TSTP Solution File: GEO202+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO202+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 06:23:20 EDT 2022
% Result : Theorem 0.59s 0.77s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 77 ( 21 unt; 44 nHn; 77 RR)
% Number of literals : 193 ( 0 equ; 32 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
distinct_points(skc3,skc5),
file('GEO202+2.p',unknown),
[] ).
cnf(2,axiom,
distinct_points(skc3,skc4),
file('GEO202+2.p',unknown),
[] ).
cnf(3,axiom,
~ distinct_points(u,u),
file('GEO202+2.p',unknown),
[] ).
cnf(6,axiom,
convergent_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),
file('GEO202+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(u,v) ),
file('GEO202+2.p',unknown),
[] ).
cnf(8,axiom,
distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),skc3),
file('GEO202+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO202+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(w,line_connecting(u,v))
| distinct_points(w,u) ),
file('GEO202+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(w,line_connecting(u,v))
| distinct_points(w,v) ),
file('GEO202+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO202+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO202+2.p',unknown),
[] ).
cnf(18,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('GEO202+2.p',unknown),
[] ).
cnf(20,plain,
( distinct_points(skc4,u)
| distinct_points(skc3,u) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.0,9.0')] ).
cnf(21,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc4))
| distinct_points(u,skc3) ),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.1')] ).
cnf(22,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc4))
| distinct_points(u,skc4) ),
inference(res,[status(thm),theory(equality)],[2,15]),
[iquote('0:Res:2.0,15.1')] ).
cnf(23,plain,
( ~ distinct_lines(u,v)
| apart_point_and_line(skc5,u)
| apart_point_and_line(skc5,v)
| apart_point_and_line(skc3,v)
| apart_point_and_line(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(24,plain,
( distinct_points(skc5,u)
| distinct_points(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(25,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc5))
| distinct_points(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.1')] ).
cnf(26,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc5))
| distinct_points(u,skc5) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.1')] ).
cnf(28,plain,
distinct_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(31,plain,
( ~ distinct_lines(u,v)
| apart_point_and_line(skc3,u)
| apart_point_and_line(skc3,v)
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v)
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),u) ),
inference(res,[status(thm),theory(equality)],[8,18]),
[iquote('0:Res:8.0,18.0')] ).
cnf(32,plain,
( distinct_points(skc3,u)
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),u) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(47,plain,
( distinct_points(skc4,u)
| distinct_points(u,v)
| distinct_points(skc3,v) ),
inference(res,[status(thm),theory(equality)],[20,9]),
[iquote('0:Res:20.1,9.0')] ).
cnf(48,plain,
( distinct_points(skc5,u)
| distinct_points(u,v)
| distinct_points(skc3,v) ),
inference(res,[status(thm),theory(equality)],[24,9]),
[iquote('0:Res:24.1,9.0')] ).
cnf(56,plain,
( distinct_points(skc4,u)
| distinct_points(u,skc3) ),
inference(res,[status(thm),theory(equality)],[47,3]),
[iquote('0:Res:47.2,3.0')] ).
cnf(58,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(skc4,v) ),
inference(res,[status(thm),theory(equality)],[56,9]),
[iquote('0:Res:56.0,9.0')] ).
cnf(65,plain,
( distinct_points(skc5,u)
| distinct_points(u,skc3) ),
inference(res,[status(thm),theory(equality)],[48,3]),
[iquote('0:Res:48.2,3.0')] ).
cnf(67,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(skc5,v) ),
inference(res,[status(thm),theory(equality)],[65,9]),
[iquote('0:Res:65.0,9.0')] ).
cnf(77,plain,
( distinct_points(u,skc3)
| distinct_points(u,skc4) ),
inference(res,[status(thm),theory(equality)],[58,3]),
[iquote('0:Res:58.2,3.0')] ).
cnf(78,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(skc4,w) ),
inference(res,[status(thm),theory(equality)],[58,9]),
[iquote('0:Res:58.2,9.0')] ).
cnf(83,plain,
( distinct_points(u,skc4)
| distinct_points(skc3,v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[77,9]),
[iquote('0:Res:77.0,9.0')] ).
cnf(91,plain,
( distinct_points(u,skc3)
| distinct_points(u,skc5) ),
inference(res,[status(thm),theory(equality)],[67,3]),
[iquote('0:Res:67.2,3.0')] ).
cnf(92,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(skc5,w) ),
inference(res,[status(thm),theory(equality)],[67,9]),
[iquote('0:Res:67.2,9.0')] ).
cnf(97,plain,
( distinct_points(u,skc5)
| distinct_points(skc3,v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[91,9]),
[iquote('0:Res:91.0,9.0')] ).
cnf(104,plain,
( distinct_points(u,skc4)
| distinct_points(skc3,u) ),
inference(res,[status(thm),theory(equality)],[83,3]),
[iquote('0:Res:83.2,3.0')] ).
cnf(113,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)],[17,9]),
[iquote('0:Res:17.2,9.0')] ).
cnf(120,plain,
( distinct_points(u,skc5)
| distinct_points(skc3,u) ),
inference(res,[status(thm),theory(equality)],[97,3]),
[iquote('0:Res:97.2,3.0')] ).
