TSTP Solution File: GEO172+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 06:22:55 EDT 2022
% Result : Theorem 0.51s 0.68s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of clauses : 80 ( 30 unt; 34 nHn; 80 RR)
% Number of literals : 155 ( 0 equ; 46 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('GEO172+3.p',unknown),
[] ).
cnf(5,axiom,
~ distinct_lines(u,u),
file('GEO172+3.p',unknown),
[] ).
cnf(6,axiom,
~ convergent_lines(u,u),
file('GEO172+3.p',unknown),
[] ).
cnf(7,axiom,
~ equal_points(skc4,intersection_point(skc5,skc3)),
file('GEO172+3.p',unknown),
[] ).
cnf(8,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO172+3.p',unknown),
[] ).
cnf(11,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO172+3.p',unknown),
[] ).
cnf(12,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO172+3.p',unknown),
[] ).
cnf(13,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(14,axiom,
( skP1(u,v)
| convergent_lines(v,u) ),
file('GEO172+3.p',unknown),
[] ).
cnf(15,axiom,
( skP1(u,v)
| unorthogonal_lines(v,u) ),
file('GEO172+3.p',unknown),
[] ).
cnf(16,axiom,
( equal_points(u,v)
| distinct_points(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(17,axiom,
( equal_lines(u,v)
| distinct_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(18,axiom,
( parallel_lines(u,v)
| convergent_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(19,axiom,
( incident_point_and_line(u,v)
| apart_point_and_line(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(20,axiom,
( orthogonal_lines(u,v)
| unorthogonal_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ distinct_lines(u,v)
| ~ equal_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ convergent_lines(u,v)
| ~ parallel_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ apart_point_and_line(u,v)
| ~ incident_point_and_line(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ unorthogonal_lines(u,v)
| ~ orthogonal_lines(u,v) ),
file('GEO172+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ distinct_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
file('GEO172+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO172+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
file('GEO172+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ convergent_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
file('GEO172+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ skP1(u,v)
| ~ skP1(w,v)
| skP1(u,w) ),
file('GEO172+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| ~ skP1(v,u) ),
file('GEO172+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('GEO172+3.p',unknown),
[] ).
cnf(58,plain,
( distinct_lines(skc3,u)
| convergent_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1,38]),
[iquote('0:Res:1.0,38.0')] ).
cnf(62,plain,
distinct_points(skc4,intersection_point(skc5,skc3)),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.1,7.0')] ).
cnf(73,plain,
skP1(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[15,11]),
[iquote('0:Res:15.1,11.0')] ).
cnf(82,plain,
skP1(u,u),
inference(res,[status(thm),theory(equality)],[14,6]),
[iquote('0:Res:14.1,6.0')] ).
cnf(84,plain,
convergent_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[13,11]),
[iquote('0:Res:13.0,11.0')] ).
cnf(118,plain,
~ parallel_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[84,26]),
[iquote('0:Res:84.0,26.0')] ).
cnf(147,plain,
( convergent_lines(skc5,u)
| distinct_lines(u,v)
| distinct_lines(skc3,v) ),
inference(res,[status(thm),theory(equality)],[58,30]),
[iquote('0:Res:58.0,30.0')] ).
cnf(148,plain,
( equal_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[17,30]),
[iquote('0:Res:17.1,30.0')] ).
cnf(153,plain,
( convergent_lines(skc5,u)
| distinct_lines(skc3,v)
| convergent_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[147,21]),
[iquote('0:Res:147.1,21.0')] ).
cnf(194,plain,
( unorthogonal_lines(u,v)
| unorthogonal_lines(u,orthogonal_through_point(v,w)) ),
inference(res,[status(thm),theory(equality)],[84,40]),
[iquote('0:Res:84.0,40.0')] ).
cnf(197,plain,
( parallel_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[18,40]),
[iquote('0:Res:18.1,40.0')] ).
cnf(203,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[194,11]),
[iquote('0:Res:194.1,11.0')] ).
