TSTP Solution File: GEO202+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 06:23:21 EDT 2022
% Result : Theorem 0.48s 0.63s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of clauses : 78 ( 29 unt; 29 nHn; 78 RR)
% Number of literals : 148 ( 0 equ; 51 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
distinct_points(skc3,skc5),
file('GEO202+3.p',unknown),
[] ).
cnf(2,axiom,
distinct_points(skc3,skc4),
file('GEO202+3.p',unknown),
[] ).
cnf(4,axiom,
~ distinct_lines(u,u),
file('GEO202+3.p',unknown),
[] ).
cnf(5,axiom,
~ convergent_lines(u,u),
file('GEO202+3.p',unknown),
[] ).
cnf(6,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO202+3.p',unknown),
[] ).
cnf(9,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO202+3.p',unknown),
[] ).
cnf(10,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO202+3.p',unknown),
[] ).
cnf(11,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(12,axiom,
( skP1(u,v)
| convergent_lines(v,u) ),
file('GEO202+3.p',unknown),
[] ).
cnf(13,axiom,
( skP1(u,v)
| unorthogonal_lines(v,u) ),
file('GEO202+3.p',unknown),
[] ).
cnf(15,axiom,
( equal_lines(u,v)
| distinct_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(16,axiom,
( parallel_lines(u,v)
| convergent_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(17,axiom,
( incident_point_and_line(u,v)
| apart_point_and_line(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(18,axiom,
( orthogonal_lines(u,v)
| unorthogonal_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(19,axiom,
convergent_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),
file('GEO202+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ distinct_lines(u,v)
| ~ equal_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ convergent_lines(u,v)
| ~ parallel_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ apart_point_and_line(u,v)
| ~ incident_point_and_line(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ unorthogonal_lines(u,v)
| ~ orthogonal_lines(u,v) ),
file('GEO202+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ distinct_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
file('GEO202+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(u,line_connecting(u,v)) ),
file('GEO202+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(v,line_connecting(u,v)) ),
file('GEO202+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO202+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
file('GEO202+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ convergent_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
file('GEO202+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ skP1(u,v)
| ~ skP1(w,v)
| skP1(u,w) ),
file('GEO202+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| ~ skP1(v,u) ),
file('GEO202+3.p',unknown),
[] ).
cnf(50,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+3.p',unknown),
[] ).
cnf(54,plain,
~ apart_point_and_line(skc3,line_connecting(skc3,skc4)),
inference(res,[status(thm),theory(equality)],[2,32]),
[iquote('0:Res:2.0,32.0')] ).
cnf(57,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)],[1,50]),
[iquote('0:Res:1.0,50.0')] ).
cnf(60,plain,
~ apart_point_and_line(skc3,line_connecting(skc3,skc5)),
inference(res,[status(thm),theory(equality)],[1,32]),
[iquote('0:Res:1.0,32.0')] ).
cnf(61,plain,
~ apart_point_and_line(skc5,line_connecting(skc3,skc5)),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.0')] ).
cnf(71,plain,
( ~ unorthogonal_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4))
| ~ skP1(line_connecting(skc3,skc4),line_connecting(skc3,skc5)) ),
inference(res,[status(thm),theory(equality)],[19,45]),
[iquote('0:Res:19.0,45.1')] ).
cnf(81,plain,
skP1(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[13,9]),
[iquote('0:Res:13.1,9.0')] ).
cnf(85,plain,
skP1(u,u),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.1,5.0')] ).
cnf(86,plain,
skP1(u,parallel_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.1,6.0')] ).
cnf(87,plain,
convergent_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.0,9.0')] ).
cnf(106,plain,
~ parallel_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[87,25]),
[iquote('0:Res:87.0,25.0')] ).
cnf(141,plain,
( equal_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[15,30]),
[iquote('0:Res:15.1,30.0')] ).
cnf(148,plain,
( parallel_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[16,40]),
[iquote('0:Res:16.1,40.0')] ).
cnf(203,plain,
( skP1(u,v)
| distinct_lines(u,w)
| convergent_lines(v,w) ),
inference(res,[status(thm),theory(equality)],[12,38]),
[iquote('0:Res:12.1,38.0')] ).
cnf(204,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[87,38]),
[iquote('0:Res:87.0,38.0')] ).
cnf(214,plain,
distinct_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[204,5]),
[iquote('0:Res:204.1,5.0')] ).
cnf(218,plain,
( distinct_lines(orthogonal_through_point(u,v),w)
| distinct_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[214,30]),
[iquote('0:Res:214.0,30.0')] ).
cnf(220,plain,
convergent_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[214,20]),
[iquote('0:Res:214.0,20.0')] ).
cnf(236,plain,
( ~ equal_lines(orthogonal_through_point(u,v),w)
| distinct_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[218,24]),
[iquote('0:Res:218.0,24.0')] ).
cnf(238,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
inference(res,[status(thm),theory(equality)],[17,37]),
[iquote('0:Res:17.1,37.0')] ).
cnf(291,plain,
( ~ skP1(u,orthogonal_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[81,44]),
[iquote('0:Res:81.0,44.0')] ).
cnf(292,plain,
( ~ skP1(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[85,44]),
[iquote('0:Res:85.0,44.0')] ).
cnf(293,plain,
( ~ skP1(u,parallel_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[86,44]),
[iquote('0:Res:86.0,44.0')] ).
cnf(297,plain,
skP1(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[81,292]),
[iquote('0:Res:81.0,292.0')] ).
cnf(307,plain,
( ~ convergent_lines(u,v)
| ~ skP1(v,u)
| orthogonal_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[18,45]),
[iquote('0:Res:18.1,45.0')] ).
