TSTP Solution File: GEO201+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.46s 0.65s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of clauses : 91 ( 32 unt; 42 nHn; 91 RR)
% Number of literals : 176 ( 0 equ; 48 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
convergent_lines(skc2,skc3),
file('GEO201+3.p',unknown),
[] ).
cnf(3,axiom,
~ distinct_lines(u,u),
file('GEO201+3.p',unknown),
[] ).
cnf(4,axiom,
~ convergent_lines(u,u),
file('GEO201+3.p',unknown),
[] ).
cnf(5,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO201+3.p',unknown),
[] ).
cnf(8,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO201+3.p',unknown),
[] ).
cnf(9,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO201+3.p',unknown),
[] ).
cnf(10,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(11,axiom,
( skP1(u,v)
| convergent_lines(v,u) ),
file('GEO201+3.p',unknown),
[] ).
cnf(12,axiom,
( skP1(u,v)
| unorthogonal_lines(v,u) ),
file('GEO201+3.p',unknown),
[] ).
cnf(13,axiom,
( equal_points(u,v)
| distinct_points(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(14,axiom,
( equal_lines(u,v)
| distinct_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(15,axiom,
( parallel_lines(u,v)
| convergent_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(16,axiom,
( incident_point_and_line(u,v)
| apart_point_and_line(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(17,axiom,
( orthogonal_lines(u,v)
| unorthogonal_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(21,axiom,
~ equal_points(intersection_point(skc2,skc3),intersection_point(skc3,skc2)),
file('GEO201+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ distinct_lines(u,v)
| ~ equal_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ convergent_lines(u,v)
| ~ parallel_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ apart_point_and_line(u,v)
| ~ incident_point_and_line(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ unorthogonal_lines(u,v)
| ~ orthogonal_lines(u,v) ),
file('GEO201+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ distinct_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
file('GEO201+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO201+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO201+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
file('GEO201+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ convergent_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
file('GEO201+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ skP1(u,v)
| ~ skP1(w,v)
| skP1(u,w) ),
file('GEO201+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| ~ skP1(v,u) ),
file('GEO201+3.p',unknown),
[] ).
cnf(48,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('GEO201+3.p',unknown),
[] ).
cnf(54,plain,
( distinct_lines(skc3,u)
| convergent_lines(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,36]),
[iquote('0:Res:1.0,36.0')] ).
cnf(58,plain,
distinct_points(intersection_point(skc2,skc3),intersection_point(skc3,skc2)),
inference(res,[status(thm),theory(equality)],[13,21]),
[iquote('0:Res:13.1,21.0')] ).
cnf(69,plain,
skP1(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.1,8.0')] ).
cnf(76,plain,
skP1(u,u),
inference(res,[status(thm),theory(equality)],[11,4]),
[iquote('0:Res:11.1,4.0')] ).
cnf(78,plain,
convergent_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(82,plain,
( equal_lines(u,v)
| convergent_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[14,18]),
[iquote('0:Res:14.1,18.0')] ).
cnf(111,plain,
~ parallel_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[78,24]),
[iquote('0:Res:78.0,24.0')] ).
cnf(137,plain,
( convergent_lines(skc2,u)
| distinct_lines(u,v)
| distinct_lines(skc3,v) ),
inference(res,[status(thm),theory(equality)],[54,28]),
[iquote('0:Res:54.0,28.0')] ).
cnf(138,plain,
( equal_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[14,28]),
[iquote('0:Res:14.1,28.0')] ).
cnf(144,plain,
( convergent_lines(skc2,u)
| distinct_lines(u,skc3) ),
inference(res,[status(thm),theory(equality)],[137,3]),
[iquote('0:Res:137.2,3.0')] ).
cnf(151,plain,
( convergent_lines(skc2,u)
| convergent_lines(u,skc3) ),
inference(res,[status(thm),theory(equality)],[144,18]),
[iquote('0:Res:144.1,18.0')] ).
cnf(154,plain,
convergent_lines(skc2,parallel_through_point(skc3,u)),
inference(res,[status(thm),theory(equality)],[151,5]),
[iquote('0:Res:151.1,5.0')] ).
cnf(190,plain,
( unorthogonal_lines(u,v)
| unorthogonal_lines(u,orthogonal_through_point(v,w)) ),
inference(res,[status(thm),theory(equality)],[78,38]),
[iquote('0:Res:78.0,38.0')] ).
cnf(195,plain,
( parallel_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[15,38]),
[iquote('0:Res:15.1,38.0')] ).
cnf(203,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
inference(res,[status(thm),theory(equality)],[16,35]),
[iquote('0:Res:16.1,35.0')] ).
cnf(204,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[190,8]),
[iquote('0:Res:190.1,8.0')] ).
