TSTP Solution File: GEO201+2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GEO201+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 20:06:14 EDT 2024

% Result   : Theorem 213.94s 32.99s
% Output   : Refutation 214.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   85 (  17 unt;   7 typ;   0 def)
%            Number of atoms       :  234 (  16 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  767 (  63   ~; 103   |;   2   &; 580   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  135 (   0   ^ 133   !;   2   ?; 135   :)

% Comments : 
%------------------------------------------------------------------------------
thf(convergent_lines_type,type,
    convergent_lines: $i > $i > $o ).

thf(distinct_points_type,type,
    distinct_points: $i > $i > $o ).

thf(intersection_point_type,type,
    intersection_point: $i > $i > $i ).

thf(distinct_lines_type,type,
    distinct_lines: $i > $i > $o ).

thf(apart_point_and_line_type,type,
    apart_point_and_line: $i > $i > $o ).

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ~ ( distinct_points @ ( intersection_point @ A @ B ) @ ( intersection_point @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( convergent_lines @ A @ B )
       => ~ ( distinct_points @ ( intersection_point @ A @ B ) @ ( intersection_point @ B @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(15,plain,
    ~ ! [A: $i,B: $i] :
        ( ( convergent_lines @ A @ B )
       => ~ ( distinct_points @ ( intersection_point @ A @ B ) @ ( intersection_point @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,plain,
    distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ ( intersection_point @ sk2 @ sk1 ),
    inference(cnf,[status(esa)],[15]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( distinct_points @ A @ B )
     => ( ( distinct_points @ A @ C )
        | ( distinct_points @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).

thf(27,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( distinct_points @ A @ B )
     => ( ( distinct_points @ A @ C )
        | ( distinct_points @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ( ( distinct_points @ A @ B )
     => ! [C: $i] :
          ( ( distinct_points @ A @ C )
          | ( distinct_points @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[27]) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( distinct_points @ A @ C )
      | ( distinct_points @ B @ C ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(3,axiom,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).

thf(18,plain,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(19,plain,
    ~ ? [A: $i] : ( distinct_points @ A @ A ),
    inference(miniscope,[status(thm)],[18]) ).

thf(20,plain,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    inference(cnf,[status(esa)],[19]) ).

thf(61,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( distinct_points @ B @ C )
      | ( ( distinct_points @ A @ C )
       != ( distinct_points @ D @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[29,20]) ).

thf(62,plain,
    ! [B: $i,A: $i] :
      ( ~ ( distinct_points @ B @ A )
      | ( distinct_points @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(75,plain,
    ! [B: $i,A: $i] :
      ( ~ ( distinct_points @ B @ A )
      | ( distinct_points @ A @ B ) ),
    inference(simp,[status(thm)],[62]) ).

thf(179,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_points @ A @ B )
      | ( ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ ( intersection_point @ sk2 @ sk1 ) )
       != ( distinct_points @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[16,75]) ).

thf(180,plain,
    distinct_points @ ( intersection_point @ sk2 @ sk1 ) @ ( intersection_point @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( intersection_point @ sk2 @ sk1 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

thf(17,plain,
    convergent_lines @ sk1 @ sk2,
    inference(cnf,[status(esa)],[15]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ( distinct_lines @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).

thf(52,plain,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ( distinct_lines @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ( distinct_lines @ A @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(88,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_lines @ A @ B )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[17,53]) ).

thf(89,plain,
    distinct_lines @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( distinct_points @ A @ B )
        & ( distinct_lines @ C @ D ) )
     => ( ( apart_point_and_line @ A @ C )
        | ( apart_point_and_line @ A @ D )
        | ( apart_point_and_line @ B @ C )
        | ( apart_point_and_line @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).

