TSTP Solution File: GEG003^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : GEG003^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 19:56:58 EDT 2024

% Result   : Theorem 73.18s 11.12s
% Output   : Refutation 73.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  125 (  28 unt;  24 typ;   8 def)
%            Number of atoms       :  311 (  81 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  793 ( 130   ~;  96   |;  32   &; 513   @)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  27 usr;  15 con; 0-3 aty)
%            Number of variables   :  146 (  25   ^ 105   !;  16   ?; 146   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mforall_prop_def,definition,
    ( mforall_prop
    = ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
        ! [C: $i > $o] : ( A @ C @ B ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(reg_type,type,
    reg: $tType ).

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

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

thf(dc_def,definition,
    ( dc
    = ( ^ [A: reg,B: reg] :
          ~ ( c @ A @ B ) ) ) ).

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

thf(ec_def,definition,
    ( ec
    = ( ^ [A: reg,B: reg] :
          ( ( c @ A @ B )
          & ~ ( o @ A @ B ) ) ) ) ).

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

thf(tpp_def,definition,
    ( tpp
    = ( ^ [A: reg,B: reg] :
          ( ( pp @ A @ B )
          & ? [C: reg] :
              ( ( ec @ C @ A )
              & ( ec @ C @ B ) ) ) ) ) ).

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

thf(ntpp_def,definition,
    ( ntpp
    = ( ^ [A: reg,B: reg] :
          ( ( pp @ A @ B )
          & ~ ? [C: reg] :
                ( ( ec @ C @ A )
                & ( ec @ C @ B ) ) ) ) ) ).

thf(catalunya_type,type,
    catalunya: reg ).

thf(france_type,type,
    france: reg ).

thf(spain_type,type,
    spain: reg ).

thf(paris_type,type,
    paris: reg ).

thf(a_type,type,
    a: $i > $i > $o ).

thf(fool_type,type,
    fool: $i > $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: ( $i > $o ) > $i > $i ).

thf(sk4_type,type,
    sk4: reg ).

thf(sk5_type,type,
    sk5: reg ).

thf(sk8_type,type,
    sk8: reg > reg ).

thf(sk9_type,type,
    sk9: reg > reg ).

thf(1,conjecture,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] :
          ( ( dc @ catalunya @ paris )
          & ( dc @ spain @ paris ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mbox @ a
        @ ^ [A: $i] :
            ( ( dc @ catalunya @ paris )
            & ( dc @ spain @ paris ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(9,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ ( a @ A @ B )
        | ( ~ ( c @ catalunya @ paris )
          & ~ ( c @ spain @ paris ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ~ ( ~ ? [A: $i,B: $i] : ( a @ A @ B )
      | ( ~ ( c @ catalunya @ paris )
        & ~ ( c @ spain @ paris ) ) ),
    inference(miniscope,[status(thm)],[9]) ).

thf(12,plain,
    a @ sk1 @ sk2,
    inference(cnf,[status(esa)],[10]) ).

thf(6,axiom,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] : ( tpp @ catalunya @ spain ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(20,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a @ A @ B )
      | ( ! [C: reg] :
            ( ( c @ C @ catalunya )
           => ( c @ C @ spain ) )
        & ~ ! [C: reg] :
              ( ( c @ C @ spain )
             => ( c @ C @ catalunya ) )
        & ? [C: reg] :
            ( ( c @ C @ catalunya )
            & ~ ? [D: reg] :
                  ( ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ C ) )
                  & ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ catalunya ) ) )
            & ( c @ C @ spain )
            & ~ ? [D: reg] :
                  ( ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ C ) )
                  & ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ spain ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(21,plain,
    ( ~ ? [A: $i,B: $i] : ( a @ A @ B )
    | ( ! [A: reg] :
          ( ( c @ A @ catalunya )
         => ( c @ A @ spain ) )
      & ~ ! [A: reg] :
            ( ( c @ A @ spain )
           => ( c @ A @ catalunya ) )
      & ? [A: reg] :
          ( ( c @ A @ catalunya )
          & ~ ? [B: reg] :
                ( ! [C: reg] :
                    ( ( c @ C @ B )
                   => ( c @ C @ A ) )
                & ! [C: reg] :
                    ( ( c @ C @ B )
                   => ( c @ C @ catalunya ) ) )
          & ( c @ A @ spain )
          & ~ ? [B: reg] :
                ( ! [C: reg] :
                    ( ( c @ C @ B )
                   => ( c @ C @ A ) )
                & ! [C: reg] :
                    ( ( c @ C @ B )
                   => ( c @ C @ spain ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[20]) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a @ A @ B )
      | ~ ( c @ sk4 @ catalunya ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(68,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c @ sk4 @ catalunya )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,32]) ).

