TSTP Solution File: GEO076-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 06:22:07 EDT 2022
% Result : Unsatisfiable 0.41s 0.59s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of clauses : 58 ( 15 unt; 27 nHn; 58 RR)
% Number of literals : 185 ( 0 equ; 107 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
point(a_point),
file('GEO076-4.p',unknown),
[] ).
cnf(2,axiom,
( ~ line(u)
| on(a_point,u) ),
file('GEO076-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ point(u)
| ~ point(v)
| equal(v,u)
| on(v,line_from_to(v,u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ point(u)
| ~ point(v)
| equal(v,u)
| on(u,line_from_to(v,u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ point(u)
| ~ point(v)
| line(line_from_to(v,u))
| equal(v,u) ),
file('GEO076-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ line(u)
| ~ line(v)
| ~ point(w)
| ~ point(x)
| ~ on(w,u)
| ~ on(x,u)
| ~ on(w,v)
| ~ on(x,v)
| equal(v,u)
| equal(x,w) ),
file('GEO076-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ line(u)
| on(point_1_on_line(u),u) ),
file('GEO076-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ line(u)
| on(point_2_on_line(u),u) ),
file('GEO076-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ line(u)
| point(point_1_on_line(u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ line(u)
| point(point_2_on_line(u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ line(u)
| ~ equal(point_2_on_line(u),point_1_on_line(u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(12,axiom,
( ~ line(u)
| ~ on(point_not_on_line(u),u) ),
file('GEO076-4.p',unknown),
[] ).
cnf(13,axiom,
( ~ line(u)
| point(point_not_on_line(u)) ),
file('GEO076-4.p',unknown),
[] ).
cnf(14,axiom,
line(at_least_one_line),
file('GEO076-4.p',unknown),
[] ).
cnf(34,plain,
on(a_point,at_least_one_line),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.0,2.0')] ).
cnf(102,plain,
( ~ line(at_least_one_line)
| ~ line(u)
| ~ point(a_point)
| ~ point(v)
| ~ on(v,at_least_one_line)
| ~ on(a_point,u)
| ~ on(v,u)
| equal(u,at_least_one_line)
| equal(v,a_point) ),
inference(res,[status(thm),theory(equality)],[34,6]),
[iquote('0:Res:34.0,6.4')] ).
cnf(117,plain,
( ~ line(u)
| ~ point(v)
| ~ on(v,at_least_one_line)
| ~ on(a_point,u)
| ~ on(v,u)
| equal(u,at_least_one_line)
| equal(v,a_point) ),
inference(ssi,[status(thm)],[102,1,14]),
[iquote('0:SSi:102.2,102.0,1.0,14.0')] ).
cnf(118,plain,
( ~ line(u)
| ~ point(v)
| ~ on(v,at_least_one_line)
| ~ on(v,u)
| equal(u,at_least_one_line)
| equal(v,a_point) ),
inference(mrr,[status(thm)],[117,2]),
[iquote('0:MRR:117.3,2.1')] ).
cnf(144,plain,
( ~ line(at_least_one_line)
| ~ line(u)
| ~ point(point_2_on_line(at_least_one_line))
| ~ on(point_2_on_line(at_least_one_line),u)
| equal(u,at_least_one_line)
| equal(point_2_on_line(at_least_one_line),a_point) ),
inference(res,[status(thm),theory(equality)],[8,118]),
[iquote('0:Res:8.1,118.2')] ).
cnf(145,plain,
( ~ line(at_least_one_line)
| ~ line(u)
| ~ point(point_1_on_line(at_least_one_line))
| ~ on(point_1_on_line(at_least_one_line),u)
| equal(u,at_least_one_line)
| equal(point_1_on_line(at_least_one_line),a_point) ),
inference(res,[status(thm),theory(equality)],[7,118]),
[iquote('0:Res:7.1,118.2')] ).