cnf(402,plain,
skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[297,291]),
[iquote('0:Res:297.0,291.0')] ).
cnf(405,plain,
skP1(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[402,292]),
[iquote('0:Res:402.0,292.0')] ).
cnf(420,plain,
( equal_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[141,4]),
[iquote('0:Res:141.2,4.0')] ).
cnf(431,plain,
( equal_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[420,20]),
[iquote('0:Res:420.1,20.0')] ).
cnf(437,plain,
( ~ parallel_lines(u,v)
| equal_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[431,25]),
[iquote('0:Res:431.1,25.0')] ).
cnf(464,plain,
( ~ parallel_lines(u,orthogonal_through_point(v,w))
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[437,236]),
[iquote('0:Res:437.1,236.0')] ).
cnf(479,plain,
( ~ orthogonal_lines(u,v)
| parallel_lines(w,v)
| unorthogonal_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[148,27]),
[iquote('0:Res:148.1,27.0')] ).
cnf(551,plain,
( skP1(u,parallel_through_point(v,w))
| distinct_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[203,6]),
[iquote('0:Res:203.2,6.0')] ).
cnf(703,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[238,10]),
[iquote('0:Res:238.2,10.0')] ).
cnf(747,plain,
( ~ skP1(orthogonal_through_point(u,v),u)
| orthogonal_lines(u,orthogonal_through_point(u,v)) ),
inference(res,[status(thm),theory(equality)],[220,307]),
[iquote('0:Res:220.0,307.0')] ).
cnf(755,plain,
orthogonal_lines(u,orthogonal_through_point(u,v)),
inference(mrr,[status(thm)],[747,297]),
[iquote('0:MRR:747.0,297.0')] ).
cnf(1037,plain,
( incident_point_and_line(u,v)
| convergent_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[703,20]),
[iquote('0:Res:703.1,20.0')] ).
cnf(1066,plain,
( distinct_lines(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[551,293]),
[iquote('0:Res:551.0,293.0')] ).
cnf(1581,plain,
( parallel_lines(u,orthogonal_through_point(v,w))
| unorthogonal_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[755,479]),
[iquote('0:Res:755.0,479.0')] ).
cnf(1591,plain,
( unorthogonal_lines(u,v)
| distinct_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[1581,464]),
[iquote('0:Res:1581.0,464.0')] ).
cnf(1594,plain,
unorthogonal_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[1581,106]),
[iquote('0:Res:1581.0,106.0')] ).
cnf(1609,plain,
( ~ skP1(line_connecting(skc3,skc4),line_connecting(skc3,skc5))
| distinct_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4)) ),
inference(res,[status(thm),theory(equality)],[1591,71]),
[iquote('0:Res:1591.0,71.0')] ).
cnf(1611,plain,
distinct_lines(line_connecting(skc3,skc5),line_connecting(skc3,skc4)),
inference(mrr,[status(thm)],[1609,1066]),
[iquote('0:MRR:1609.0,1066.1')] ).
cnf(1613,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)],[1611,57]),
[iquote('0:Res:1611.0,57.0')] ).
cnf(1619,plain,
apart_point_and_line(skc5,line_connecting(skc3,skc4)),
inference(mrr,[status(thm)],[1613,61,54,60]),
[iquote('0:MRR:1613.0,1613.2,1613.3,61.0,54.0,60.0')] ).
cnf(1627,plain,
~ incident_point_and_line(skc5,line_connecting(skc3,skc4)),
inference(res,[status(thm),theory(equality)],[1619,26]),
[iquote('0:Res:1619.0,26.0')] ).
cnf(1654,plain,
( ~ convergent_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w))
| ~ skP1(orthogonal_through_point(orthogonal_through_point(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[1594,45]),
[iquote('0:Res:1594.0,45.0')] ).
cnf(1656,plain,
~ convergent_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(mrr,[status(thm)],[1654,405]),
[iquote('0:MRR:1654.1,405.0')] ).
cnf(1812,plain,
incident_point_and_line(u,v),
inference(res,[status(thm),theory(equality)],[1037,1656]),
[iquote('0:Res:1037.1,1656.0')] ).
cnf(1813,plain,
$false,
inference(unc,[status(thm)],[1812,1627]),
[iquote('0:UnC:1812.0,1627.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 17:07:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.48/0.63
% 0.48/0.63 SPASS V 3.9
% 0.48/0.63 SPASS beiseite: Proof found.
% 0.48/0.63 % SZS status Theorem
% 0.48/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.63 SPASS derived 1723 clauses, backtracked 0 clauses, performed 0 splits and kept 995 clauses.
% 0.48/0.63 SPASS allocated 98649 KBytes.
% 0.48/0.63 SPASS spent 0:00:00.28 on the problem.
% 0.48/0.63 0:00:00.03 for the input.
% 0.48/0.63 0:00:00.03 for the FLOTTER CNF translation.
% 0.48/0.63 0:00:00.02 for inferences.
% 0.48/0.63 0:00:00.00 for the backtracking.
% 0.48/0.63 0:00:00.17 for the reduction.
% 0.48/0.63
% 0.48/0.63
% 0.48/0.63 Here is a proof with depth 10, length 78 :
% 0.48/0.63 % SZS output start Refutation
% See solution above
% 0.48/0.64 Formulae used in the proof : con apart2 apart3 cp1 ooc1 ooc2 coipo1 cotno1 ax2 a3 a4 a5 p1 apart5 ci1 ci2 ceq2 ceq3 couo1 cu1
% 0.48/0.64
%------------------------------------------------------------------------------