TSTP Solution File: GEO205+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 06:23:23 EDT 2022
% Result : Theorem 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 17 unt; 16 nHn; 40 RR)
% Number of literals : 83 ( 0 equ; 27 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
convergent_lines(skc5,skc3),
file('GEO205+2.p',unknown),
[] ).
cnf(2,axiom,
~ distinct_lines(skc3,skc4),
file('GEO205+2.p',unknown),
[] ).
cnf(3,axiom,
~ distinct_points(u,u),
file('GEO205+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(u,v) ),
file('GEO205+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO205+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO205+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO205+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ convergent_lines(skc5,skc4)
| distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)) ),
file('GEO205+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO205+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO205+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ distinct_lines(u,v)
| ~ distinct_points(w,x)
| apart_point_and_line(x,u)
| apart_point_and_line(x,v)
| apart_point_and_line(w,v)
| apart_point_and_line(w,u) ),
file('GEO205+2.p',unknown),
[] ).
cnf(18,plain,
( convergent_lines(skc3,u)
| convergent_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(19,plain,
distinct_lines(skc5,skc3),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(20,plain,
( ~ apart_point_and_line(u,skc5)
| distinct_points(u,intersection_point(skc5,skc3)) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.1')] ).
cnf(21,plain,
( ~ apart_point_and_line(u,skc3)
| distinct_points(u,intersection_point(skc5,skc3)) ),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.0,16.1')] ).
cnf(22,plain,
~ convergent_lines(skc3,skc4),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.1,2.0')] ).
cnf(25,plain,
( ~ apart_point_and_line(u,skc3)
| apart_point_and_line(u,skc4) ),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.2,2.0')] ).
cnf(28,plain,
convergent_lines(skc5,skc4),
inference(res,[status(thm),theory(equality)],[18,22]),
[iquote('0:Res:18.0,22.0')] ).
cnf(30,plain,
distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)),
inference(mrr,[status(thm)],[12,28]),
[iquote('0:MRR:12.0,28.0')] ).
cnf(42,plain,
~ apart_point_and_line(intersection_point(skc5,skc3),skc3),
inference(res,[status(thm),theory(equality)],[21,3]),
[iquote('0:Res:21.1,3.0')] ).
cnf(49,plain,
~ apart_point_and_line(intersection_point(skc5,skc3),skc5),
inference(res,[status(thm),theory(equality)],[20,3]),
[iquote('0:Res:20.1,3.0')] ).
cnf(75,plain,
( distinct_points(intersection_point(skc5,skc4),u)
| distinct_points(intersection_point(skc5,skc3),u) ),
inference(res,[status(thm),theory(equality)],[30,7]),
[iquote('0:Res:30.0,7.0')] ).
cnf(162,plain,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(intersection_point(u,v),x)
| distinct_points(w,x) ),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.2,7.0')] ).
cnf(182,plain,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(intersection_point(u,v),x)
| distinct_points(w,x) ),
inference(res,[status(thm),theory(equality)],[15,7]),
[iquote('0:Res:15.2,7.0')] ).
cnf(302,plain,
( ~ distinct_points(u,v)
| apart_point_and_line(v,skc5)
| apart_point_and_line(v,skc3)
| apart_point_and_line(u,skc3)
| apart_point_and_line(u,skc5) ),
inference(res,[status(thm),theory(equality)],[19,17]),
[iquote('0:Res:19.0,17.0')] ).
cnf(395,plain,
distinct_points(intersection_point(skc5,skc4),intersection_point(skc5,skc3)),
inference(res,[status(thm),theory(equality)],[75,3]),
[iquote('0:Res:75.1,3.0')] ).
cnf(574,plain,
( ~ apart_point_and_line(u,skc4)
| distinct_points(intersection_point(skc5,skc4),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[28,162]),
[iquote('0:Res:28.0,162.0')] ).
cnf(637,plain,
( ~ apart_point_and_line(u,skc5)
| distinct_points(intersection_point(skc5,skc4),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[28,182]),
[iquote('0:Res:28.0,182.0')] ).
cnf(1048,plain,
( apart_point_and_line(intersection_point(skc5,skc3),skc5)
| apart_point_and_line(intersection_point(skc5,skc3),skc3)
| apart_point_and_line(intersection_point(skc5,skc4),skc3)
| apart_point_and_line(intersection_point(skc5,skc4),skc5) ),
inference(res,[status(thm),theory(equality)],[395,302]),
[iquote('0:Res:395.0,302.0')] ).
cnf(1055,plain,
( apart_point_and_line(intersection_point(skc5,skc4),skc3)
| apart_point_and_line(intersection_point(skc5,skc4),skc5) ),
inference(mrr,[status(thm)],[1048,49,42]),
[iquote('0:MRR:1048.0,1048.1,49.0,42.0')] ).
cnf(1061,plain,
( apart_point_and_line(intersection_point(skc5,skc4),skc5)
| apart_point_and_line(intersection_point(skc5,skc4),skc4) ),
inference(res,[status(thm),theory(equality)],[1055,25]),
[iquote('0:Res:1055.0,25.0')] ).
cnf(1066,plain,
apart_point_and_line(intersection_point(skc5,skc4),skc5),
inference(spt,[spt(split,[position(s1)])],[1061]),
[iquote('1:Spt:1061.0')] ).
cnf(1067,plain,
( distinct_points(intersection_point(skc5,skc4),u)
| distinct_points(intersection_point(skc5,skc4),u) ),
inference(res,[status(thm),theory(equality)],[1066,637]),
[iquote('1:Res:1066.0,637.0')] ).
cnf(1076,plain,
distinct_points(intersection_point(skc5,skc4),u),
inference(obv,[status(thm),theory(equality)],[1067]),
[iquote('1:Obv:1067.0')] ).
cnf(1077,plain,
$false,
inference(unc,[status(thm)],[1076,3]),
[iquote('1:UnC:1076.0,3.0')] ).
cnf(1078,plain,
~ apart_point_and_line(intersection_point(skc5,skc4),skc5),
inference(spt,[spt(split,[position(sa)])],[1077,1066]),
[iquote('1:Spt:1077.0,1061.0,1066.0')] ).
cnf(1079,plain,
apart_point_and_line(intersection_point(skc5,skc4),skc4),
inference(spt,[spt(split,[position(s2)])],[1061]),
[iquote('1:Spt:1077.0,1061.1')] ).
cnf(1085,plain,
( distinct_points(intersection_point(skc5,skc4),u)
| distinct_points(intersection_point(skc5,skc4),u) ),
inference(res,[status(thm),theory(equality)],[1079,574]),
[iquote('1:Res:1079.0,574.0')] ).
cnf(1091,plain,
distinct_points(intersection_point(skc5,skc4),u),
inference(obv,[status(thm),theory(equality)],[1085]),
[iquote('1:Obv:1085.0')] ).
cnf(1092,plain,
$false,
inference(unc,[status(thm)],[1091,3]),
[iquote('1:UnC:1091.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Sat Jun 18 16:12:59 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 1003 clauses, backtracked 7 clauses, performed 1 splits and kept 476 clauses.
% 0.47/0.64 SPASS allocated 85629 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.25 on the problem.
% 0.47/0.64 0:00:00.03 for the input.
% 0.47/0.64 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.02 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.15 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 6, length 40 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.65 Formulae used in the proof : con apart1 ceq3 apart4 apart6 ceq2 con2 cu1
% 0.47/0.65
%------------------------------------------------------------------------------