TSTP Solution File: GEO077-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO077-4 : TPTP v8.1.0. Released v1.0.0.
% 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 06:22:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 18 unt; 13 nHn; 34 RR)
% Number of literals : 124 ( 0 equ; 65 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
point(point1),
file('GEO077-4.p',unknown),
[] ).
cnf(2,axiom,
point(point2),
file('GEO077-4.p',unknown),
[] ).
cnf(3,axiom,
point(point3),
file('GEO077-4.p',unknown),
[] ).
cnf(4,axiom,
line(a_line),
file('GEO077-4.p',unknown),
[] ).
cnf(5,axiom,
on(point1,a_line),
file('GEO077-4.p',unknown),
[] ).
cnf(6,axiom,
on(point2,a_line),
file('GEO077-4.p',unknown),
[] ).
cnf(7,axiom,
~ on(point3,a_line),
file('GEO077-4.p',unknown),
[] ).
cnf(8,axiom,
~ equal(point2,point1),
file('GEO077-4.p',unknown),
[] ).
cnf(9,axiom,
~ equal(point3,point1),
file('GEO077-4.p',unknown),
[] ).
cnf(10,axiom,
~ equal(point3,point2),
file('GEO077-4.p',unknown),
[] ).
cnf(11,axiom,
collinear(point1,point2,point3),
file('GEO077-4.p',unknown),
[] ).
cnf(15,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('GEO077-4.p',unknown),
[] ).
cnf(38,axiom,
( ~ point(u)
| ~ point(v)
| ~ point(w)
| ~ collinear(w,v,u)
| equal(v,u)
| equal(w,u)
| equal(w,v)
| on(w,line_through_3_points(w,v,u)) ),
file('GEO077-4.p',unknown),
[] ).
cnf(39,axiom,
( ~ point(u)
| ~ point(v)
| ~ point(w)
| ~ collinear(w,v,u)
| equal(v,u)
| equal(w,u)
| equal(w,v)
| on(v,line_through_3_points(w,v,u)) ),
file('GEO077-4.p',unknown),
[] ).
cnf(40,axiom,
( ~ point(u)
| ~ point(v)
| ~ point(w)
| ~ collinear(w,v,u)
| equal(v,u)
| equal(w,u)
| equal(w,v)
| on(u,line_through_3_points(w,v,u)) ),
file('GEO077-4.p',unknown),
[] ).
cnf(41,axiom,
( ~ point(u)
| ~ point(v)
| ~ point(w)
| ~ collinear(w,v,u)
| line(line_through_3_points(w,v,u))
| equal(v,u)
| equal(w,u)
| equal(w,v) ),
file('GEO077-4.p',unknown),
[] ).
cnf(43,plain,
( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| equal(point2,point1)
| equal(point3,point1)
| equal(point3,point2)
| on(point3,line_through_3_points(point1,point2,point3)) ),
inference(res,[status(thm),theory(equality)],[11,40]),
[iquote('0:Res:11.0,40.3')] ).
cnf(44,plain,
( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| equal(point2,point1)
| equal(point3,point1)
| equal(point3,point2)
| on(point2,line_through_3_points(point1,point2,point3)) ),
inference(res,[status(thm),theory(equality)],[11,39]),
[iquote('0:Res:11.0,39.3')] ).
cnf(45,plain,
( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| equal(point2,point1)
| equal(point3,point1)
| equal(point3,point2)
| on(point1,line_through_3_points(point1,point2,point3)) ),
inference(res,[status(thm),theory(equality)],[11,38]),
[iquote('0:Res:11.0,38.3')] ).
cnf(46,plain,
( ~ point(point1)
| ~ point(point2)
| ~ point(point3)
| equal(point2,point1)
| equal(point3,point1)
| equal(point3,point2)
| line(line_through_3_points(point1,point2,point3)) ),
inference(res,[status(thm),theory(equality)],[11,41]),
[iquote('0:Res:11.0,41.3')] ).
cnf(47,plain,
line(line_through_3_points(point1,point2,point3)),
inference(mrr,[status(thm)],[46,1,2,3,8,9,10]),
[iquote('0:MRR:46.0,46.1,46.2,46.3,46.4,46.5,1.0,2.0,3.0,8.0,9.0,10.0')] ).