thf(69,plain,
    ~ ( c @ sk4 @ catalunya ),
    inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(30,plain,
    ! [C: reg,B: $i,A: $i] :
      ( ~ ( a @ A @ B )
      | ( c @ ( sk8 @ C ) @ C )
      | ( c @ ( sk9 @ C ) @ C ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(37,plain,
    ! [C: reg,B: $i,A: $i] :
      ( ~ ( a @ A @ B )
      | ( c @ ( sk8 @ C ) @ C )
      | ( c @ ( sk9 @ C ) @ C ) ),
    inference(simp,[status(thm)],[30]) ).

thf(3,axiom,
    ! [A: reg] : ( c @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_reflexive) ).

thf(13,plain,
    ! [A: reg] : ( c @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ! [A: reg] : ( c @ A @ A ),
    inference(cnf,[status(esa)],[13]) ).

thf(5,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ a @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).

thf(17,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( fool @ A @ C )
            | ( B @ C ) )
      | ! [C: $i] :
          ( ~ ( a @ A @ C )
          | ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(18,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( fool @ A @ ( sk3 @ B @ A ) )
      | ~ ( a @ A @ C )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(157,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( fool @ A @ ( sk3 @ B @ A ) )
      | ( B @ C )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[12,18]) ).

thf(158,plain,
    ! [A: $i > $o] :
      ( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
      | ( A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(195,plain,
    ! [A: $i > $o] :
      ( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
      | ( A @ sk2 ) ),
    inference(simp,[status(thm)],[158]) ).

thf(222,plain,
    ( ( fool @ sk1
      @ ( sk3
        @ ^ [A: $i] : $false
        @ sk1 ) )
    | $false ),
    inference(prim_subst,[status(thm)],[195:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(238,plain,
    ( fool @ sk1
    @ ( sk3
      @ ^ [A: $i] : $false
      @ sk1 ) ),
    inference(simp,[status(thm)],[222]) ).

thf(11,plain,
    ( ( c @ catalunya @ paris )
    | ( c @ spain @ paris ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(63,plain,
    ( ( c @ catalunya @ paris )
    | ( ( c @ spain @ paris )
     != ( c @ catalunya @ paris ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[11]) ).

thf(65,plain,
    ( ( c @ catalunya @ paris )
    | ( spain != catalunya )
    | ( paris != paris ) ),
    inference(simp,[status(thm)],[63]) ).

thf(66,plain,
    ( ( c @ catalunya @ paris )
    | ( spain != catalunya ) ),
    inference(simp,[status(thm)],[65]) ).

thf(4,axiom,
    ! [A: reg,B: reg] :
      ( ( c @ A @ B )
     => ( c @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_symmetric) ).

thf(15,plain,
    ! [A: reg,B: reg] :
      ( ( c @ A @ B )
     => ( c @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,plain,
    ! [B: reg,A: reg] :
      ( ~ ( c @ A @ B )
      | ( c @ B @ A ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(93,plain,
    ! [B: reg,A: reg] :
      ( ~ ( c @ A @ B )
      | ( ( c @ B @ A )
       != ( c @ sk4 @ catalunya ) ) ),
    inference(paramod_ordered,[status(thm)],[16,69]) ).

thf(94,plain,
    ~ ( c @ catalunya @ sk4 ),
    inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( catalunya )),bind(B,$thf( sk4 ))]]) ).

thf(108,plain,
    ( ( spain != catalunya )
    | ( ( c @ catalunya @ sk4 )
     != ( c @ catalunya @ paris ) ) ),
    inference(paramod_ordered,[status(thm)],[66,94]) ).