cnf(150,plain,
( ~ line(u)
| ~ on(point_1_on_line(at_least_one_line),u)
| equal(u,at_least_one_line)
| equal(point_1_on_line(at_least_one_line),a_point) ),
inference(ssi,[status(thm)],[145,9,14]),
[iquote('0:SSi:145.2,145.0,9.0,14.0,14.1')] ).
cnf(151,plain,
( ~ line(u)
| ~ on(point_2_on_line(at_least_one_line),u)
| equal(u,at_least_one_line)
| equal(point_2_on_line(at_least_one_line),a_point) ),
inference(ssi,[status(thm)],[144,10,14]),
[iquote('0:SSi:144.2,144.0,10.0,14.0,14.1')] ).
cnf(192,plain,
( ~ line(u)
| ~ on(point_1_on_line(at_least_one_line),u)
| equal(u,at_least_one_line) ),
inference(spt,[spt(split,[position(s1)])],[150]),
[iquote('1:Spt:150.0,150.1,150.2')] ).
cnf(195,plain,
( ~ point(u)
| ~ point(point_1_on_line(at_least_one_line))
| ~ line(line_from_to(point_1_on_line(at_least_one_line),u))
| equal(point_1_on_line(at_least_one_line),u)
| equal(line_from_to(point_1_on_line(at_least_one_line),u),at_least_one_line) ),
inference(res,[status(thm),theory(equality)],[3,192]),
[iquote('1:Res:3.3,192.1')] ).
cnf(202,plain,
( ~ point(u)
| ~ line(line_from_to(point_1_on_line(at_least_one_line),u))
| equal(point_1_on_line(at_least_one_line),u)
| equal(line_from_to(point_1_on_line(at_least_one_line),u),at_least_one_line) ),
inference(ssi,[status(thm)],[195,9,14]),
[iquote('1:SSi:195.1,9.0,14.1')] ).
cnf(228,plain,
( ~ point(u)
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(u)
| equal(point_1_on_line(at_least_one_line),u)
| equal(line_from_to(point_1_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_1_on_line(at_least_one_line),u) ),
inference(sor,[status(thm)],[202,5]),
[iquote('1:SoR:202.1,5.2')] ).
cnf(229,plain,
( ~ point(point_1_on_line(at_least_one_line))
| ~ point(u)
| equal(line_from_to(point_1_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_1_on_line(at_least_one_line),u) ),
inference(obv,[status(thm),theory(equality)],[228]),
[iquote('1:Obv:228.3')] ).
cnf(230,plain,
( ~ point(u)
| equal(line_from_to(point_1_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_1_on_line(at_least_one_line),u) ),
inference(ssi,[status(thm)],[229,9,14]),
[iquote('1:SSi:229.0,9.0,14.1')] ).
cnf(232,plain,
( ~ point(u)
| ~ point(u)
| ~ point(point_1_on_line(at_least_one_line))
| equal(point_1_on_line(at_least_one_line),u)
| equal(point_1_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(spr,[status(thm),theory(equality)],[230,4]),
[iquote('1:SpR:230.1,4.3')] ).
cnf(236,plain,
( ~ point(u)
| ~ point(point_1_on_line(at_least_one_line))
| equal(point_1_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(obv,[status(thm),theory(equality)],[232]),
[iquote('1:Obv:232.3')] ).
cnf(237,plain,
( ~ point(u)
| equal(point_1_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(ssi,[status(thm)],[236,9,14]),
[iquote('1:SSi:236.1,9.0,14.1')] ).
cnf(279,plain,
( ~ point(point_not_on_line(at_least_one_line))
| ~ line(at_least_one_line)
| equal(point_not_on_line(at_least_one_line),point_1_on_line(at_least_one_line)) ),
inference(res,[status(thm),theory(equality)],[237,12]),
[iquote('1:Res:237.2,12.1')] ).
