TSTP Solution File: GEO211+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO211+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Fri May 19 11:09:57 EDT 2023
% Result : Theorem 3.47s 1.82s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 53 ( 18 unt; 9 typ; 0 def)
% Number of atoms : 114 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 336 ( 16 ~; 32 |; 10 &; 250 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 103 ( 0 ^; 103 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(unorthogonal_lines_type,type,
unorthogonal_lines: $i > $i > $o ).
thf(distinct_points_type,type,
distinct_points: $i > $i > $o ).
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(intersection_point_type,type,
intersection_point: $i > $i > $i ).
thf(parallel_through_point_type,type,
parallel_through_point: $i > $i > $i ).
thf(line_connecting_type,type,
line_connecting: $i > $i > $i ).
thf(distinct_lines_type,type,
distinct_lines: $i > $i > $o ).
thf(orthogonal_through_point_type,type,
orthogonal_through_point: $i > $i > $i ).
thf(18,axiom,
! [A: $i] :
~ ( convergent_lines @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(69,plain,
! [A: $i] :
~ ( convergent_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ A @ B )
=> ( ( distinct_lines @ A @ C )
| ( distinct_lines @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ A @ B )
=> ( ( distinct_lines @ A @ C )
| ( distinct_lines @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( convergent_lines @ A @ B )
& ( unorthogonal_lines @ A @ B ) )
=> ( ( ( convergent_lines @ A @ C )
& ( unorthogonal_lines @ A @ C ) )
| ( ( convergent_lines @ B @ C )
& ( unorthogonal_lines @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(78,plain,
! [A: $i,B: $i,C: $i] :
( ( ( convergent_lines @ A @ B )
& ( unorthogonal_lines @ A @ B ) )
=> ( ( ( convergent_lines @ A @ C )
& ( unorthogonal_lines @ A @ C ) )
| ( ( convergent_lines @ B @ C )
& ( unorthogonal_lines @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
| ( unorthogonal_lines @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
| ( unorthogonal_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ B @ C )
=> ( ( apart_point_and_line @ A @ B )
| ( apart_point_and_line @ A @ C )
| ( convergent_lines @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ B @ C )
=> ( ( apart_point_and_line @ A @ B )
| ( apart_point_and_line @ A @ C )
| ( convergent_lines @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(53,plain,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( apart_point_and_line @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( apart_point_and_line @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( apart_point_and_line @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( apart_point_and_line @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(59,plain,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( convergent_lines @ ( parallel_through_point @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(35,plain,
! [A: $i,B: $i] :
~ ( convergent_lines @ ( parallel_through_point @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,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(48,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)],[10]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i] : ( unorthogonal_lines @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( unorthogonal_lines @ A @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i] : ( unorthogonal_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( distinct_lines @ B @ C )
=> ( ( apart_point_and_line @ A @ B )
| ( apart_point_and_line @ A @ C )
| ( unorthogonal_lines @ B @ D )
| ( unorthogonal_lines @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
thf(75,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( distinct_lines @ B @ C )
=> ( ( apart_point_and_line @ A @ B )
| ( apart_point_and_line @ A @ C )
| ( unorthogonal_lines @ B @ D )
| ( unorthogonal_lines @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( convergent_lines @ A @ B )
=> ( ( convergent_lines @ A @ C )
| ( convergent_lines @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
thf(62,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)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(42,plain,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,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(25,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)],[3]) ).
thf(4,axiom,
! [A: $i] :
~ ( distinct_points @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(28,plain,
! [A: $i] :
~ ( distinct_points @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( apart_point_and_line @ C @ ( line_connecting @ A @ B ) )
=> ( ( distinct_points @ C @ A )
& ( distinct_points @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( apart_point_and_line @ C @ ( line_connecting @ A @ B ) )
=> ( ( distinct_points @ C @ A )
& ( distinct_points @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( apart_point_and_line @ A @ B )
=> ( ( distinct_lines @ B @ C )
| ( apart_point_and_line @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( apart_point_and_line @ A @ B )
=> ( ( distinct_lines @ B @ C )
| ( apart_point_and_line @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ( distinct_lines @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ( distinct_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,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(31,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)],[5]) ).
thf(86,plain,
$false,
inference(e,[status(thm)],[69,56,78,84,65,53,45,59,35,48,72,23,75,62,42,25,28,38,50,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO211+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:42:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.04 % [INFO] Parsing done (150ms).
% 1.30/1.05 % [INFO] Running in sequential loop mode.
% 1.80/1.26 % [INFO] eprover registered as external prover.
% 1.80/1.26 % [INFO] cvc4 registered as external prover.
% 1.80/1.26 % [INFO] Scanning for conjecture ...
% 1.80/1.31 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 2.06/1.35 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.06/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.35/1.39 % [INFO] Type checking passed.
% 2.35/1.39 % [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 ...
% 3.47/1.82 % External prover 'e' found a proof!
% 3.47/1.82 % [INFO] Killing All external provers ...
% 3.47/1.82 % Time passed: 1304ms (effective reasoning time: 767ms)
% 3.47/1.82 % 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)>
% 3.47/1.82 % Axioms used in derivation (20): con2, ouo1, apart4, ceq2, oac1, apart5, apart1, occu1, con1, apart2, cp2, apart3, ooc1, ceq3, cup1, apart6, ooc2, cp1, ceq1, cu1
% 3.47/1.82 % No. of inferences in proof: 44
% 3.47/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1304 ms resp. 767 ms w/o parsing
% 3.83/1.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------