/0.56  # Preprocessing time       : 0.001 s
% 0.96/0.56  # Presaturation interreduction done
% 0.96/0.56  
% 0.96/0.56  # Proof found!
% 0.96/0.56  # SZS status Theorem
% 0.96/0.56  # SZS output start CNFRefutation
% See solution above
% 0.96/0.56  # Parsed axioms                        : 30
% 0.96/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.96/0.56  # Initial clauses                      : 43
% 0.96/0.56  # Removed in clause preprocessing      : 15
% 0.96/0.56  # Initial clauses in saturation        : 28
% 0.96/0.56  # Processed clauses                    : 902
% 0.96/0.56  # ...of these trivial                  : 7
% 0.96/0.56  # ...subsumed                          : 288
% 0.96/0.56  # ...remaining for further processing  : 607
% 0.96/0.56  # Other redundant clauses eliminated   : 0
% 0.96/0.56  # Clauses deleted for lack of memory   : 0
% 0.96/0.56  # Backward-subsumed                    : 53
% 0.96/0.56  # Backward-rewritten                   : 82
% 0.96/0.56  # Generated clauses                    : 4416
% 0.96/0.56  # ...of the previous two non-redundant : 2519
% 0.96/0.56  # ...aggressively subsumed             : 0
% 0.96/0.56  # Contextual simplify-reflections      : 61
% 0.96/0.56  # Paramodulations                      : 4416
% 0.96/0.56  # Factorizations                       : 0
% 0.96/0.56  # NegExts                              : 0
% 0.96/0.56  # Equation resolutions                 : 0
% 0.96/0.56  # Disequality decompositions           : 0
% 0.96/0.56  # Total rewrite steps                  : 3653
% 0.96/0.56  # ...of those cached                   : 3611
% 0.96/0.56  # Propositional unsat checks           : 0
% 0.96/0.56  #    Propositional check models        : 0
% 0.96/0.56  #    Propositional check unsatisfiable : 0
% 0.96/0.56  #    Propositional clauses             : 0
% 0.96/0.56  #    Propositional clauses after purity: 0
% 0.96/0.56  #    Propositional unsat core size     : 0
% 0.96/0.56  #    Propositional preprocessing time  : 0.000
% 0.96/0.56  #    Propositional encoding time       : 0.000
% 0.96/0.56  #    Propositional solver time         : 0.000
% 0.96/0.56  #    Success case prop preproc time    : 0.000
% 0.96/0.56  #    Success case prop encoding time   : 0.000
% 0.96/0.56  #    Success case prop solver time     : 0.000
% 0.96/0.56  # Current number of processed clauses  : 444
% 0.96/0.56  #    Positive orientable unit clauses  : 50
% 0.96/0.56  #    Positive unorientable unit clauses: 0
% 0.96/0.56  #    Negative unit clauses             : 7
% 0.96/0.56  #    Non-unit-clauses                  : 387
% 0.96/0.56  # Current number of unprocessed clauses: 1606
% 0.96/0.56  # ...number of literals in the above   : 7369
% 0.96/0.56  # Current number of archived formulas  : 0
% 0.96/0.56  # Current number of archived clauses   : 163
% 0.96/0.56  # Clause-clause subsumption calls (NU) : 44812
% 0.96/0.56  # Rec. Clause-clause subsumption calls : 16945
% 0.96/0.56  # Non-unit clause-clause subsumptions  : 391
% 0.96/0.56  # Unit Clause-clause subsumption calls : 1433
% 0.96/0.56  # Rewrite failures with RHS unbound    : 0
% 0.96/0.56  # BW rewrite match attempts            : 23
% 0.96/0.56  # BW rewrite match successes           : 7
% 0.96/0.56  # Condensation attempts                : 902
% 0.96/0.56  # Condensation successes               : 0
% 0.96/0.56  # Termbank termtop insertions          : 105788
% 0.96/0.56  # Search garbage collected termcells   : 786
% 0.96/0.56  
% 0.96/0.56  # -------------------------------------------------
% 0.96/0.56  # User time                : 0.127 s
% 0.96/0.56  # System time              : 0.007 s
% 0.96/0.56  # Total time               : 0.134 s
% 0.96/0.56  # Maximum resident set size: 1952 pages
% 0.96/0.56  
% 0.96/0.56  # -------------------------------------------------
% 0.96/0.56  # User time                : 0.633 s
% 0.96/0.56  # System time              : 0.049 s
% 0.96/0.56  # Total time               : 0.682 s
% 0.96/0.56  # Maximum resident set size: 1740 pages
% 0.96/0.56  % E---3.1 exiting
% 0.96/0.56  % E exiting
%------------------------------------------------------------------------------