TSTP Solution File: GEO205+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO205+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 5.71s 5.88s
% Output : Refutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of clauses : 82 ( 30 unt; 34 nHn; 82 RR)
% Number of literals : 160 ( 0 equ; 53 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
convergent_lines(skc5,skc3),
file('GEO205+3.p',unknown),
[] ).
cnf(2,axiom,
equal_lines(skc3,skc4),
file('GEO205+3.p',unknown),
[] ).
cnf(3,axiom,
~ distinct_points(u,u),
file('GEO205+3.p',unknown),
[] ).
cnf(5,axiom,
~ convergent_lines(u,u),
file('GEO205+3.p',unknown),
[] ).
cnf(6,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO205+3.p',unknown),
[] ).
cnf(9,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO205+3.p',unknown),
[] ).
cnf(10,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO205+3.p',unknown),
[] ).
cnf(11,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(12,axiom,
( skP1(u,v)
| convergent_lines(v,u) ),
file('GEO205+3.p',unknown),
[] ).
cnf(13,axiom,
( skP1(u,v)
| unorthogonal_lines(v,u) ),
file('GEO205+3.p',unknown),
[] ).
cnf(14,axiom,
( equal_points(u,v)
| distinct_points(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(15,axiom,
( equal_lines(u,v)
| distinct_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(16,axiom,
( parallel_lines(u,v)
| convergent_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(17,axiom,
( incident_point_and_line(u,v)
| apart_point_and_line(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(18,axiom,
( orthogonal_lines(u,v)
| unorthogonal_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ distinct_lines(u,v)
| ~ equal_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ convergent_lines(u,v)
| ~ parallel_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ apart_point_and_line(u,v)
| ~ incident_point_and_line(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ unorthogonal_lines(u,v)
| ~ orthogonal_lines(u,v) ),
file('GEO205+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO205+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ distinct_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
file('GEO205+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO205+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
file('GEO205+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ convergent_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
file('GEO205+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ skP1(u,v)
| ~ skP1(w,v)
| skP1(u,w) ),
file('GEO205+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ convergent_lines(skc5,skc4)
| ~ equal_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)) ),
file('GEO205+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| ~ skP1(v,u) ),
file('GEO205+3.p',unknown),
[] ).
cnf(49,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+3.p',unknown),
[] ).
cnf(50,plain,
~ distinct_lines(skc3,skc4),
inference(res,[status(thm),theory(equality)],[2,23]),
[iquote('0:Res:2.0,23.0')] ).
cnf(56,plain,
( distinct_lines(skc3,u)
| convergent_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1,36]),
[iquote('0:Res:1.0,36.0')] ).
cnf(64,plain,
convergent_lines(skc5,skc4),
inference(res,[status(thm),theory(equality)],[56,50]),
[iquote('0:Res:56.0,50.0')] ).
cnf(66,plain,
~ equal_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)),
inference(mrr,[status(thm)],[43,64]),
[iquote('0:MRR:43.0,64.0')] ).
cnf(73,plain,
skP1(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[13,9]),
[iquote('0:Res:13.1,9.0')] ).
cnf(80,plain,
skP1(u,u),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.1,5.0')] ).
cnf(82,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(117,plain,
~ parallel_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[82,24]),
[iquote('0:Res:82.0,24.0')] ).
cnf(150,plain,
( equal_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
inference(res,[status(thm),theory(equality)],[14,27]),
[iquote('0:Res:14.1,27.0')] ).
cnf(160,plain,
( distinct_points(intersection_point(skc5,skc4),u)
| distinct_points(intersection_point(skc5,skc3),u) ),
inference(res,[status(thm),theory(equality)],[150,66]),
[iquote('0:Res:150.0,66.0')] ).
cnf(172,plain,
( convergent_lines(skc5,u)
| distinct_lines(u,v)
| distinct_lines(skc3,v) ),
inference(res,[status(thm),theory(equality)],[56,28]),
[iquote('0:Res:56.0,28.0')] ).
cnf(179,plain,
( convergent_lines(skc5,u)
| distinct_lines(u,skc4) ),
inference(res,[status(thm),theory(equality)],[172,50]),
[iquote('0:Res:172.2,50.0')] ).
