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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEU003+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:37:26 AM UTC 2026

% Result   : Theorem 33.47s 7.69s
% Output   : Refutation 29.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   76 (  13 unt;   0 typ;   0 def)
%            Number of atoms       :  227 (  15 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  571 (  30   ~;   2   |;  82   &; 390   @)
%                                         (   5 <=>;  62  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :  126 (   0   ^; 103   !;  23   ?; 126   :)

% Comments : 
%------------------------------------------------------------------------------
thf(relation_decl,type,
    relation: $i > $o ).

thf(function_decl,type,
    function: $i > $o ).

thf(relation_dom_decl,type,
    relation_dom: $i > $i ).

thf(relation_composition_decl,type,
    relation_composition: $i > $i > $i ).

thf(subset_decl,type,
    subset: $i > $i > $o ).

thf(relation_rng_decl,type,
    relation_rng: $i > $i ).

thf(empty_decl,type,
    empty: $i > $o ).

thf(in_decl,type,
    in: $i > $i > $o ).

thf(element_decl,type,
    element: $i > $i > $o ).

thf(powerset_decl,type,
    powerset: $i > $i ).

thf(empty_set_decl,type,
    empty_set: $i ).

thf(relation_empty_yielding_decl,type,
    relation_empty_yielding: $i > $o ).

thf(apply_decl,type,
    apply: $i > $i > $i ).

thf(26,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A @ relation ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(115,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A @ relation ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ empty ) )
     => ( ( A @ ( B @ relation_composition ) @ relation )
        & ( A @ ( B @ relation_composition ) @ empty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).

thf(142,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ empty ) )
     => ( ( A @ ( B @ relation_composition ) @ relation )
        & ( A @ ( B @ relation_composition ) @ empty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( ( A @ relation )
        & ~ ( A @ empty ) )
     => ~ ( A @ relation_dom @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

thf(185,plain,
    ! [A: $i] :
      ( ( ( A @ relation )
        & ~ ( A @ empty ) )
     => ~ ( A @ relation_dom @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(4,axiom,
    ? [A: $i] : ( A @ empty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(52,plain,
    ? [A: $i] : ( A @ empty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( B @ ( A @ in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(57,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( B @ ( A @ in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(28,axiom,
    ( ( empty_set @ relation_empty_yielding )
    & ( empty_set @ relation )
    & ( empty_set @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).

thf(121,plain,
    ( ( empty_set @ relation_empty_yielding )
    & ( empty_set @ relation )
    & ( empty_set @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ element ) )
     => ( ( B @ ( A @ in ) )
        | ( B @ empty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(66,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ element ) )
     => ( ( B @ ( A @ in ) )
        | ( B @ empty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(72,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ( A @ function )
        & ( A @ relation ) )
     => ! [B: $i] :
          ( ( B
            = ( A @ relation_rng ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ in ) )
            <=> ? [D: $i] :
                  ( ( C
                    = ( D @ ( A @ apply ) ) )
                  & ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).

thf(158,plain,
    ! [A: $i] :
      ( ( ( A @ function )
        & ( A @ relation ) )
     => ! [B: $i] :
          ( ( ! [C: $i] :
                ( ( ? [D: $i] :
                      ( ( C
                        = ( D @ ( A @ apply ) ) )
                      & ( A @ relation_dom @ ( D @ in ) ) )
                 => ( B @ ( C @ in ) ) )
                & ( ( B @ ( C @ in ) )
                 => ? [D: $i] :
                      ( ( C
                        = ( D @ ( A @ apply ) ) )
                      & ( A @ relation_dom @ ( D @ in ) ) ) ) )
           => ( B
              = ( A @ relation_rng ) ) )
          & ( ( B
              = ( A @ relation_rng ) )
           => ! [C: $i] :
                ( ( ? [D: $i] :
                      ( ( C
                        = ( D @ ( A @ apply ) ) )
                      & ( A @ relation_dom @ ( D @ in ) ) )
                 => ( B @ ( C @ in ) ) )
                & ( ( B @ ( C @ in ) )
                 => ? [D: $i] :
                      ( ( C
                        = ( D @ ( A @ apply ) ) )
                      & ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( ( A @ relation_dom @ relation )
        & ( A @ relation_dom @ empty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

thf(146,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( ( A @ relation_dom @ relation )
        & ( A @ relation_dom @ empty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A @ function ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(100,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( A @ function ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(32,axiom,
    ? [A: $i] :
      ( ( A @ relation )
      & ( A @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(138,plain,
    ? [A: $i] :
      ( ( A @ relation )
      & ( A @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(18,axiom,
    ? [A: $i] :
      ( ( A @ relation_empty_yielding )
      & ( A @ relation ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).