cnf(143,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)],[16,9]),
[iquote('0:Res:16.2,9.0')] ).
cnf(147,plain,
( distinct_points(skc3,u)
| distinct_points(u,v)
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v) ),
inference(res,[status(thm),theory(equality)],[32,9]),
[iquote('0:Res:32.1,9.0')] ).
cnf(229,plain,
( ~ distinct_points(u,v)
| apart_point_and_line(v,line_connecting(skc3,skc5))
| apart_point_and_line(v,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[28,18]),
[iquote('0:Res:28.0,18.0')] ).
cnf(266,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(v,skc4) ),
inference(res,[status(thm),theory(equality)],[78,3]),
[iquote('0:Res:78.3,3.0')] ).
cnf(276,plain,
( apart_point_and_line(skc5,line_connecting(skc3,skc5))
| apart_point_and_line(skc5,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[28,23]),
[iquote('0:Res:28.0,23.0')] ).
cnf(306,plain,
( distinct_points(u,skc3)
| distinct_points(u,v)
| distinct_points(v,skc5) ),
inference(res,[status(thm),theory(equality)],[92,3]),
[iquote('0:Res:92.3,3.0')] ).
cnf(375,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc4))
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[6,113]),
[iquote('0:Res:6.0,113.0')] ).
cnf(420,plain,
( ~ apart_point_and_line(u,line_connecting(skc3,skc5))
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[6,143]),
[iquote('0:Res:6.0,143.0')] ).
cnf(552,plain,
( apart_point_and_line(skc3,line_connecting(skc3,skc5))
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc4))
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[28,31]),
[iquote('0:Res:28.0,31.0')] ).
cnf(955,plain,
apart_point_and_line(skc5,line_connecting(skc3,skc5)),
inference(spt,[spt(split,[position(s1)])],[276]),
[iquote('1:Spt:276.0')] ).
cnf(963,plain,
( ~ distinct_points(skc3,skc5)
| distinct_points(skc5,skc5) ),
inference(res,[status(thm),theory(equality)],[955,15]),
[iquote('1:Res:955.0,15.1')] ).
cnf(965,plain,
$false,
inference(mrr,[status(thm)],[963,120,3]),
[iquote('1:MRR:963.0,963.1,120.1,3.0')] ).
cnf(967,plain,
~ apart_point_and_line(skc5,line_connecting(skc3,skc5)),
inference(spt,[spt(split,[position(sa)])],[965,955]),
[iquote('1:Spt:965.0,276.0,955.0')] ).
cnf(968,plain,
( apart_point_and_line(skc5,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc5)) ),
inference(spt,[spt(split,[position(s2)])],[276]),
[iquote('1:Spt:965.0,276.1,276.2,276.3')] ).
cnf(1091,plain,
( distinct_points(u,v)
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v)
| apart_point_and_line(u,line_connecting(skc3,skc5))
| apart_point_and_line(u,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[147,229]),
[iquote('0:Res:147.0,229.0')] ).
cnf(1159,plain,
( distinct_points(u,skc3)
| distinct_points(v,skc5)
| apart_point_and_line(v,line_connecting(skc3,skc5))
| apart_point_and_line(v,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[306,229]),
[iquote('0:Res:306.1,229.0')] ).
cnf(1161,plain,
( distinct_points(u,skc3)
| distinct_points(v,skc4)
| apart_point_and_line(v,line_connecting(skc3,skc5))
| apart_point_and_line(v,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc4))
| apart_point_and_line(u,line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[266,229]),
[iquote('0:Res:266.1,229.0')] ).
cnf(1247,plain,
( distinct_points(u,skc3)
| distinct_points(v,skc4)
| apart_point_and_line(v,line_connecting(skc3,skc5)) ),
inference(mrr,[status(thm)],[1161,22,21,25]),
[iquote('0:MRR:1161.3,1161.4,1161.5,22.0,21.0,25.0')] ).
cnf(1248,plain,
( distinct_points(u,skc3)
| distinct_points(v,skc5)
| apart_point_and_line(v,line_connecting(skc3,skc4)) ),
inference(mrr,[status(thm)],[1159,26,21,25]),
[iquote('0:MRR:1159.2,1159.4,1159.5,26.0,21.0,25.0')] ).
cnf(1257,plain,
( distinct_points(u,v)
| distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),v)
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc5)) ),
inference(mrr,[status(thm)],[1091,420,375]),
[iquote('0:MRR:1091.2,1091.3,420.0,375.0')] ).
cnf(1285,plain,
distinct_points(u,skc3),
inference(spt,[spt(split,[position(s2s1)])],[1247]),
[iquote('2:Spt:1247.0')] ).
cnf(1286,plain,
$false,
inference(unc,[status(thm)],[1285,3]),
[iquote('2:UnC:1285.0,3.0')] ).
cnf(1287,plain,
( distinct_points(u,skc4)
| apart_point_and_line(u,line_connecting(skc3,skc5)) ),
inference(spt,[spt(split,[position(s2s2)])],[1247]),
[iquote('2:Spt:1286.0,1247.1,1247.2')] ).
