TSTP Solution File: GEO218+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:10:00 EDT 2023
% Result : Theorem 3.64s 1.79s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 39
% Syntax : Number of formulae : 68 ( 13 unt; 12 typ; 0 def)
% Number of atoms : 152 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 467 ( 51 ~; 28 |; 26 &; 320 @)
% ( 3 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 129 ( 0 ^; 129 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(parallel_lines_type,type,
parallel_lines: $i > $i > $o ).
thf(orthogonal_lines_type,type,
orthogonal_lines: $i > $i > $o ).
thf(distinct_lines_type,type,
distinct_lines: $i > $i > $o ).
thf(equal_lines_type,type,
equal_lines: $i > $i > $o ).
thf(apart_point_and_line_type,type,
apart_point_and_line: $i > $i > $o ).
thf(unorthogonal_lines_type,type,
unorthogonal_lines: $i > $i > $o ).
thf(orthogonal_through_point_type,type,
orthogonal_through_point: $i > $i > $i ).
thf(parallel_through_point_type,type,
parallel_through_point: $i > $i > $i ).
thf(line_type,type,
line: $i > $o ).
thf(point_type,type,
point: $i > $o ).
thf(convergent_lines_type,type,
convergent_lines: $i > $i > $o ).
thf(intersection_point_type,type,
intersection_point: $i > $i > $i ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( point @ B ) )
=> ( line @ ( orthogonal_through_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orth1) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( point @ B ) )
=> ( line @ ( orthogonal_through_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( convergent_lines @ A @ B )
=> ( ( distinct_lines @ B @ C )
| ( convergent_lines @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( convergent_lines @ A @ B )
=> ( ( distinct_lines @ B @ C )
| ( convergent_lines @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( point @ B ) )
=> ( line @ ( parallel_through_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',par1) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( point @ B ) )
=> ( line @ ( parallel_through_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
thf(53,plain,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',ouo1) ).
thf(41,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)],[5]) ).
thf(17,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',ax6) ).
thf(73,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)],[17]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( ~ ( convergent_lines @ A @ B )
& ~ ( unorthogonal_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(64,plain,
! [A: $i,B: $i] :
~ ( ~ ( convergent_lines @ A @ B )
& ~ ( unorthogonal_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(44,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)],[6]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',oac1) ).
thf(76,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)],[18]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(95,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)],[25]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
=> ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( equal_lines @ A @ B )
<=> ~ ( distinct_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( equal_lines @ A @ B )
=> ~ ( distinct_lines @ A @ B ) )
& ( ~ ( distinct_lines @ A @ B )
=> ( equal_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,axiom,
! [A: $i] :
~ ( convergent_lines @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(100,plain,
! [A: $i] :
~ ( convergent_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( distinct_lines @ A @ B )
=> ( convergent_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(93,plain,
! [A: $i,B: $i] :
( ( distinct_lines @ A @ B )
=> ( convergent_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( parallel_lines @ A @ B )
& ( orthogonal_lines @ A @ C ) )
=> ( orthogonal_lines @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( parallel_lines @ A @ B )
& ( orthogonal_lines @ A @ C ) )
=> ( orthogonal_lines @ B @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( parallel_lines @ A @ B )
& ( orthogonal_lines @ A @ C ) )
=> ( orthogonal_lines @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
thf(70,plain,
! [A: $i,B: $i] :
~ ( unorthogonal_lines @ ( orthogonal_through_point @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ A @ B )
=> ( ( distinct_lines @ A @ C )
| ( distinct_lines @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(33,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)],[3]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( orthogonal_lines @ A @ B )
<=> ~ ( unorthogonal_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( orthogonal_lines @ A @ B )
=> ~ ( unorthogonal_lines @ A @ B ) )
& ( ~ ( unorthogonal_lines @ A @ B )
=> ( orthogonal_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( unorthogonal_lines @ A @ B )
& ~ ( unorthogonal_lines @ A @ C ) )
=> ~ ( convergent_lines @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( unorthogonal_lines @ A @ B )
& ~ ( unorthogonal_lines @ A @ C ) )
=> ~ ( convergent_lines @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( parallel_lines @ A @ B )
<=> ~ ( convergent_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( ( parallel_lines @ A @ B )
=> ~ ( convergent_lines @ A @ B ) )
& ( ~ ( convergent_lines @ A @ B )
=> ( parallel_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
thf(50,plain,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( orthogonal_through_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( convergent_lines @ ( parallel_through_point @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
thf(67,plain,
! [A: $i,B: $i] :
~ ( convergent_lines @ ( parallel_through_point @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',cup1) ).
thf(58,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)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
| ( unorthogonal_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
| ( unorthogonal_lines @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(47,plain,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( line @ B )
& ( convergent_lines @ A @ B ) )
=> ( point @ ( intersection_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int1) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( line @ B )
& ( convergent_lines @ A @ B ) )
=> ( point @ ( intersection_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(113,plain,
$false,
inference(e,[status(thm)],[56,84,89,60,53,41,73,64,44,76,95,87,36,100,93,29,70,33,103,91,108,50,67,58,82,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 04:20:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/0.98 % [INFO] Parsing done (139ms).
% 1.36/0.99 % [INFO] Running in sequential loop mode.
% 1.84/1.18 % [INFO] eprover registered as external prover.
% 1.84/1.19 % [INFO] cvc4 registered as external prover.
% 1.84/1.19 % [INFO] Scanning for conjecture ...
% 1.98/1.24 % [INFO] Found a conjecture and 35 axioms. Running axiom selection ...
% 2.02/1.28 % [INFO] Axiom selection finished. Selected 26 axioms (removed 9 axioms).
% 2.30/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.32 % [INFO] Type checking passed.
% 2.30/1.33 % [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 ...
% 3.27/1.75 % External prover 'e' found a proof!
% 3.27/1.75 % [INFO] Killing All external provers ...
% 3.27/1.75 % Time passed: 1229ms (effective reasoning time: 754ms)
% 3.27/1.75 % 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)>
% 3.64/1.79 % Axioms used in derivation (26): par1, ouo1, ooc2, a5, ceq2, oac1, orth1, ci3, cp1, ax2, a3, occu1, apart2, cp2, apart3, ooc1, ceq3, ax6, cup1, ci4, couo1, int1, apart5, coipo1, p1, cotno1
% 3.64/1.79 % No. of inferences in proof: 56
% 3.64/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1229 ms resp. 754 ms w/o parsing
% 3.83/1.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.83/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------