TSTP Solution File: GEO172+2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 20:06:02 EDT 2024
% Result : Theorem 123.59s 22.43s
% Output : Refutation 123.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 168 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 508 ( 48 ~; 70 |; 8 &; 366 @)
% ( 0 <=>; 16 =>; 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 : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 0 ^ 96 !; 1 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(convergent_lines_type,type,
convergent_lines: $i > $i > $o ).
thf(apart_point_and_line_type,type,
apart_point_and_line: $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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(15,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)],[2]) ).
thf(16,plain,
distinct_points @ sk3 @ ( intersection_point @ sk1 @ sk2 ),
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/sandbox/benchmark/theBenchmark.p',apart4) ).
thf(29,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(30,plain,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ! [C: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ),
inference(miniscope,[status(thm)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( distinct_points @ A @ B )
| ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ),
inference(cnf,[status(esa)],[30]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C )
| ( ( distinct_points @ sk3 @ ( intersection_point @ sk1 @ sk2 ) )
!= ( distinct_points @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,31]) ).
thf(64,plain,
! [A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk3 )),bind(B,$thf( intersection_point @ sk1 @ sk2 )),bind(C,$thf( C ))]]) ).
thf(71,plain,
! [A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A ) ),
inference(simp,[status(thm)],[64]) ).
thf(78,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ B @ D )
| ( distinct_points @ C @ D )
| ( ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A )
!= ( distinct_points @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[71,31]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
| ( distinct_points @ A @ B ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( A )),bind(B,$thf( intersection_point @ sk1 @ sk2 )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
| ( distinct_points @ A @ B ) ),
inference(simp,[status(thm)],[79]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( distinct_points @ sk3 @ A )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
| ( ( distinct_points @ A @ B )
!= ( distinct_points @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[84]) ).
thf(152,plain,
( ( distinct_points @ sk3 @ sk3 )
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(3,axiom,
! [A: $i] :
~ ( distinct_points @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(20,plain,
! [A: $i] :
~ ( distinct_points @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
~ ? [A: $i] : ( distinct_points @ A @ A ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [A: $i] :
~ ( distinct_points @ A @ A ),
inference(cnf,[status(esa)],[21]) ).
thf(165,plain,
( $false
| ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 ) ),
inference(rewrite,[status(thm)],[152,22]) ).
thf(166,plain,
distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3,
inference(simp,[status(thm)],[165]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ( distinct_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( convergent_lines @ A @ B )
| ( distinct_lines @ A @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( distinct_lines @ A @ B )
| ( ( convergent_lines @ sk1 @ sk2 )
!= ( convergent_lines @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,55]) ).
thf(91,plain,
distinct_lines @ sk1 @ sk2,
inference(pattern_uni,[status(thm)],[90:[bind(A,$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/sandbox/benchmark/theBenchmark.p',cu1) ).
thf(46,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(47,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)],[46]) ).
thf(758,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)],[91,47]) ).
thf(759,plain,
! [B: $i,A: $i] :
( ~ ( distinct_points @ A @ B )
| ( apart_point_and_line @ A @ sk1 )
| ( apart_point_and_line @ A @ sk2 )
| ( apart_point_and_line @ B @ sk1 )
| ( apart_point_and_line @ B @ sk2 ) ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk2 ))]]) ).
thf(48121,plain,
! [B: $i,A: $i] :
( ( apart_point_and_line @ A @ sk1 )
| ( apart_point_and_line @ A @ sk2 )
| ( apart_point_and_line @ B @ sk1 )
| ( apart_point_and_line @ B @ sk2 )
| ( ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 )
!= ( distinct_points @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[166,759]) ).
thf(48122,plain,
( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
| ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
| ( apart_point_and_line @ sk3 @ sk1 )
| ( apart_point_and_line @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[48121:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(17,plain,
~ ( apart_point_and_line @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[15]) ).
thf(18,plain,
~ ( apart_point_and_line @ sk3 @ sk1 ),
inference(cnf,[status(esa)],[15]) ).
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/sandbox/benchmark/theBenchmark.p',con2) ).
thf(42,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(43,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)],[42]) ).
thf(45,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)],[43]) ).
thf(666,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)],[19,45]) ).
thf(667,plain,
! [A: $i] :
( ~ ( apart_point_and_line @ A @ sk1 )
| ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(682,plain,
! [A: $i] :
( ~ ( apart_point_and_line @ A @ sk1 )
| ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ~ ( apart_point_and_line @ A @ sk1 )
| ( ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) )
!= ( distinct_points @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[682,22]) ).
thf(1099,plain,
~ ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).
thf(44,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)],[43]) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( apart_point_and_line @ C @ B )
| ( distinct_points @ C @ ( intersection_point @ A @ B ) )
| ( ( convergent_lines @ sk1 @ sk2 )
!= ( convergent_lines @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,44]) ).
thf(518,plain,
! [A: $i] :
( ~ ( apart_point_and_line @ A @ sk2 )
| ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[517:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(522,plain,
! [A: $i] :
( ~ ( apart_point_and_line @ A @ sk2 )
| ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(622,plain,
! [B: $i,A: $i] :
( ~ ( apart_point_and_line @ A @ sk2 )
| ( ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) )
!= ( distinct_points @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[522,22]) ).
thf(623,plain,
~ ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).
thf(48333,plain,
( $false
| $false
| $false
| $false ),
inference(rewrite,[status(thm)],[48122,17,18,1099,623]) ).
thf(48334,plain,
$false,
inference(simp,[status(thm)],[48333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% 0.00/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 14:21:08 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.93/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.08 % [INFO] Parsing done (168ms).
% 1.34/1.10 % [INFO] Running in sequential loop mode.
% 1.80/1.43 % [INFO] nitpick registered as external prover.
% 1.80/1.44 % [INFO] Scanning for conjecture ...
% 2.04/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.08/1.56 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.08/1.59 % [INFO] Problem is first-order (TPTP FOF).
% 2.08/1.59 % [INFO] Type checking passed.
% 2.08/1.60 % [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 ...
% 123.59/22.42 % [INFO] Killing All external provers ...
% 123.59/22.42 % Time passed: 21961ms (effective reasoning time: 21321ms)
% 123.59/22.42 % 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)>
% 123.59/22.43 % Axioms used in derivation (5): con2, ceq3, apart4, apart1, cu1
% 123.59/22.43 % No. of inferences in proof: 54
% 123.59/22.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21961 ms resp. 21321 ms w/o parsing
% 123.64/22.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 123.64/22.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------