thf(44,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( distinct_points @ A @ B )
        & ( distinct_lines @ C @ D ) )
     => ( ( apart_point_and_line @ A @ C )
        | ( apart_point_and_line @ A @ D )
        | ( apart_point_and_line @ B @ C )
        | ( apart_point_and_line @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(45,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ~ ( distinct_lines @ C @ D )
      | ( apart_point_and_line @ A @ C )
      | ( apart_point_and_line @ A @ D )
      | ( apart_point_and_line @ B @ C )
      | ( apart_point_and_line @ B @ D ) ),
    inference(cnf,[status(esa)],[44]) ).

thf(573,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( apart_point_and_line @ A @ C )
      | ( apart_point_and_line @ A @ D )
      | ( apart_point_and_line @ B @ C )
      | ( apart_point_and_line @ B @ D )
      | ( ( distinct_lines @ sk1 @ sk2 )
       != ( distinct_lines @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[89,45]) ).

thf(574,plain,
    ! [B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( apart_point_and_line @ A @ sk1 )
      | ( apart_point_and_line @ A @ sk2 )
      | ( apart_point_and_line @ B @ sk1 )
      | ( apart_point_and_line @ B @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk2 ))]]) ).

thf(52103,plain,
    ! [B: $i,A: $i] :
      ( ( apart_point_and_line @ A @ sk1 )
      | ( apart_point_and_line @ A @ sk2 )
      | ( apart_point_and_line @ B @ sk1 )
      | ( apart_point_and_line @ B @ sk2 )
      | ( ( distinct_points @ ( intersection_point @ sk2 @ sk1 ) @ ( intersection_point @ sk1 @ sk2 ) )
       != ( distinct_points @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[180,574]) ).

thf(52104,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk2 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[52103:[bind(A,$thf( intersection_point @ sk2 @ sk1 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( convergent_lines @ A @ C )
        | ( convergent_lines @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).

thf(33,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( convergent_lines @ A @ C )
        | ( convergent_lines @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(34,plain,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ! [C: $i] :
          ( ( convergent_lines @ A @ C )
          | ( convergent_lines @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[33]) ).

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ( convergent_lines @ A @ C )
      | ( convergent_lines @ B @ C ) ),
    inference(cnf,[status(esa)],[34]) ).

thf(5,axiom,
    ! [A: $i] :
      ~ ( convergent_lines @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).

thf(24,plain,
    ! [A: $i] :
      ~ ( convergent_lines @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(25,plain,
    ~ ? [A: $i] : ( convergent_lines @ A @ A ),
    inference(miniscope,[status(thm)],[24]) ).

thf(26,plain,
    ! [A: $i] :
      ~ ( convergent_lines @ A @ A ),
    inference(cnf,[status(esa)],[25]) ).

thf(300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ( convergent_lines @ B @ C )
      | ( ( convergent_lines @ A @ C )
       != ( convergent_lines @ D @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[35,26]) ).

thf(301,plain,
    ! [B: $i,A: $i] :
      ( ~ ( convergent_lines @ B @ A )
      | ( convergent_lines @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(312,plain,
    ! [B: $i,A: $i] :
      ( ~ ( convergent_lines @ B @ A )
      | ( convergent_lines @ A @ B ) ),
    inference(simp,[status(thm)],[301]) ).

thf(2081,plain,
    ! [B: $i,A: $i] :
      ( ( convergent_lines @ A @ B )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[17,312]) ).

thf(2082,plain,
    convergent_lines @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[2081:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( ( apart_point_and_line @ C @ A )
          | ( apart_point_and_line @ C @ B ) )
       => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).

thf(40,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( ( apart_point_and_line @ C @ A )
          | ( apart_point_and_line @ C @ B ) )
       => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(41,plain,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ! [C: $i] :
          ( ( ( apart_point_and_line @ C @ A )
            | ( apart_point_and_line @ C @ B ) )
         => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[40]) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(2136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk2 @ sk1 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2082,43]) ).

thf(2137,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[2136:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(2150,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[2137]) ).

