TSTP Solution File: GEO177+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO177+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 06:22:59 EDT 2022
% Result : Theorem 0.42s 0.58s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 41 ( 17 unt; 14 nHn; 41 RR)
% Number of literals : 72 ( 0 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 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(5,axiom,
~ convergent_lines(u,u),
file('GEO177+3.p',unknown),
[] ).
cnf(11,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO177+3.p',unknown),
[] ).
cnf(12,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO177+3.p',unknown),
[] ).
cnf(13,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO177+3.p',unknown),
[] ).
cnf(14,axiom,
( skP1(u,v)
| convergent_lines(v,u) ),
file('GEO177+3.p',unknown),
[] ).
cnf(15,axiom,
( skP1(u,v)
| unorthogonal_lines(v,u) ),
file('GEO177+3.p',unknown),
[] ).
cnf(18,axiom,
( parallel_lines(u,v)
| convergent_lines(u,v) ),
file('GEO177+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v) ),
file('GEO177+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ convergent_lines(u,v)
| ~ parallel_lines(u,v) ),
file('GEO177+3.p',unknown),
[] ).
cnf(29,axiom,
( apart_point_and_line(skc6,line_connecting(skc4,skc5))
| apart_point_and_line(skc7,line_connecting(skc4,skc5)) ),
file('GEO177+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO177+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ apart_point_and_line(u,v)
| distinct_lines(v,w)
| apart_point_and_line(u,w) ),
file('GEO177+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ convergent_lines(u,v)
| unorthogonal_lines(w,v)
| unorthogonal_lines(w,u) ),
file('GEO177+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ skP1(u,v)
| ~ skP1(w,v)
| skP1(u,w) ),
file('GEO177+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| ~ skP1(v,u) ),
file('GEO177+3.p',unknown),
[] ).
cnf(134,plain,
skP1(u,u),
inference(res,[status(thm),theory(equality)],[14,5]),
[iquote('0:Res:14.1,5.0')] ).
cnf(136,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(138,plain,
skP1(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[15,11]),
[iquote('0:Res:15.1,11.0')] ).
cnf(154,plain,
( ~ distinct_lines(u,v)
| ~ parallel_lines(u,v) ),
inference(res,[status(thm),theory(equality)],[21,26]),
[iquote('0:Res:21.1,26.0')] ).
cnf(213,plain,
( parallel_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[18,32]),
[iquote('0:Res:18.1,32.0')] ).
cnf(231,plain,
( unorthogonal_lines(u,v)
| unorthogonal_lines(u,orthogonal_through_point(v,w)) ),
inference(res,[status(thm),theory(equality)],[136,41]),
[iquote('0:Res:136.0,41.0')] ).
cnf(244,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(res,[status(thm),theory(equality)],[231,11]),
[iquote('0:Res:231.1,11.0')] ).
cnf(304,plain,
( apart_point_and_line(skc7,line_connecting(skc4,skc5))
| distinct_lines(line_connecting(skc4,skc5),u)
| apart_point_and_line(skc6,u) ),
inference(res,[status(thm),theory(equality)],[29,38]),
[iquote('0:Res:29.0,38.0')] ).
cnf(355,plain,
( ~ skP1(u,v)
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[134,45]),
[iquote('0:Res:134.0,45.0')] ).
cnf(357,plain,
( ~ skP1(u,orthogonal_through_point(v,w))
| skP1(v,u) ),
inference(res,[status(thm),theory(equality)],[138,45]),
[iquote('0:Res:138.0,45.0')] ).
cnf(363,plain,
skP1(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[138,355]),
[iquote('0:Res:138.0,355.0')] ).
cnf(368,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)],[244,46]),
[iquote('0:Res:244.0,46.0')] ).
cnf(517,plain,
( parallel_lines(u,v)
| convergent_lines(v,u) ),
inference(res,[status(thm),theory(equality)],[213,5]),
[iquote('0:Res:213.2,5.0')] ).
cnf(963,plain,
skP1(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[363,357]),
[iquote('0:Res:363.0,357.0')] ).