cnf(208,plain,
( distinct_lines(parallel_through_point(skc3,u),v)
| convergent_lines(skc2,v) ),
inference(res,[status(thm),theory(equality)],[154,36]),
[iquote('0:Res:154.0,36.0')] ).
cnf(218,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[78,36]),
[iquote('0:Res:78.0,36.0')] ).
cnf(223,plain,
( parallel_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[15,36]),
[iquote('0:Res:15.1,36.0')] ).
cnf(238,plain,
( ~ equal_lines(parallel_through_point(skc3,u),v)
| convergent_lines(skc2,v) ),
inference(res,[status(thm),theory(equality)],[208,23]),
[iquote('0:Res:208.0,23.0')] ).
cnf(256,plain,
( equal_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[82,29]),
[iquote('0:Res:82.1,29.0')] ).
cnf(266,plain,
distinct_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[218,4]),
[iquote('0:Res:218.1,4.0')] ).
cnf(273,plain,
convergent_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[266,18]),
[iquote('0:Res:266.0,18.0')] ).
cnf(291,plain,
( ~ skP1(u,orthogonal_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[69,42]),
[iquote('0:Res:69.0,42.0')] ).
cnf(292,plain,
( ~ skP1(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[76,42]),
[iquote('0:Res:76.0,42.0')] ).
cnf(294,plain,
skP1(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[69,292]),
[iquote('0:Res:69.0,292.0')] ).
cnf(307,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u)
| ~ skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[204,43]),
[iquote('0:Res:204.0,43.0')] ).
cnf(311,plain,
( ~ convergent_lines(u,v)
| ~ skP1(v,u)
| orthogonal_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[17,43]),
[iquote('0:Res:17.1,43.0')] ).
cnf(391,plain,
( ~ distinct_points(u,v)
| equal_lines(w,x)
| apart_point_and_line(v,w)
| apart_point_and_line(v,x)
| apart_point_and_line(u,x)
| apart_point_and_line(u,w) ),
inference(res,[status(thm),theory(equality)],[14,48]),
[iquote('0:Res:14.1,48.0')] ).
cnf(423,plain,
( equal_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[138,3]),
[iquote('0:Res:138.2,3.0')] ).
cnf(434,plain,
( equal_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[423,18]),
[iquote('0:Res:423.1,18.0')] ).
cnf(436,plain,
equal_lines(u,parallel_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[434,5]),
[iquote('0:Res:434.1,5.0')] ).
cnf(443,plain,
convergent_lines(skc2,parallel_through_point(parallel_through_point(skc3,u),v)),
inference(res,[status(thm),theory(equality)],[436,238]),
[iquote('0:Res:436.0,238.0')] ).
cnf(458,plain,
~ parallel_lines(skc2,parallel_through_point(parallel_through_point(skc3,u),v)),
inference(res,[status(thm),theory(equality)],[443,24]),
[iquote('0:Res:443.0,24.0')] ).
cnf(518,plain,
( ~ orthogonal_lines(u,v)
| parallel_lines(w,v)
| unorthogonal_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[195,26]),
[iquote('0:Res:195.1,26.0')] ).
cnf(545,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[203,9]),
[iquote('0:Res:203.2,9.0')] ).
cnf(557,plain,
( incident_point_and_line(u,v)
| convergent_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[545,18]),
[iquote('0:Res:545.1,18.0')] ).
cnf(611,plain,
( parallel_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[223,4]),
[iquote('0:Res:223.2,4.0')] ).
cnf(612,plain,
( parallel_lines(parallel_through_point(u,v),w)
| distinct_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[223,5]),
[iquote('0:Res:223.2,5.0')] ).
cnf(622,plain,
( parallel_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[611,18]),
[iquote('0:Res:611.1,18.0')] ).
cnf(628,plain,
( ~ parallel_lines(u,v)
| parallel_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[622,24]),
[iquote('0:Res:622.1,24.0')] ).
cnf(737,plain,
( ~ skP1(orthogonal_through_point(u,v),u)
| orthogonal_lines(u,orthogonal_through_point(u,v)) ),
inference(res,[status(thm),theory(equality)],[273,311]),
[iquote('0:Res:273.0,311.0')] ).
cnf(744,plain,
orthogonal_lines(u,orthogonal_through_point(u,v)),
inference(mrr,[status(thm)],[737,294]),
[iquote('0:MRR:737.0,294.0')] ).
cnf(857,plain,
( equal_lines(u,v)
| apart_point_and_line(intersection_point(skc3,skc2),u)
| apart_point_and_line(intersection_point(skc3,skc2),v)
| apart_point_and_line(intersection_point(skc2,skc3),v)
| apart_point_and_line(intersection_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[58,391]),
[iquote('0:Res:58.0,391.0')] ).