thf(88,plain,
    ? [A: $i] :
      ( ( A @ relation_empty_yielding )
      & ( A @ relation ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ function )
        & ( B @ relation ) )
     => ! [C: $i] :
          ( ( ( C @ function )
            & ( C @ relation ) )
         => ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
          <=> ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
              & ( C @ relation_dom @ ( A @ in ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

thf(102,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ function )
        & ( B @ relation ) )
     => ! [C: $i] :
          ( ( ( C @ function )
            & ( C @ relation ) )
         => ( ( ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
                & ( C @ relation_dom @ ( A @ in ) ) )
             => ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) ) )
            & ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
             => ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
                & ( C @ relation_dom @ ( A @ in ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ( B @ ( A @ element ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(60,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ( B @ ( A @ element ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(27,axiom,
    ? [A: $i] :
      ( ( A @ relation )
      & ~ ( A @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(117,plain,
    ? [A: $i] :
      ( ( A @ relation )
      & ~ ( A @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( A @ empty )
     => ( ( A @ relation_rng @ relation )
        & ( A @ relation_rng @ empty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

thf(92,plain,
    ! [A: $i] :
      ( ( A @ empty )
     => ( ( A @ relation_rng @ relation )
        & ( A @ relation_rng @ empty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(9,axiom,
    empty_set @ empty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(65,plain,
    empty_set @ empty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ empty ) )
     => ( ( B @ ( A @ relation_composition ) @ relation )
        & ( B @ ( A @ relation_composition ) @ empty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).

thf(109,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ empty ) )
     => ( ( B @ ( A @ relation_composition ) @ relation )
        & ( B @ ( A @ relation_composition ) @ empty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ~ ( A @ ( B @ in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(77,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ in ) )
     => ~ ( A @ ( B @ in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ function )
        & ( B @ relation )
        & ( A @ function )
        & ( A @ relation ) )
     => ( ( B @ ( A @ relation_composition ) @ function )
        & ( B @ ( A @ relation_composition ) @ relation ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

thf(96,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ function )
        & ( B @ relation )
        & ( A @ function )
        & ( A @ relation ) )
     => ( ( B @ ( A @ relation_composition ) @ function )
        & ( B @ ( A @ relation_composition ) @ relation ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(31,axiom,
    ( ( empty_set @ relation )
    & ( empty_set @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(134,plain,
    ( ( empty_set @ relation )
    & ( empty_set @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ powerset @ ( A @ element ) )
    <=> ( B @ ( A @ subset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(128,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ subset ) )
       => ( B @ powerset @ ( A @ element ) ) )
      & ( ( B @ powerset @ ( A @ element ) )
       => ( B @ ( A @ subset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ empty )
        & ( C @ powerset @ ( B @ element ) )
        & ( B @ ( A @ in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(54,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ empty )
        & ( C @ powerset @ ( B @ element ) )
        & ( B @ ( A @ in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ element ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(86,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ element ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(38,axiom,
    ? [A: $i] :
      ( ( A @ function )
      & ( A @ relation ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(187,plain,
    ? [A: $i] :
      ( ( A @ function )
      & ( A @ relation ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(25,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(113,plain,
    ! [A: $i] : ( A @ ( A @ subset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ( A @ function )
        & ( A @ relation ) )
     => ! [B: $i] :
          ( ( ( B @ function )
            & ( B @ relation ) )
         => ( ( ( A @ ( B @ relation_composition ) @ relation_dom )
              = ( B @ relation_dom ) )
           => ( A @ relation_dom @ ( B @ relation_rng @ subset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( A @ function )
          & ( A @ relation ) )
       => ! [B: $i] :
            ( ( ( B @ function )
              & ( B @ relation ) )
           => ( ( ( A @ ( B @ relation_composition ) @ relation_dom )
                = ( B @ relation_dom ) )
             => ( A @ relation_dom @ ( B @ relation_rng @ subset ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(39,plain,
    ~ ! [A: $i] :
        ( ( ( A @ function )
          & ( A @ relation ) )
       => ! [B: $i] :
            ( ( ( B @ function )
              & ( B @ relation ) )
           => ( ( ( A @ ( B @ relation_composition ) @ relation_dom )
                = ( B @ relation_dom ) )
             => ( A @ relation_dom @ ( B @ relation_rng @ subset ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( A != B )
        & ( A @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ empty )
        & ( A != B )
        & ( A @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ subset ) )
    <=> ! [C: $i] :
          ( ( A @ ( C @ in ) )
         => ( B @ ( C @ in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