cnf(1495,plain,
distinct_points(u,skc3),
inference(spt,[spt(split,[position(s2s2s1)])],[1248]),
[iquote('3:Spt:1248.0')] ).
cnf(1496,plain,
$false,
inference(unc,[status(thm)],[1495,3]),
[iquote('3:UnC:1495.0,3.0')] ).
cnf(1497,plain,
( distinct_points(u,skc5)
| apart_point_and_line(u,line_connecting(skc3,skc4)) ),
inference(spt,[spt(split,[position(s2s2s2)])],[1248]),
[iquote('3:Spt:1496.0,1248.1,1248.2')] ).
cnf(1668,plain,
apart_point_and_line(skc3,line_connecting(skc3,skc5)),
inference(spt,[spt(split,[position(s2s2s2s1)])],[552]),
[iquote('4:Spt:552.0')] ).
cnf(1675,plain,
( ~ distinct_points(skc3,skc5)
| distinct_points(skc3,skc3) ),
inference(res,[status(thm),theory(equality)],[1668,14]),
[iquote('4:Res:1668.0,14.1')] ).
cnf(1678,plain,
$false,
inference(mrr,[status(thm)],[1675,120,3]),
[iquote('4:MRR:1675.0,1675.1,120.0,3.0')] ).
cnf(1680,plain,
~ apart_point_and_line(skc3,line_connecting(skc3,skc5)),
inference(spt,[spt(split,[position(s2s2s2sa)])],[1678,1668]),
[iquote('4:Spt:1678.0,552.0,1668.0')] ).
cnf(1681,plain,
( apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc4))
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc5)) ),
inference(spt,[spt(split,[position(s2s2s2s2)])],[552]),
[iquote('4:Spt:1678.0,552.1,552.2,552.3')] ).
cnf(1693,plain,
( distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),u)
| apart_point_and_line(skc3,line_connecting(skc3,skc4))
| apart_point_and_line(skc3,line_connecting(skc3,skc5)) ),
inference(con,[status(thm)],[1257]),
[iquote('0:Con:1257.0')] ).
cnf(1694,plain,
( distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),u)
| apart_point_and_line(skc3,line_connecting(skc3,skc4)) ),
inference(mrr,[status(thm)],[1693,1680]),
[iquote('4:MRR:1693.2,1680.0')] ).
cnf(1724,plain,
apart_point_and_line(skc3,line_connecting(skc3,skc4)),
inference(spt,[spt(split,[position(s2s2s2s2s1)])],[1681]),
[iquote('5:Spt:1681.0')] ).
cnf(1732,plain,
( ~ distinct_points(skc3,skc4)
| distinct_points(skc3,skc3) ),
inference(res,[status(thm),theory(equality)],[1724,14]),
[iquote('5:Res:1724.0,14.1')] ).
cnf(1735,plain,
$false,
inference(mrr,[status(thm)],[1732,104,3]),
[iquote('5:MRR:1732.0,1732.1,104.0,3.0')] ).
cnf(1736,plain,
~ apart_point_and_line(skc3,line_connecting(skc3,skc4)),
inference(spt,[spt(split,[position(s2s2s2s2sa)])],[1735,1724]),
[iquote('5:Spt:1735.0,1681.0,1724.0')] ).
cnf(1737,plain,
( apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc4))
| apart_point_and_line(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),line_connecting(skc3,skc5)) ),
inference(spt,[spt(split,[position(s2s2s2s2s2)])],[1681]),
[iquote('5:Spt:1735.0,1681.1,1681.2')] ).
cnf(1738,plain,
distinct_points(intersection_point(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),u),
inference(mrr,[status(thm)],[1694,1736]),
[iquote('5:MRR:1694.1,1736.0')] ).
cnf(1739,plain,
$false,
inference(unc,[status(thm)],[1738,3]),
[iquote('5:UnC:1738.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO202+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 00:45:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.59/0.77
% 0.59/0.77 SPASS V 3.9
% 0.59/0.77 SPASS beiseite: Proof found.
% 0.59/0.77 % SZS status Theorem
% 0.59/0.77 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.77 SPASS derived 1515 clauses, backtracked 167 clauses, performed 7 splits and kept 789 clauses.
% 0.59/0.77 SPASS allocated 86445 KBytes.
% 0.59/0.77 SPASS spent 0:00:00.41 on the problem.
% 0.59/0.77 0:00:00.04 for the input.
% 0.59/0.77 0:00:00.03 for the FLOTTER CNF translation.
% 0.59/0.77 0:00:00.03 for inferences.
% 0.59/0.77 0:00:00.00 for the backtracking.
% 0.59/0.77 0:00:00.29 for the reduction.
% 0.59/0.77
% 0.59/0.77
% 0.59/0.77 Here is a proof with depth 8, length 77 :
% 0.59/0.77 % SZS output start Refutation
% See solution above
% 0.59/0.78 Formulae used in the proof : con apart1 ceq3 apart4 con1 con2 cu1
% 0.59/0.78
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