cnf(862,plain,
( distinct_lines(u,v)
| parallel_lines(u,parallel_through_point(v,w)) ),
inference(res,[status(thm),theory(equality)],[612,628]),
[iquote('0:Res:612.0,628.0')] ).
cnf(938,plain,
distinct_lines(skc2,parallel_through_point(skc3,u)),
inference(res,[status(thm),theory(equality)],[862,458]),
[iquote('0:Res:862.1,458.0')] ).
cnf(951,plain,
( distinct_lines(parallel_through_point(skc3,u),v)
| distinct_lines(skc2,v) ),
inference(res,[status(thm),theory(equality)],[938,28]),
[iquote('0:Res:938.0,28.0')] ).
cnf(960,plain,
( ~ equal_lines(parallel_through_point(skc3,u),v)
| distinct_lines(skc2,v) ),
inference(res,[status(thm),theory(equality)],[951,23]),
[iquote('0:Res:951.0,23.0')] ).
cnf(1016,plain,
skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[294,291]),
[iquote('0:Res:294.0,291.0')] ).
cnf(1020,plain,
~ convergent_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(mrr,[status(thm)],[307,1016]),
[iquote('0:MRR:307.1,1016.0')] ).
cnf(1021,plain,
skP1(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[1016,292]),
[iquote('0:Res:1016.0,292.0')] ).
cnf(1157,plain,
( equal_lines(parallel_through_point(u,v),w)
| convergent_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[256,5]),
[iquote('0:Res:256.2,5.0')] ).
cnf(1444,plain,
( convergent_lines(u,skc3)
| distinct_lines(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1157,960]),
[iquote('0:Res:1157.0,960.0')] ).
cnf(1450,plain,
( ~ equal_lines(skc2,u)
| convergent_lines(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1444,23]),
[iquote('0:Res:1444.1,23.0')] ).
cnf(1475,plain,
~ equal_lines(skc2,orthogonal_through_point(orthogonal_through_point(skc3,u),v)),
inference(res,[status(thm),theory(equality)],[1450,1020]),
[iquote('0:Res:1450.1,1020.0')] ).
cnf(1839,plain,
( parallel_lines(u,orthogonal_through_point(v,w))
| unorthogonal_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[744,518]),
[iquote('0:Res:744.0,518.0')] ).
cnf(1851,plain,
unorthogonal_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[1839,111]),
[iquote('0:Res:1839.0,111.0')] ).
cnf(1876,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)],[1851,43]),
[iquote('0:Res:1851.0,43.0')] ).
cnf(1878,plain,
~ convergent_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(mrr,[status(thm)],[1876,1021]),
[iquote('0:MRR:1876.1,1021.0')] ).
cnf(1913,plain,
incident_point_and_line(u,v),
inference(res,[status(thm),theory(equality)],[557,1878]),
[iquote('0:Res:557.1,1878.0')] ).
cnf(1918,plain,
~ apart_point_and_line(u,v),
inference(mrr,[status(thm)],[25,1913]),
[iquote('0:MRR:25.1,1913.0')] ).
cnf(1940,plain,
equal_lines(u,v),
inference(mrr,[status(thm)],[857,1918]),
[iquote('0:MRR:857.1,857.4,857.2,857.3,1918.0')] ).
cnf(2038,plain,
$false,
inference(unc,[status(thm)],[1940,1475]),
[iquote('0:UnC:1940.0,1475.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 01:10:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.65
% 0.46/0.65 SPASS V 3.9
% 0.46/0.65 SPASS beiseite: Proof found.
% 0.46/0.65 % SZS status Theorem
% 0.46/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.65 SPASS derived 1975 clauses, backtracked 0 clauses, performed 0 splits and kept 1155 clauses.
% 0.46/0.65 SPASS allocated 98814 KBytes.
% 0.46/0.65 SPASS spent 0:00:00.30 on the problem.
% 0.46/0.65 0:00:00.04 for the input.
% 0.46/0.65 0:00:00.03 for the FLOTTER CNF translation.
% 0.46/0.65 0:00:00.02 for inferences.
% 0.46/0.65 0:00:00.00 for the backtracking.
% 0.46/0.65 0:00:00.19 for the reduction.
% 0.46/0.65
% 0.46/0.65
% 0.46/0.65 Here is a proof with depth 15, length 91 :
% 0.46/0.65 % SZS output start Refutation
% See solution above
% 0.46/0.66 Formulae used in the proof : con apart2 apart3 cp1 ooc1 ooc2 coipo1 cotno1 ax1 ax2 a3 a4 a5 p1 apart5 ax6 ceq2 ceq3 couo1 cu1
% 0.46/0.66
%------------------------------------------------------------------------------