TSTP Solution File: GEO010-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO010-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : 600s
% DateTime : Sat Jul 16 06:21:31 EDT 2022
% Result : Unsatisfiable 0.39s 0.58s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of clauses : 68 ( 30 unt; 8 nHn; 68 RR)
% Number of literals : 128 ( 0 equ; 62 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
colinear(a,b,c),
file('GEO010-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
file('GEO010-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO010-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO010-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO010-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO010-1.p',unknown),
[] ).
cnf(15,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO010-1.p',unknown),
[] ).
cnf(16,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO010-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ colinear(u,v,w)
| between(u,w,v)
| between(v,u,w)
| between(u,v,w) ),
file('GEO010-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ between(u,v,w)
| colinear(u,v,w) ),
file('GEO010-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ between(u,v,w)
| colinear(v,u,w) ),
file('GEO010-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ between(u,v,w)
| colinear(u,w,v) ),
file('GEO010-1.p',unknown),
[] ).
cnf(31,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.0,7.0')] ).
cnf(32,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[31,15]),
[iquote('0:SpR:31.0,15.0')] ).
cnf(47,plain,
( between(a,c,b)
| between(b,a,c)
| between(a,b,c) ),
inference(res,[status(thm),theory(equality)],[1,23]),
[iquote('0:Res:1.0,23.0')] ).
cnf(55,plain,
( between(a,c,b)
| between(a,b,c)
| colinear(b,a,c) ),
inference(res,[status(thm),theory(equality)],[47,24]),
[iquote('0:Res:47.1,24.0')] ).
cnf(58,plain,
( between(a,c,b)
| colinear(b,a,c) ),
inference(mrr,[status(thm)],[55,25]),
[iquote('0:MRR:55.1,25.0')] ).
cnf(62,plain,
between(a,c,b),
inference(spt,[spt(split,[position(s1)])],[58]),
[iquote('1:Spt:58.0')] ).
cnf(64,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[62,24]),
[iquote('1:Res:62.0,24.0')] ).
cnf(65,plain,
colinear(c,a,b),
inference(res,[status(thm),theory(equality)],[62,25]),
[iquote('1:Res:62.0,25.0')] ).
cnf(67,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(mrr,[status(thm)],[2,64]),
[iquote('1:MRR:2.4,64.0')] ).
cnf(68,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(mrr,[status(thm)],[67,65]),
[iquote('1:MRR:67.1,65.0')] ).
cnf(76,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| equal(outer_pasch(x,u,u,w,v),u) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.2,3.0')] ).
cnf(559,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(spr,[status(thm),theory(equality)],[76,10]),
[iquote('0:SpR:76.2,10.2')] ).
cnf(561,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[559]),
[iquote('0:Obv:559.1')] ).
cnf(668,plain,
( ~ between(a,u,c)
| between(b,u,a) ),
inference(res,[status(thm),theory(equality)],[62,561]),
[iquote('1:Res:62.0,561.0')] ).
cnf(680,plain,
( ~ between(a,u,c)
| colinear(b,u,a) ),
inference(res,[status(thm),theory(equality)],[668,24]),
[iquote('1:Res:668.1,24.0')] ).
cnf(681,plain,
( ~ between(a,u,c)
| colinear(u,b,a) ),
inference(res,[status(thm),theory(equality)],[668,25]),
[iquote('1:Res:668.1,25.0')] ).
cnf(682,plain,
( ~ between(a,u,c)
| colinear(b,a,u) ),
inference(res,[status(thm),theory(equality)],[668,26]),
[iquote('1:Res:668.1,26.0')] ).
cnf(683,plain,
colinear(b,c,a),
inference(res,[status(thm),theory(equality)],[32,680]),
[iquote('1:Res:32.0,680.0')] ).
cnf(686,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,a,c) ),
inference(mrr,[status(thm)],[68,683]),
[iquote('1:MRR:68.1,683.0')] ).
cnf(688,plain,
colinear(c,b,a),
inference(res,[status(thm),theory(equality)],[32,681]),
[iquote('1:Res:32.0,681.0')] ).
cnf(691,plain,
~ colinear(b,a,c),
inference(mrr,[status(thm)],[686,688]),
[iquote('1:MRR:686.0,688.0')] ).
cnf(693,plain,
colinear(b,a,c),
inference(res,[status(thm),theory(equality)],[32,682]),
[iquote('1:Res:32.0,682.0')] ).
cnf(696,plain,
$false,
inference(mrr,[status(thm)],[693,691]),
[iquote('1:MRR:693.0,691.0')] ).
cnf(697,plain,
~ between(a,c,b),
inference(spt,[spt(split,[position(sa)])],[696,62]),
[iquote('1:Spt:696.0,58.0,62.0')] ).
cnf(698,plain,
colinear(b,a,c),
inference(spt,[spt(split,[position(s2)])],[58]),
[iquote('1:Spt:696.0,58.1')] ).
cnf(699,plain,
( between(b,a,c)
| between(a,b,c) ),
inference(mrr,[status(thm)],[47,697]),
[iquote('1:MRR:47.0,697.0')] ).
cnf(702,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[2,698]),
[iquote('1:MRR:2.3,698.0')] ).
cnf(704,plain,
between(b,a,c),
inference(spt,[spt(split,[position(s2s1)])],[699]),
[iquote('2:Spt:699.0')] ).
cnf(705,plain,
( ~ between(b,u,a)
| between(c,u,b) ),
inference(res,[status(thm),theory(equality)],[704,561]),
[iquote('2:Res:704.0,561.0')] ).