cnf(205,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
inference(res,[status(thm),theory(equality)],[19,37]),
[iquote('0:Res:19.1,37.0')] ).
cnf(218,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[84,38]),
[iquote('0:Res:84.0,38.0')] ).
cnf(221,plain,
( parallel_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[18,38]),
[iquote('0:Res:18.1,38.0')] ).
cnf(233,plain,
distinct_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[218,6]),
[iquote('0:Res:218.1,6.0')] ).
cnf(239,plain,
convergent_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[233,21]),
[iquote('0:Res:233.0,21.0')] ).
cnf(283,plain,
( ~ skP1(u,orthogonal_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[73,44]),
[iquote('0:Res:73.0,44.0')] ).
cnf(284,plain,
( ~ skP1(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[82,44]),
[iquote('0:Res:82.0,44.0')] ).
cnf(286,plain,
skP1(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[73,284]),
[iquote('0:Res:73.0,284.0')] ).
cnf(302,plain,
( convergent_lines(skc5,parallel_through_point(u,v))
| distinct_lines(skc3,u) ),
inference(res,[status(thm),theory(equality)],[153,8]),
[iquote('0:Res:153.2,8.0')] ).
cnf(312,plain,
( ~ convergent_lines(u,v)
| ~ skP1(v,u)
| orthogonal_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[20,45]),
[iquote('0:Res:20.1,45.0')] ).
cnf(316,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)],[203,45]),
[iquote('0:Res:203.0,45.0')] ).
cnf(321,plain,
( ~ parallel_lines(skc5,parallel_through_point(u,v))
| distinct_lines(skc3,u) ),
inference(res,[status(thm),theory(equality)],[302,26]),
[iquote('0:Res:302.0,26.0')] ).
cnf(407,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)],[17,50]),
[iquote('0:Res:17.1,50.0')] ).
cnf(438,plain,
( equal_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[148,5]),
[iquote('0:Res:148.2,5.0')] ).
cnf(449,plain,
( equal_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[438,21]),
[iquote('0:Res:438.1,21.0')] ).
cnf(541,plain,
( ~ orthogonal_lines(u,v)
| parallel_lines(w,v)
| unorthogonal_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[197,28]),
[iquote('0:Res:197.1,28.0')] ).
cnf(566,plain,
( incident_point_and_line(u,v)
| distinct_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[205,12]),
[iquote('0:Res:205.2,12.0')] ).
cnf(634,plain,
( parallel_lines(u,v)
| distinct_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[221,6]),
[iquote('0:Res:221.2,6.0')] ).
cnf(645,plain,
( parallel_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[634,21]),
[iquote('0:Res:634.1,21.0')] ).
cnf(647,plain,
parallel_lines(u,parallel_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[645,8]),
[iquote('0:Res:645.1,8.0')] ).
cnf(652,plain,
distinct_lines(skc3,skc5),
inference(res,[status(thm),theory(equality)],[647,321]),
[iquote('0:Res:647.0,321.0')] ).
cnf(660,plain,
( distinct_lines(skc5,u)
| distinct_lines(skc3,u) ),
inference(res,[status(thm),theory(equality)],[652,30]),
[iquote('0:Res:652.0,30.0')] ).
cnf(682,plain,
( ~ equal_lines(skc3,u)
| distinct_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[660,25]),
[iquote('0:Res:660.1,25.0')] ).
cnf(711,plain,
( ~ equal_lines(skc3,u)
| ~ equal_lines(skc5,u) ),
inference(res,[status(thm),theory(equality)],[682,25]),
[iquote('0:Res:682.1,25.0')] ).
cnf(745,plain,
( ~ skP1(orthogonal_through_point(u,v),u)
| orthogonal_lines(u,orthogonal_through_point(u,v)) ),
inference(res,[status(thm),theory(equality)],[239,312]),
[iquote('0:Res:239.0,312.0')] ).
cnf(755,plain,
orthogonal_lines(u,orthogonal_through_point(u,v)),
inference(mrr,[status(thm)],[745,286]),
[iquote('0:MRR:745.0,286.0')] ).