thf(150,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) )
       => ( B @ ( A @ subset ) ) )
      & ( ( B @ ( A @ subset ) )
       => ! [C: $i] :
            ( ( A @ ( C @ in ) )
           => ( B @ ( C @ in ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ powerset @ ( B @ element ) )
        & ( B @ ( A @ in ) ) )
     => ( C @ ( A @ element ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(75,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ powerset @ ( B @ element ) )
        & ( B @ ( A @ in ) ) )
     => ( C @ ( A @ element ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(16,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ empty )
      & ( A @ powerset @ ( B @ element ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(82,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ empty )
      & ( A @ powerset @ ( B @ element ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ( A @ relation )
        & ~ ( A @ empty ) )
     => ~ ( A @ relation_rng @ empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

thf(107,plain,
    ! [A: $i] :
      ( ( ( A @ relation )
        & ~ ( A @ empty ) )
     => ~ ( A @ relation_rng @ empty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ relation ) )
     => ( B @ ( A @ relation_composition ) @ relation ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

thf(126,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ relation )
        & ( A @ relation ) )
     => ( B @ ( A @ relation_composition ) @ relation ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(15,axiom,
    ! [A: $i] :
      ~ ( A @ powerset @ empty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(79,plain,
    ! [A: $i] :
      ~ ( A @ powerset @ empty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ~ ( A @ empty )
     => ? [B: $i] :
          ( ~ ( B @ empty )
          & ( A @ powerset @ ( B @ element ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(68,plain,
    ! [A: $i] :
      ( ~ ( A @ empty )
     => ? [B: $i] :
          ( ~ ( B @ empty )
          & ( A @ powerset @ ( B @ element ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ? [A: $i] :
      ~ ( A @ empty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(62,plain,
    ? [A: $i] :
      ~ ( A @ empty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(16443,plain,
    $false,
    inference(e,[status(thm)],[115,142,185,52,57,121,66,72,158,146,100,138,88,102,60,117,92,65,109,77,96,134,128,54,86,187,113,39,48,150,75,82,107,126,79,68,62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU003+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.42  % Computer : n010.cluster.edu
% 0.13/0.42  % Model    : x86_64 x86_64
% 0.13/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42  % Memory   : 8046.5625MB
% 0.13/0.42  % OS       : Linux 6.8.0-71-generic
% 0.13/0.42  % CPULimit : 300
% 0.13/0.42  % WCLimit  : 300
% 0.13/0.42  % DateTime : Sat Sep 26 08:30:32 UTC 2026
% 0.13/0.43  % CPUTime  : 
% 0.13/0.43  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.36/1.23  % [INFO] 	 Parsing done (216ms). 
% 1.36/1.24  % [INFO] 	 Running in sequential loop mode. 
% 2.12/1.65  % [INFO] 	 eprover registered as external prover. 
% 2.12/1.66  % [INFO] 	 Scanning for conjecture ... 
% 2.35/1.77  % [INFO] 	 Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ... 
% 2.51/1.85  % [INFO] 	 Axiom selection finished. Selected 36 axioms (removed 0 axioms). 
% 2.75/1.91  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.75/1.91  % [INFO] 	 Type checking passed. 
% 2.75/1.92  % [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 ... 
% 33.47/7.69  % External prover 'e' found a proof!
% 33.47/7.69  % [INFO] 	 Killing All external provers ... 
% 33.47/7.69  % Time passed: 7122ms (effective reasoning time: 6439ms)
% 33.47/7.69  % 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)>
% 33.47/7.69  % Axioms used in derivation (36): fc9_relat_1, fc1_funct_1, cc1_relat_1, rc1_funct_1, t5_subset, t4_subset, fc5_relat_1, rc2_relat_1, fc6_relat_1, d5_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc10_relat_1, rc1_subset_1, t3_subset, existence_m1_subset_1, d3_tarski, rc1_relat_1, dt_k5_relat_1, reflexivity_r1_tarski, t21_funct_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 33.47/7.69  % No. of inferences in proof: 76
% 33.47/7.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7122 ms resp. 6439 ms w/o parsing
% 29.98/7.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.98/7.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------