cnf(710,plain,
colinear(b,c,a),
inference(res,[status(thm),theory(equality)],[704,26]),
[iquote('2:Res:704.0,26.0')] ).
cnf(711,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[702,710]),
[iquote('2:MRR:702.2,710.0')] ).
cnf(716,plain,
( ~ between(b,u,a)
| colinear(c,u,b) ),
inference(res,[status(thm),theory(equality)],[705,24]),
[iquote('2:Res:705.1,24.0')] ).
cnf(717,plain,
( ~ between(b,u,a)
| colinear(u,c,b) ),
inference(res,[status(thm),theory(equality)],[705,25]),
[iquote('2:Res:705.1,25.0')] ).
cnf(719,plain,
colinear(c,a,b),
inference(res,[status(thm),theory(equality)],[32,716]),
[iquote('2:Res:32.0,716.0')] ).
cnf(721,plain,
( ~ colinear(c,b,a)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[711,719]),
[iquote('2:MRR:711.1,719.0')] ).
cnf(722,plain,
( between(c,b,a)
| between(a,c,b)
| between(c,a,b) ),
inference(res,[status(thm),theory(equality)],[719,23]),
[iquote('2:Res:719.0,23.0')] ).
cnf(723,plain,
( between(c,b,a)
| between(c,a,b) ),
inference(mrr,[status(thm)],[722,697]),
[iquote('2:MRR:722.1,697.0')] ).
cnf(727,plain,
( between(c,a,b)
| colinear(c,b,a) ),
inference(res,[status(thm),theory(equality)],[723,24]),
[iquote('2:Res:723.0,24.0')] ).
cnf(730,plain,
colinear(c,b,a),
inference(mrr,[status(thm)],[727,26]),
[iquote('2:MRR:727.0,26.0')] ).
cnf(731,plain,
~ colinear(a,c,b),
inference(mrr,[status(thm)],[721,730]),
[iquote('2:MRR:721.0,730.0')] ).
cnf(736,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[32,717]),
[iquote('2:Res:32.0,717.0')] ).
cnf(738,plain,
$false,
inference(mrr,[status(thm)],[736,731]),
[iquote('2:MRR:736.0,731.0')] ).
cnf(739,plain,
~ between(b,a,c),
inference(spt,[spt(split,[position(s2sa)])],[738,704]),
[iquote('2:Spt:738.0,699.0,704.0')] ).
cnf(740,plain,
between(a,b,c),
inference(spt,[spt(split,[position(s2s2)])],[699]),
[iquote('2:Spt:738.0,699.1')] ).
cnf(741,plain,
( ~ between(a,u,b)
| between(c,u,a) ),
inference(res,[status(thm),theory(equality)],[740,561]),
[iquote('2:Res:740.0,561.0')] ).
cnf(746,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[740,26]),
[iquote('2:Res:740.0,26.0')] ).
cnf(747,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(mrr,[status(thm)],[702,746]),
[iquote('2:MRR:702.3,746.0')] ).
cnf(752,plain,
( ~ between(a,u,b)
| colinear(c,u,a) ),
inference(res,[status(thm),theory(equality)],[741,24]),
[iquote('2:Res:741.1,24.0')] ).
cnf(753,plain,
( ~ between(a,u,b)
| colinear(u,c,a) ),
inference(res,[status(thm),theory(equality)],[741,25]),
[iquote('2:Res:741.1,25.0')] ).
cnf(754,plain,
( ~ between(a,u,b)
| colinear(c,a,u) ),
inference(res,[status(thm),theory(equality)],[741,26]),
[iquote('2:Res:741.1,26.0')] ).
cnf(755,plain,
colinear(c,b,a),
inference(res,[status(thm),theory(equality)],[32,752]),
[iquote('2:Res:32.0,752.0')] ).
cnf(757,plain,
( ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(mrr,[status(thm)],[747,755]),
[iquote('2:MRR:747.0,755.0')] ).
cnf(759,plain,
colinear(b,c,a),
inference(res,[status(thm),theory(equality)],[32,753]),
[iquote('2:Res:32.0,753.0')] ).
cnf(761,plain,
~ colinear(c,a,b),
inference(mrr,[status(thm)],[757,759]),
[iquote('2:MRR:757.1,759.0')] ).
cnf(777,plain,
colinear(c,a,b),
inference(res,[status(thm),theory(equality)],[32,754]),
[iquote('2:Res:32.0,754.0')] ).
cnf(779,plain,
$false,
inference(mrr,[status(thm)],[777,761]),
[iquote('2:MRR:777.0,761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO010-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 06:38:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.39/0.58
% 0.39/0.58 SPASS V 3.9
% 0.39/0.58 SPASS beiseite: Proof found.
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.58 SPASS derived 652 clauses, backtracked 11 clauses, performed 2 splits and kept 357 clauses.
% 0.39/0.58 SPASS allocated 63896 KBytes.
% 0.39/0.58 SPASS spent 0:00:00.22 on the problem.
% 0.39/0.58 0:00:00.04 for the input.
% 0.39/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.58 0:00:00.01 for inferences.
% 0.39/0.58 0:00:00.00 for the backtracking.
% 0.39/0.58 0:00:00.15 for the reduction.
% 0.39/0.58
% 0.39/0.58
% 0.39/0.58 Here is a proof with depth 7, length 68 :
% 0.39/0.58 % SZS output start Refutation
% See solution above
% 0.39/0.58 Formulae used in the proof : abc_colinear prove_colinear_in_all_orders identity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2 colinearity1 colinearity2 colinearity3 colinearity4
% 0.39/0.58
%------------------------------------------------------------------------------