cnf(286,plain,
equal(point_not_on_line(at_least_one_line),point_1_on_line(at_least_one_line)),
inference(ssi,[status(thm)],[279,14,13]),
[iquote('1:SSi:279.1,279.0,14.0,13.1,14.0')] ).
cnf(298,plain,
( ~ line(at_least_one_line)
| ~ on(point_1_on_line(at_least_one_line),at_least_one_line) ),
inference(spl,[status(thm),theory(equality)],[286,12]),
[iquote('1:SpL:286.0,12.1')] ).
cnf(299,plain,
~ on(point_1_on_line(at_least_one_line),at_least_one_line),
inference(ssi,[status(thm)],[298,14]),
[iquote('1:SSi:298.0,14.0')] ).
cnf(301,plain,
~ line(at_least_one_line),
inference(res,[status(thm),theory(equality)],[7,299]),
[iquote('1:Res:7.1,299.0')] ).
cnf(302,plain,
$false,
inference(ssi,[status(thm)],[301,14]),
[iquote('1:SSi:301.0,14.0')] ).
cnf(303,plain,
equal(point_1_on_line(at_least_one_line),a_point),
inference(spt,[spt(split,[position(s2)])],[150]),
[iquote('1:Spt:302.0,150.3')] ).
cnf(307,plain,
( ~ line(u)
| ~ on(point_2_on_line(at_least_one_line),u)
| equal(u,at_least_one_line) ),
inference(spt,[spt(split,[position(s2s1)])],[151]),
[iquote('2:Spt:151.0,151.1,151.2')] ).
cnf(310,plain,
( ~ point(u)
| ~ point(point_2_on_line(at_least_one_line))
| ~ line(line_from_to(point_2_on_line(at_least_one_line),u))
| equal(point_2_on_line(at_least_one_line),u)
| equal(line_from_to(point_2_on_line(at_least_one_line),u),at_least_one_line) ),
inference(res,[status(thm),theory(equality)],[3,307]),
[iquote('2:Res:3.3,307.1')] ).
cnf(317,plain,
( ~ point(u)
| ~ line(line_from_to(point_2_on_line(at_least_one_line),u))
| equal(point_2_on_line(at_least_one_line),u)
| equal(line_from_to(point_2_on_line(at_least_one_line),u),at_least_one_line) ),
inference(ssi,[status(thm)],[310,10,14]),
[iquote('2:SSi:310.1,10.0,14.1')] ).
cnf(397,plain,
( ~ point(u)
| ~ point(point_2_on_line(at_least_one_line))
| ~ point(u)
| equal(point_2_on_line(at_least_one_line),u)
| equal(line_from_to(point_2_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_2_on_line(at_least_one_line),u) ),
inference(sor,[status(thm)],[317,5]),
[iquote('2:SoR:317.1,5.2')] ).
cnf(398,plain,
( ~ point(point_2_on_line(at_least_one_line))
| ~ point(u)
| equal(line_from_to(point_2_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_2_on_line(at_least_one_line),u) ),
inference(obv,[status(thm),theory(equality)],[397]),
[iquote('2:Obv:397.3')] ).
cnf(399,plain,
( ~ point(u)
| equal(line_from_to(point_2_on_line(at_least_one_line),u),at_least_one_line)
| equal(point_2_on_line(at_least_one_line),u) ),
inference(ssi,[status(thm)],[398,10,14]),
[iquote('2:SSi:398.0,10.0,14.1')] ).
cnf(401,plain,
( ~ point(u)
| ~ point(u)
| ~ point(point_2_on_line(at_least_one_line))
| equal(point_2_on_line(at_least_one_line),u)
| equal(point_2_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(spr,[status(thm),theory(equality)],[399,4]),
[iquote('2:SpR:399.1,4.3')] ).
cnf(405,plain,
( ~ point(u)
| ~ point(point_2_on_line(at_least_one_line))
| equal(point_2_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(obv,[status(thm),theory(equality)],[401]),
[iquote('2:Obv:401.3')] ).