cnf(966,plain,
~ convergent_lines(orthogonal_through_point(orthogonal_through_point(u,v),w),u),
inference(mrr,[status(thm)],[368,963]),
[iquote('0:MRR:368.1,963.0')] ).
cnf(981,plain,
apart_point_and_line(skc7,line_connecting(skc4,skc5)),
inference(spt,[spt(split,[position(s1)])],[304]),
[iquote('1:Spt:304.0')] ).
cnf(982,plain,
( distinct_lines(line_connecting(skc4,skc5),u)
| apart_point_and_line(skc7,u) ),
inference(res,[status(thm),theory(equality)],[981,38]),
[iquote('1:Res:981.0,38.0')] ).
cnf(1158,plain,
( ~ parallel_lines(line_connecting(skc4,skc5),u)
| apart_point_and_line(skc7,u) ),
inference(res,[status(thm),theory(equality)],[982,154]),
[iquote('1:Res:982.0,154.0')] ).
cnf(1210,plain,
parallel_lines(u,orthogonal_through_point(orthogonal_through_point(u,v),w)),
inference(res,[status(thm),theory(equality)],[517,966]),
[iquote('0:Res:517.1,966.0')] ).
cnf(1450,plain,
apart_point_and_line(skc7,orthogonal_through_point(orthogonal_through_point(line_connecting(skc4,skc5),u),v)),
inference(res,[status(thm),theory(equality)],[1210,1158]),
[iquote('1:Res:1210.0,1158.0')] ).
cnf(1455,plain,
$false,
inference(unc,[status(thm)],[1450,12]),
[iquote('1:UnC:1450.0,12.0')] ).
cnf(1456,plain,
~ apart_point_and_line(skc7,line_connecting(skc4,skc5)),
inference(spt,[spt(split,[position(sa)])],[1455,981]),
[iquote('1:Spt:1455.0,304.0,981.0')] ).
cnf(1457,plain,
( distinct_lines(line_connecting(skc4,skc5),u)
| apart_point_and_line(skc6,u) ),
inference(spt,[spt(split,[position(s2)])],[304]),
[iquote('1:Spt:1455.0,304.1,304.2')] ).
cnf(1469,plain,
( ~ parallel_lines(line_connecting(skc4,skc5),u)
| apart_point_and_line(skc6,u) ),
inference(res,[status(thm),theory(equality)],[1457,154]),
[iquote('1:Res:1457.0,154.0')] ).
cnf(1492,plain,
apart_point_and_line(skc6,orthogonal_through_point(orthogonal_through_point(line_connecting(skc4,skc5),u),v)),
inference(res,[status(thm),theory(equality)],[1210,1469]),
[iquote('1:Res:1210.0,1469.0')] ).
cnf(1497,plain,
$false,
inference(unc,[status(thm)],[1492,12]),
[iquote('1:UnC:1492.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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 : Sat Jun 18 03:30:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.58
% 0.42/0.58 SPASS V 3.9
% 0.42/0.58 SPASS beiseite: Proof found.
% 0.42/0.58 % SZS status Theorem
% 0.42/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.58 SPASS derived 1386 clauses, backtracked 7 clauses, performed 2 splits and kept 871 clauses.
% 0.42/0.58 SPASS allocated 98521 KBytes.
% 0.42/0.58 SPASS spent 0:00:00.24 on the problem.
% 0.42/0.58 0:00:00.04 for the input.
% 0.42/0.58 0:00:00.03 for the FLOTTER CNF translation.
% 0.42/0.58 0:00:00.01 for inferences.
% 0.42/0.58 0:00:00.00 for the backtracking.
% 0.42/0.58 0:00:00.13 for the reduction.
% 0.42/0.58
% 0.42/0.58
% 0.42/0.58 Here is a proof with depth 6, length 41 :
% 0.42/0.58 % SZS output start Refutation
% See solution above
% 0.42/0.58 Formulae used in the proof : apart3 ooc1 ooc2 coipo1 cotno1 a3 p1 con ax6 ceq2 couo1
% 0.42/0.58
%------------------------------------------------------------------------------