thf(53572,plain,
    ! [A: $i] :
      ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
      | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
      | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) )
      | ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk2 )
       != ( apart_point_and_line @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[52104,2150]) ).

thf(53573,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
    | ( distinct_points @ ( intersection_point @ sk2 @ sk1 ) @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[53572:[bind(A,$thf( intersection_point @ sk2 @ sk1 ))]]) ).

thf(61398,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[53573,20]) ).

thf(61399,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 ) ),
    inference(simp,[status(thm)],[61398]) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(2116,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk2 @ sk1 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2082,42]) ).

thf(2117,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[2116:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(2148,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[2117]) ).

thf(61560,plain,
    ! [A: $i] :
      ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
      | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk2 @ sk1 ) )
      | ( ( apart_point_and_line @ ( intersection_point @ sk2 @ sk1 ) @ sk1 )
       != ( apart_point_and_line @ A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[61399,2148]) ).

thf(61561,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
    | ( distinct_points @ ( intersection_point @ sk2 @ sk1 ) @ ( intersection_point @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[61560:[bind(A,$thf( intersection_point @ sk2 @ sk1 ))]]) ).

thf(73582,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[61561,20]) ).

thf(73583,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 ) ),
    inference(simp,[status(thm)],[73582]) ).

thf(222,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ D @ E )
      | ( ( distinct_points @ C @ ( intersection_point @ A @ B ) )
       != ( distinct_points @ E @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[42,75]) ).

thf(223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ B @ C )
      | ~ ( apart_point_and_line @ A @ C )
      | ( distinct_points @ ( intersection_point @ B @ C ) @ A ) ),
    inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( intersection_point @ F @ G )),bind(E,$thf( C ))]]) ).

thf(228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ B @ C )
      | ~ ( apart_point_and_line @ A @ C )
      | ( distinct_points @ ( intersection_point @ B @ C ) @ A ) ),
    inference(simp,[status(thm)],[223]) ).

thf(7996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ A @ C )
      | ( distinct_points @ ( intersection_point @ B @ C ) @ A )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[17,228]) ).

thf(7997,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A ) ),
    inference(pattern_uni,[status(thm)],[7996:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).

thf(73619,plain,
    ! [A: $i] :
      ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A )
      | ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
       != ( apart_point_and_line @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[73583,7997]) ).

thf(73620,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[73619:[bind(A,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

thf(75498,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[73620,20]) ).

thf(75499,plain,
    apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1,
    inference(simp,[status(thm)],[75498]) ).

thf(391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[17,43]) ).

thf(392,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(398,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(simp,[status(thm)],[392]) ).

thf(75628,plain,
    ! [A: $i] :
      ( ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) )
      | ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
       != ( apart_point_and_line @ A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[75499,398]) ).

thf(75629,plain,
    distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ ( intersection_point @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[75628:[bind(A,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

thf(76076,plain,
    $false,
    inference(rewrite,[status(thm)],[75629,20]) ).

thf(76077,plain,
    $false,
    inference(simp,[status(thm)],[76076]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GEO201+2 : TPTP v8.2.0. Released v3.3.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n010.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sun May 19 13:41:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.92/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/0.99  % [INFO] 	 Parsing done (121ms). 
% 1.26/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.70/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 1.86/1.29  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 1.86/1.31  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.09/1.31  % [INFO] 	 Type checking passed. 
% 2.09/1.32  % [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 ... 
% 213.94/32.99  % [INFO] 	 Killing All external provers ... 
% 213.94/32.99  % Time passed: 32452ms (effective reasoning time: 31986ms)
% 213.94/32.99  % 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)>
% 213.94/32.99  % Axioms used in derivation (7): apart3, con2, ceq3, apart6, apart4, apart1, cu1
% 213.94/32.99  % No. of inferences in proof: 78
% 213.94/32.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32452 ms resp. 31986 ms w/o parsing
% 214.10/33.06  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 214.10/33.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------