cnf(406,plain,
( ~ point(u)
| equal(point_2_on_line(at_least_one_line),u)
| on(u,at_least_one_line) ),
inference(ssi,[status(thm)],[405,10,14]),
[iquote('2:SSi:405.1,10.0,14.1')] ).
cnf(446,plain,
( ~ point(point_not_on_line(at_least_one_line))
| ~ line(at_least_one_line)
| equal(point_not_on_line(at_least_one_line),point_2_on_line(at_least_one_line)) ),
inference(res,[status(thm),theory(equality)],[406,12]),
[iquote('2:Res:406.2,12.1')] ).
cnf(457,plain,
equal(point_not_on_line(at_least_one_line),point_2_on_line(at_least_one_line)),
inference(ssi,[status(thm)],[446,14,13]),
[iquote('2:SSi:446.1,446.0,14.0,13.1,14.0')] ).
cnf(474,plain,
( ~ line(at_least_one_line)
| ~ on(point_2_on_line(at_least_one_line),at_least_one_line) ),
inference(spl,[status(thm),theory(equality)],[457,12]),
[iquote('2:SpL:457.0,12.1')] ).
cnf(475,plain,
~ on(point_2_on_line(at_least_one_line),at_least_one_line),
inference(ssi,[status(thm)],[474,14]),
[iquote('2:SSi:474.0,14.0')] ).
cnf(477,plain,
~ line(at_least_one_line),
inference(res,[status(thm),theory(equality)],[8,475]),
[iquote('2:Res:8.1,475.0')] ).
cnf(478,plain,
$false,
inference(ssi,[status(thm)],[477,14]),
[iquote('2:SSi:477.0,14.0')] ).
cnf(479,plain,
equal(point_2_on_line(at_least_one_line),a_point),
inference(spt,[spt(split,[position(s2s2)])],[151]),
[iquote('2:Spt:478.0,151.3')] ).
cnf(483,plain,
( ~ line(at_least_one_line)
| ~ equal(point_1_on_line(at_least_one_line),a_point) ),
inference(spl,[status(thm),theory(equality)],[479,11]),
[iquote('2:SpL:479.0,11.1')] ).
cnf(485,plain,
( ~ line(at_least_one_line)
| ~ equal(a_point,a_point) ),
inference(rew,[status(thm),theory(equality)],[303,483]),
[iquote('2:Rew:303.0,483.1')] ).
cnf(486,plain,
~ line(at_least_one_line),
inference(obv,[status(thm),theory(equality)],[485]),
[iquote('2:Obv:485.1')] ).
cnf(487,plain,
$false,
inference(ssi,[status(thm)],[486,14]),
[iquote('2:SSi:486.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 09:14:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.41/0.59
% 0.41/0.59 SPASS V 3.9
% 0.41/0.59 SPASS beiseite: Proof found.
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.59 SPASS derived 209 clauses, backtracked 3 clauses, performed 3 splits and kept 142 clauses.
% 0.41/0.59 SPASS allocated 82683 KBytes.
% 0.41/0.59 SPASS spent 0:00:00.23 on the problem.
% 0.41/0.59 0:00:00.03 for the input.
% 0.41/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.59 0:00:00.01 for inferences.
% 0.41/0.59 0:00:00.00 for the backtracking.
% 0.41/0.59 0:00:00.16 for the reduction.
% 0.41/0.59
% 0.41/0.59
% 0.41/0.59 Here is a proof with depth 10, length 58 :
% 0.41/0.59 % SZS output start Refutation
% See solution above
% 0.41/0.59 Formulae used in the proof : there_is_a_point prove_point_is_not_on_every_line axiom_G1A axiom_G1B axiom_G1C axiom_G1D axiom_G2A axiom_G2B axiom_G2C axiom_G2D axiom_G2E axiom_G3A axiom_G3B axiom_G4A
% 0.41/0.59
%------------------------------------------------------------------------------