cnf(188,plain,
( convergent_lines(skc5,u)
| convergent_lines(u,skc4) ),
inference(res,[status(thm),theory(equality)],[179,19]),
[iquote('0:Res:179.1,19.0')] ).
cnf(193,plain,
( ~ parallel_lines(skc5,u)
| convergent_lines(u,skc4) ),
inference(res,[status(thm),theory(equality)],[188,24]),
[iquote('0:Res:188.0,24.0')] ).
cnf(208,plain,
( parallel_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[16,38]),
[iquote('0:Res:16.1,38.0')] ).
cnf(220,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
inference(res,[status(thm),theory(equality)],[17,35]),
[iquote('0:Res:17.1,35.0')] ).
cnf(235,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[82,36]),
[iquote('0:Res:82.0,36.0')] ).
cnf(238,plain,
( parallel_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[16,36]),
[iquote('0:Res:16.1,36.0')] ).
cnf(284,plain,
( ~ parallel_lines(skc5,u)
| ~ parallel_lines(u,skc4) ),
inference(res,[status(thm),theory(equality)],[193,24]),
[iquote('0:Res:193.1,24.0')] ).
cnf(306,plain,
( ~ skP1(u,orthogonal_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[73,42]),
[iquote('0:Res:73.0,42.0')] ).
cnf(307,plain,
( ~ skP1(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[80,42]),
[iquote('0:Res:80.0,42.0')] ).
cnf(326,plain,
( ~ convergent_lines(u,v)
| ~ skP1(v,u)
| orthogonal_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[18,44]),
[iquote('0:Res:18.1,44.0')] ).
cnf(336,plain,
skP1(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[73,307]),
[iquote('0:Res:73.0,307.0')] ).
cnf(376,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)],[15,49]),
[iquote('0:Res:15.1,49.0')] ).
cnf(492,plain,
( ~ orthogonal_lines(u,v)
| parallel_lines(w,v)
| unorthogonal_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[208,26]),
[iquote('0:Res:208.1,26.0')] ).
cnf(522,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[220,10]),
[iquote('0:Res:220.2,10.0')] ).
cnf(597,plain,
( parallel_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[238,5]),
[iquote('0:Res:238.2,5.0')] ).
cnf(598,plain,
( parallel_lines(parallel_through_point(u,v),w)
| distinct_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[238,6]),
[iquote('0:Res:238.2,6.0')] ).
cnf(644,plain,
( parallel_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[597,19]),
[iquote('0:Res:597.1,19.0')] ).
cnf(668,plain,
parallel_lines(u,parallel_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[644,6]),
[iquote('0:Res:644.1,6.0')] ).
cnf(679,plain,
~ parallel_lines(parallel_through_point(skc5,u),skc4),
inference(res,[status(thm),theory(equality)],[668,284]),
[iquote('0:Res:668.0,284.0')] ).
cnf(895,plain,
distinct_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[235,5]),
[iquote('0:Res:235.1,5.0')] ).
cnf(910,plain,
convergent_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[895,19]),
[iquote('0:Res:895.0,19.0')] ).
cnf(911,plain,
( ~ skP1(orthogonal_through_point(u,v),u)
| orthogonal_lines(u,orthogonal_through_point(u,v)) ),
inference(res,[status(thm),theory(equality)],[910,326]),
[iquote('0:Res:910.0,326.0')] ).
cnf(916,plain,
orthogonal_lines(u,orthogonal_through_point(u,v)),
inference(mrr,[status(thm)],[911,336]),
[iquote('0:MRR:911.0,336.0')] ).
cnf(1021,plain,
( incident_point_and_line(u,v)
| convergent_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[522,19]),
[iquote('0:Res:522.1,19.0')] ).
cnf(1040,plain,
distinct_lines(skc4,skc5),
inference(res,[status(thm),theory(equality)],[598,679]),
[iquote('0:Res:598.0,679.0')] ).
cnf(1054,plain,
( distinct_lines(skc5,u)
| distinct_lines(skc4,u) ),
inference(res,[status(thm),theory(equality)],[1040,28]),
[iquote('0:Res:1040.0,28.0')] ).