thf(113,plain,
    ( ( spain != catalunya )
    | ( catalunya != catalunya )
    | ( sk4 != paris ) ),
    inference(simp,[status(thm)],[108]) ).

thf(116,plain,
    ( ( spain != catalunya )
    | ( sk4 != paris ) ),
    inference(simp,[status(thm)],[113]) ).

thf(19,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ ( sk3 @ B @ A ) )
      | ~ ( a @ A @ C )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(263,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ ( sk3 @ B @ A ) )
      | ( B @ C )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[12,19]) ).

thf(264,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk3 @ A @ sk1 ) )
      | ( A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(331,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk3 @ A @ sk1 ) )
      | ( A @ sk2 ) ),
    inference(simp,[status(thm)],[264]) ).

thf(412,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A
            @ ( sk3
              @ ^ [B: $i] :
                  ~ ( A @ B )
              @ sk1 ) )
      | ~ ( A @ sk2 ) ),
    inference(prim_subst,[status(thm)],[331:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(451,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk2 )
      | ( A
        @ ( sk3
          @ ^ [B: $i] :
              ~ ( A @ B )
          @ sk1 ) ) ),
    inference(cnf,[status(esa)],[412]) ).

thf(452,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk2 )
      | ( A
        @ ( sk3
          @ ^ [B: $i] :
              ~ ( A @ B )
          @ sk1 ) ) ),
    inference(simp,[status(thm)],[451]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a @ A @ B )
      | ( c @ sk5 @ catalunya ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(470,plain,
    ! [B: $i,A: $i] :
      ( ( c @ sk5 @ catalunya )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,25]) ).

thf(471,plain,
    c @ sk5 @ catalunya,
    inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(84,plain,
    ! [C: reg,B: $i,A: $i] :
      ( ( c @ ( sk8 @ C ) @ C )
      | ( c @ ( sk9 @ C ) @ C )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,37]) ).

thf(85,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( c @ ( sk9 @ A ) @ A ) ),
    inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(90,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( c @ ( sk9 @ A ) @ A ) ),
    inference(simp,[status(thm)],[85]) ).

thf(137,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( ( c @ ( sk9 @ A ) @ A )
       != ( c @ catalunya @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[90,94]) ).

thf(140,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( ( sk9 @ A )
       != catalunya )
      | ( A != sk4 ) ),
    inference(simp,[status(thm)],[137]) ).

thf(145,plain,
    ( ( c @ ( sk8 @ sk4 ) @ sk4 )
    | ( ( sk9 @ sk4 )
     != catalunya ) ),
    inference(simp,[status(thm)],[140]) ).

thf(204,plain,
    ! [B: reg,A: reg] :
      ( ( ( sk9 @ sk4 )
       != catalunya )
      | ( c @ B @ A )
      | ( ( c @ ( sk8 @ sk4 ) @ sk4 )
       != ( c @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[145,16]) ).

thf(205,plain,
    ( ( ( sk9 @ sk4 )
     != catalunya )
    | ( c @ sk4 @ ( sk8 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( sk8 @ sk4 )),bind(B,$thf( sk4 ))]]) ).

thf(78,plain,
    ( ( c @ catalunya @ paris )
    | ( ( c @ sk4 @ catalunya )
     != ( c @ spain @ paris ) ) ),
    inference(paramod_ordered,[status(thm)],[11,69]) ).

thf(81,plain,
    ( ( c @ catalunya @ paris )
    | ( sk4 != spain )
    | ( paris != catalunya ) ),
    inference(simp,[status(thm)],[78]) ).

thf(404,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( A @ sk2 )
      | ( B @ sk2 )
      | ( ( fool @ sk1 @ ( sk3 @ A @ sk1 ) )
       != ( B @ ( sk3 @ B @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[195,331]) ).

thf(417,plain,
    ( ( fool @ sk1 @ sk2 )
    | ( fool @ sk1 @ sk2 ) ),
    inference(pre_uni,[status(thm)],[404:[bind(A,$thf( fool @ sk1 )),bind(B,$thf( fool @ sk1 ))]]) ).