cnf(48,plain,
on(point1,line_through_3_points(point1,point2,point3)),
inference(mrr,[status(thm)],[45,1,2,3,8,9,10]),
[iquote('0:MRR:45.0,45.1,45.2,45.3,45.4,45.5,1.0,2.0,3.0,8.0,9.0,10.0')] ).
cnf(49,plain,
on(point2,line_through_3_points(point1,point2,point3)),
inference(mrr,[status(thm)],[44,1,2,3,8,9,10]),
[iquote('0:MRR:44.0,44.1,44.2,44.3,44.4,44.5,1.0,2.0,3.0,8.0,9.0,10.0')] ).
cnf(50,plain,
on(point3,line_through_3_points(point1,point2,point3)),
inference(mrr,[status(thm)],[43,1,2,3,8,9,10]),
[iquote('0:MRR:43.0,43.1,43.2,43.3,43.4,43.5,1.0,2.0,3.0,8.0,9.0,10.0')] ).
cnf(127,plain,
( ~ line(a_line)
| ~ line(u)
| ~ point(point1)
| ~ point(v)
| ~ on(v,a_line)
| ~ on(point1,u)
| ~ on(v,u)
| equal(u,a_line)
| equal(v,point1) ),
inference(res,[status(thm),theory(equality)],[5,15]),
[iquote('0:Res:5.0,15.4')] ).
cnf(144,plain,
( ~ line(u)
| ~ point(v)
| ~ on(v,a_line)
| ~ on(point1,u)
| ~ on(v,u)
| equal(u,a_line)
| equal(v,point1) ),
inference(ssi,[status(thm)],[127,1,4]),
[iquote('0:SSi:127.2,127.0,1.0,4.0')] ).
cnf(169,plain,
( ~ line(u)
| ~ point(point2)
| ~ on(point1,u)
| ~ on(point2,u)
| equal(u,a_line)
| equal(point2,point1) ),
inference(res,[status(thm),theory(equality)],[6,144]),
[iquote('0:Res:6.0,144.2')] ).
cnf(176,plain,
( ~ line(u)
| ~ on(point1,u)
| ~ on(point2,u)
| equal(u,a_line)
| equal(point2,point1) ),
inference(ssi,[status(thm)],[169,2]),
[iquote('0:SSi:169.1,2.0')] ).
cnf(177,plain,
( ~ line(u)
| ~ on(point1,u)
| ~ on(point2,u)
| equal(u,a_line) ),
inference(mrr,[status(thm)],[176,8]),
[iquote('0:MRR:176.4,8.0')] ).
cnf(184,plain,
( ~ line(line_through_3_points(point1,point2,point3))
| ~ on(point1,line_through_3_points(point1,point2,point3))
| equal(line_through_3_points(point1,point2,point3),a_line) ),
inference(res,[status(thm),theory(equality)],[49,177]),
[iquote('0:Res:49.0,177.2')] ).
cnf(193,plain,
( ~ on(point1,line_through_3_points(point1,point2,point3))
| equal(line_through_3_points(point1,point2,point3),a_line) ),
inference(ssi,[status(thm)],[184,47]),
[iquote('0:SSi:184.0,47.0')] ).
cnf(194,plain,
equal(line_through_3_points(point1,point2,point3),a_line),
inference(mrr,[status(thm)],[193,48]),
[iquote('0:MRR:193.0,48.0')] ).
cnf(196,plain,
on(point3,a_line),
inference(rew,[status(thm),theory(equality)],[194,50]),
[iquote('0:Rew:194.0,50.0')] ).
cnf(202,plain,
$false,
inference(mrr,[status(thm)],[196,7]),
[iquote('0:MRR:196.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO077-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 12:08:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 73 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses.
% 0.19/0.48 SPASS allocated 82245 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.00 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 3, length 34 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : point1 point2 point3 line point1_on_line point2_on_line point3_not_on_line point1_not_point2 point1_not_point3 point2_not_point3 prove_points_noncollinear axiom_G1D axiom_G10A axiom_G10B axiom_G10C axiom_G10D
% 0.19/0.48
%------------------------------------------------------------------------------