cnf(1090,plain,
( ~ equal_lines(skc4,u)
| distinct_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1054,23]),
[iquote('0:Res:1054.1,23.0')] ).
cnf(1143,plain,
( ~ equal_lines(skc4,u)
| ~ distinct_points(v,w)
| apart_point_and_line(w,skc5)
| apart_point_and_line(w,u)
| apart_point_and_line(v,u)
| apart_point_and_line(v,skc5) ),
inference(res,[status(thm),theory(equality)],[1090,49]),
[iquote('0:Res:1090.1,49.0')] ).
cnf(1237,plain,
skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[336,306]),
[iquote('0:Res:336.0,306.0')] ).
cnf(1246,plain,
skP1(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[1237,307]),
[iquote('0:Res:1237.0,307.0')] ).
cnf(1491,plain,
distinct_points(intersection_point(skc5,skc4),intersection_point(skc5,skc3)),
inference(res,[status(thm),theory(equality)],[160,3]),
[iquote('0:Res:160.1,3.0')] ).
cnf(1893,plain,
( parallel_lines(u,orthogonal_through_point(v,w))
| unorthogonal_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[916,492]),
[iquote('0:Res:916.0,492.0')] ).
cnf(10222,plain,
unorthogonal_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[1893,117]),
[iquote('0:Res:1893.0,117.0')] ).
cnf(10429,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)],[10222,44]),
[iquote('0:Res:10222.0,44.0')] ).
cnf(10431,plain,
~ convergent_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(mrr,[status(thm)],[10429,1246]),
[iquote('0:MRR:10429.1,1246.0')] ).
cnf(11115,plain,
incident_point_and_line(u,v),
inference(res,[status(thm),theory(equality)],[1021,10431]),
[iquote('0:Res:1021.1,10431.0')] ).
cnf(11116,plain,
~ apart_point_and_line(u,v),
inference(mrr,[status(thm)],[25,11115]),
[iquote('0:MRR:25.1,11115.0')] ).
cnf(11156,plain,
( ~ distinct_points(u,v)
| equal_lines(w,x) ),
inference(mrr,[status(thm)],[376,11116]),
[iquote('0:MRR:376.3,376.2,376.4,376.5,11116.0')] ).
cnf(11725,plain,
( ~ equal_lines(skc4,u)
| ~ distinct_points(v,w) ),
inference(mrr,[status(thm)],[1143,11116]),
[iquote('0:MRR:1143.2,1143.5,1143.4,1143.3,11116.0')] ).
cnf(12681,plain,
~ distinct_points(u,v),
inference(mrr,[status(thm)],[11725,11156]),
[iquote('0:MRR:11725.0,11156.1')] ).
cnf(12682,plain,
$false,
inference(unc,[status(thm)],[12681,1491]),
[iquote('0:UnC:12681.0,1491.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO205+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 : Fri Jun 17 23:20:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.71/5.88
% 5.71/5.88 SPASS V 3.9
% 5.71/5.88 SPASS beiseite: Proof found.
% 5.71/5.88 % SZS status Theorem
% 5.71/5.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/5.88 SPASS derived 12505 clauses, backtracked 0 clauses, performed 1 splits and kept 6451 clauses.
% 5.71/5.88 SPASS allocated 105481 KBytes.
% 5.71/5.88 SPASS spent 0:00:05.50 on the problem.
% 5.71/5.88 0:00:00.04 for the input.
% 5.71/5.88 0:00:00.03 for the FLOTTER CNF translation.
% 5.71/5.88 0:00:00.10 for inferences.
% 5.71/5.88 0:00:00.02 for the backtracking.
% 5.71/5.88 0:00:05.23 for the reduction.
% 5.71/5.88
% 5.71/5.88
% 5.71/5.88 Here is a proof with depth 11, length 82 :
% 5.71/5.88 % SZS output start Refutation
% See solution above
% 5.71/5.88 Formulae used in the proof : con apart1 apart3 cp1 ooc1 ooc2 coipo1 cotno1 ax1 ax2 a3 a4 a5 p1 apart4 apart5 ceq2 ceq3 couo1 cu1
% 5.71/5.88
%------------------------------------------------------------------------------