thf(455,plain,
    fool @ sk1 @ sk2,
    inference(simp,[status(thm)],[417]) ).

thf(103,plain,
    ! [B: reg,A: reg] :
      ( ( c @ catalunya @ paris )
      | ( c @ B @ A )
      | ( ( c @ spain @ paris )
       != ( c @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[11,16]) ).

thf(104,plain,
    ( ( c @ catalunya @ paris )
    | ( c @ paris @ spain ) ),
    inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( spain )),bind(B,$thf( paris ))]]) ).

thf(76,plain,
    ! [A: reg] :
      ( ( c @ A @ A )
     != ( c @ sk4 @ catalunya ) ),
    inference(paramod_ordered,[status(thm)],[14,69]) ).

thf(79,plain,
    ! [A: reg] :
      ( ( A != sk4 )
      | ( A != catalunya ) ),
    inference(simp,[status(thm)],[76]) ).

thf(82,plain,
    sk4 != catalunya,
    inference(simp,[status(thm)],[79]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a @ A @ B )
      | ( c @ sk5 @ spain ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(613,plain,
    ! [B: $i,A: $i] :
      ( ( c @ sk5 @ spain )
      | ( ( a @ sk1 @ sk2 )
       != ( a @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,28]) ).

thf(614,plain,
    c @ sk5 @ spain,
    inference(pattern_uni,[status(thm)],[613:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(134,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( ( c @ ( sk9 @ A ) @ A )
       != ( c @ sk4 @ catalunya ) ) ),
    inference(paramod_ordered,[status(thm)],[90,69]) ).

thf(139,plain,
    ! [A: reg] :
      ( ( c @ ( sk8 @ A ) @ A )
      | ( ( sk9 @ A )
       != sk4 )
      | ( A != catalunya ) ),
    inference(simp,[status(thm)],[134]) ).

thf(144,plain,
    ( ( c @ ( sk8 @ catalunya ) @ catalunya )
    | ( ( sk9 @ catalunya )
     != sk4 ) ),
    inference(simp,[status(thm)],[139]) ).

thf(196,plain,
    ( ( ( sk9 @ catalunya )
     != sk4 )
    | ( ( c @ ( sk8 @ catalunya ) @ catalunya )
     != ( c @ sk4 @ catalunya ) ) ),
    inference(paramod_ordered,[status(thm)],[144,69]) ).

thf(200,plain,
    ( ( ( sk9 @ catalunya )
     != sk4 )
    | ( ( sk8 @ catalunya )
     != sk4 )
    | ( catalunya != catalunya ) ),
    inference(simp,[status(thm)],[196]) ).

thf(202,plain,
    ( ( ( sk9 @ catalunya )
     != sk4 )
    | ( ( sk8 @ catalunya )
     != sk4 ) ),
    inference(simp,[status(thm)],[200]) ).

thf(482,plain,
    ! [B: reg,A: reg] :
      ( ( c @ B @ A )
      | ( ( c @ sk5 @ catalunya )
       != ( c @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[471,16]) ).

thf(483,plain,
    c @ catalunya @ sk5,
    inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( sk5 )),bind(B,$thf( catalunya ))]]) ).

thf(197,plain,
    ! [B: reg,A: reg] :
      ( ( ( sk9 @ catalunya )
       != sk4 )
      | ( c @ B @ A )
      | ( ( c @ ( sk8 @ catalunya ) @ catalunya )
       != ( c @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[144,16]) ).

thf(198,plain,
    ( ( ( sk9 @ catalunya )
     != sk4 )
    | ( c @ catalunya @ ( sk8 @ catalunya ) ) ),
    inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( sk8 @ catalunya )),bind(B,$thf( catalunya ))]]) ).

thf(479,plain,
    ( ( c @ sk5 @ catalunya )
   != ( c @ sk4 @ catalunya ) ),
    inference(paramod_ordered,[status(thm)],[471,69]) ).

thf(487,plain,
    ( ( sk5 != sk4 )
    | ( catalunya != catalunya ) ),
    inference(simp,[status(thm)],[479]) ).

thf(490,plain,
    sk5 != sk4,
    inference(simp,[status(thm)],[487]) ).

