TSTP Solution File: GEO011-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO011-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 06:21:32 EDT 2022
% Result : Unsatisfiable 0.40s 0.56s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 30 ( 16 unt; 4 nHn; 30 RR)
% Number of literals : 54 ( 0 equ; 24 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(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('GEO011-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO011-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO011-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO011-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO011-1.p',unknown),
[] ).
cnf(14,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO011-1.p',unknown),
[] ).
cnf(15,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO011-1.p',unknown),
[] ).
cnf(16,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('GEO011-1.p',unknown),
[] ).
cnf(17,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('GEO011-1.p',unknown),
[] ).
cnf(18,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('GEO011-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ colinear(u,v,w)
| between(u,w,v)
| between(v,u,w)
| between(u,v,w) ),
file('GEO011-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ between(u,v,w)
| colinear(u,v,w) ),
file('GEO011-1.p',unknown),
[] ).
cnf(26,plain,
( between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.0')] ).
cnf(27,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
inference(mrr,[status(thm)],[26,16]),
[iquote('0:MRR:26.0,16.0')] ).
cnf(34,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| colinear(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
inference(res,[status(thm),theory(equality)],[27,23]),
[iquote('0:Res:27.1,23.0')] ).
cnf(37,plain,
between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2),
inference(spt,[spt(split,[position(s1)])],[34]),
[iquote('1:Spt:34.0')] ).
cnf(42,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[15,6]),
[iquote('0:Res:15.0,6.0')] ).
cnf(43,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[42,14]),
[iquote('0:SpR:42.0,14.0')] ).
cnf(89,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| equal(outer_pasch(x,u,u,w,v),u) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.2,2.0')] ).
cnf(712,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)],[89,9]),
[iquote('0:SpR:89.2,9.2')] ).
cnf(714,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[712]),
[iquote('0:Obv:712.1')] ).
cnf(716,plain,
( ~ between(lower_dimension_point_1,u,lower_dimension_point_3)
| between(lower_dimension_point_2,u,lower_dimension_point_1) ),
inference(res,[status(thm),theory(equality)],[37,714]),
[iquote('1:Res:37.0,714.0')] ).
cnf(725,plain,
~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_3),
inference(res,[status(thm),theory(equality)],[716,17]),
[iquote('1:Res:716.1,17.0')] ).
cnf(732,plain,
$false,
inference(mrr,[status(thm)],[725,43]),
[iquote('1:MRR:725.0,43.0')] ).
cnf(733,plain,
~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2),
inference(spt,[spt(split,[position(sa)])],[732,37]),
[iquote('1:Spt:732.0,34.0,37.0')] ).
cnf(734,plain,
colinear(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3),
inference(spt,[spt(split,[position(s2)])],[34]),
[iquote('1:Spt:732.0,34.1')] ).
cnf(735,plain,
between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3),
inference(mrr,[status(thm)],[27,733]),
[iquote('1:MRR:27.0,733.0')] ).
cnf(738,plain,
( ~ between(lower_dimension_point_2,u,lower_dimension_point_1)
| between(lower_dimension_point_3,u,lower_dimension_point_2) ),
inference(res,[status(thm),theory(equality)],[735,714]),
[iquote('1:Res:735.0,714.0')] ).
cnf(745,plain,
~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1),
inference(res,[status(thm),theory(equality)],[738,18]),
[iquote('1:Res:738.1,18.0')] ).
cnf(752,plain,
$false,
inference(mrr,[status(thm)],[745,43]),
[iquote('1:MRR:745.0,43.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO011-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 01:38:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.40/0.56
% 0.40/0.56 SPASS V 3.9
% 0.40/0.56 SPASS beiseite: Proof found.
% 0.40/0.56 % SZS status Theorem
% 0.40/0.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.56 SPASS derived 622 clauses, backtracked 7 clauses, performed 1 splits and kept 310 clauses.
% 0.40/0.56 SPASS allocated 63868 KBytes.
% 0.40/0.56 SPASS spent 0:00:00.21 on the problem.
% 0.40/0.56 0:00:00.04 for the input.
% 0.40/0.56 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.56 0:00:00.01 for inferences.
% 0.40/0.56 0:00:00.00 for the backtracking.
% 0.40/0.56 0:00:00.14 for the reduction.
% 0.40/0.56
% 0.40/0.56
% 0.40/0.56 Here is a proof with depth 5, length 30 :
% 0.40/0.56 % SZS output start Refutation
% See solution above
% 0.40/0.56 Formulae used in the proof : prove_lower_dimension_points_not_colinear identity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2 lower_dimension1 lower_dimension2 lower_dimension3 colinearity1 colinearity2
% 0.40/0.56
%------------------------------------------------------------------------------