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