thf(206,plain,
    ( ( ( sk9 @ sk4 )
     != catalunya )
    | ( ( c @ ( sk8 @ sk4 ) @ sk4 )
     != ( c @ catalunya @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[145,94]) ).

thf(208,plain,
    ( ( ( sk9 @ sk4 )
     != catalunya )
    | ( ( sk8 @ sk4 )
     != catalunya )
    | ( sk4 != sk4 ) ),
    inference(simp,[status(thm)],[206]) ).

thf(209,plain,
    ( ( ( sk9 @ sk4 )
     != catalunya )
    | ( ( sk8 @ sk4 )
     != catalunya ) ),
    inference(simp,[status(thm)],[208]) ).

thf(8,axiom,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] : ( ntpp @ paris @ france ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(50,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a @ A @ B )
      | ( ! [C: reg] :
            ( ( c @ C @ paris )
           => ( c @ C @ france ) )
        & ~ ! [C: reg] :
              ( ( c @ C @ france )
             => ( c @ C @ paris ) )
        & ~ ? [C: reg] :
              ( ( c @ C @ paris )
              & ~ ? [D: reg] :
                    ( ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ C ) )
                    & ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ paris ) ) )
              & ( c @ C @ france )
              & ~ ? [D: reg] :
                    ( ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ C ) )
                    & ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ france ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(150,plain,
    ( ( sk4 != spain )
    | ( paris != catalunya )
    | ( ( c @ catalunya @ sk4 )
     != ( c @ catalunya @ paris ) ) ),
    inference(paramod_ordered,[status(thm)],[81,94]) ).

thf(152,plain,
    ( ( sk4 != spain )
    | ( paris != catalunya )
    | ( catalunya != catalunya )
    | ( sk4 != paris ) ),
    inference(simp,[status(thm)],[150]) ).

thf(154,plain,
    ( ( sk4 != spain )
    | ( paris != catalunya )
    | ( sk4 != paris ) ),
    inference(simp,[status(thm)],[152]) ).

thf(7,axiom,
    ( mvalid
    @ ( mbox @ fool
      @ ^ [A: $i] : ( ec @ spain @ france ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(43,plain,
    ! [A: $i,B: $i] :
      ( ~ ( fool @ A @ B )
      | ( ( c @ spain @ france )
        & ~ ? [C: reg] :
              ( ! [D: reg] :
                  ( ( c @ D @ C )
                 => ( c @ D @ spain ) )
              & ! [D: reg] :
                  ( ( c @ D @ C )
                 => ( c @ D @ france ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(99,plain,
    ! [B: reg,A: reg] :
      ( ( spain != catalunya )
      | ( c @ B @ A )
      | ( ( c @ catalunya @ paris )
       != ( c @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[66,16]) ).

thf(100,plain,
    ( ( spain != catalunya )
    | ( c @ paris @ catalunya ) ),
    inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( catalunya )),bind(B,$thf( paris ))]]) ).

thf(26295,plain,
    $false,
    inference(e,[status(thm)],[69,37,14,20,238,116,452,9,471,13,205,17,81,455,18,104,82,19,15,614,202,12,144,483,66,198,490,209,145,50,331,16,154,11,43,195,94,90,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEG003^1 : TPTP v8.2.0. Released v4.1.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n028.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sat May 18 21:54:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.83/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.99  % [INFO] 	 Parsing done (145ms). 
% 1.23/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.83/1.20  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 2.30/1.33  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 2.30/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.30/1.34  % [INFO] 	 Type checking passed. 
% 2.30/1.34  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 73.18/11.11  % External prover 'e' found a proof!
% 73.18/11.11  % [INFO] 	 Killing All external provers ... 
% 73.18/11.12  % Time passed: 10597ms (effective reasoning time: 10110ms)
% 73.18/11.12  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 73.18/11.12  % Axioms used in derivation (6): ax1, ax2, c_symmetric, i_axiom_for_fool_a, ax3, c_reflexive
% 73.18/11.12  % No. of inferences in proof: 93
% 73.18/11.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10597 ms resp. 10110 ms w/o parsing
% 73.18/11.16  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 73.18/11.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------