cnf(872,plain,
( equal_lines(u,v)
| apart_point_and_line(intersection_point(skc5,skc3),u)
| apart_point_and_line(intersection_point(skc5,skc3),v)
| apart_point_and_line(skc4,v)
| apart_point_and_line(skc4,u) ),
inference(res,[status(thm),theory(equality)],[62,407]),
[iquote('0:Res:62.0,407.0')] ).
cnf(931,plain,
( incident_point_and_line(u,v)
| convergent_lines(v,orthogonal_through_point(w,u)) ),
inference(res,[status(thm),theory(equality)],[566,21]),
[iquote('0:Res:566.1,21.0')] ).
cnf(1042,plain,
skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[286,283]),
[iquote('0:Res:286.0,283.0')] ).
cnf(1045,plain,
~ convergent_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(mrr,[status(thm)],[316,1042]),
[iquote('0:MRR:316.1,1042.0')] ).
cnf(1046,plain,
skP1(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[1042,284]),
[iquote('0:Res:1042.0,284.0')] ).
cnf(1234,plain,
equal_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[449,1045]),
[iquote('0:Res:449.1,1045.0')] ).
cnf(1325,plain,
~ equal_lines(skc5,orthogonal_through_point(orthogonal_through_point(skc3,u),v)),
inference(res,[status(thm),theory(equality)],[1234,711]),
[iquote('0:Res:1234.0,711.0')] ).
cnf(1823,plain,
( parallel_lines(u,orthogonal_through_point(v,w))
| unorthogonal_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[755,541]),
[iquote('0:Res:755.0,541.0')] ).
cnf(1923,plain,
unorthogonal_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[1823,118]),
[iquote('0:Res:1823.0,118.0')] ).
cnf(1977,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)],[1923,45]),
[iquote('0:Res:1923.0,45.0')] ).
cnf(1979,plain,
~ convergent_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(mrr,[status(thm)],[1977,1046]),
[iquote('0:MRR:1977.1,1046.0')] ).
cnf(2084,plain,
incident_point_and_line(u,v),
inference(res,[status(thm),theory(equality)],[931,1979]),
[iquote('0:Res:931.1,1979.0')] ).
cnf(2085,plain,
~ apart_point_and_line(u,v),
inference(mrr,[status(thm)],[27,2084]),
[iquote('0:MRR:27.1,2084.0')] ).
cnf(2108,plain,
equal_lines(u,v),
inference(mrr,[status(thm)],[872,2085]),
[iquote('0:MRR:872.4,872.1,872.2,872.3,2085.0')] ).
cnf(2207,plain,
$false,
inference(unc,[status(thm)],[2108,1325]),
[iquote('0:UnC:2108.0,1325.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 01:07:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.68
% 0.51/0.68 SPASS V 3.9
% 0.51/0.68 SPASS beiseite: Proof found.
% 0.51/0.68 % SZS status Theorem
% 0.51/0.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.68 SPASS derived 2139 clauses, backtracked 0 clauses, performed 0 splits and kept 1284 clauses.
% 0.51/0.68 SPASS allocated 98909 KBytes.
% 0.51/0.68 SPASS spent 0:00:00.33 on the problem.
% 0.51/0.68 0:00:00.04 for the input.
% 0.51/0.68 0:00:00.03 for the FLOTTER CNF translation.
% 0.51/0.68 0:00:00.02 for inferences.
% 0.51/0.68 0:00:00.00 for the backtracking.
% 0.51/0.68 0:00:00.21 for the reduction.
% 0.51/0.68
% 0.51/0.68
% 0.51/0.68 Here is a proof with depth 10, length 80 :
% 0.51/0.68 % SZS output start Refutation
% See solution above
% 0.51/0.68 Formulae used in the proof : con apart2 apart3 cp1 ooc1 ooc2 coipo1 cotno1 ax1 ax2 a3 a4 a5 p1 apart5 ceq2 ceq3 couo1 cu1
% 0.51/0.68
%------------------------------------------------------------------------------