TSTP Solution File: GEO201+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 06:23:20 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 17 unt; 15 nHn; 37 RR)
% Number of literals : 77 ( 0 equ; 25 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
convergent_lines(skc2,skc3),
file('GEO201+2.p',unknown),
[] ).
cnf(2,axiom,
~ distinct_points(u,u),
file('GEO201+2.p',unknown),
[] ).
cnf(3,axiom,
~ distinct_lines(u,u),
file('GEO201+2.p',unknown),
[] ).
cnf(4,axiom,
~ convergent_lines(u,u),
file('GEO201+2.p',unknown),
[] ).
cnf(5,axiom,
distinct_points(intersection_point(skc2,skc3),intersection_point(skc3,skc2)),
file('GEO201+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(u,v) ),
file('GEO201+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO201+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ distinct_lines(u,v)
| distinct_lines(v,w)
| distinct_lines(u,w) ),
file('GEO201+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO201+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO201+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO201+2.p',unknown),
[] ).
cnf(16,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('GEO201+2.p',unknown),
[] ).
cnf(17,plain,
( convergent_lines(skc3,u)
| convergent_lines(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(18,plain,
distinct_lines(skc2,skc3),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(19,plain,
( ~ apart_point_and_line(u,skc2)
| distinct_points(u,intersection_point(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.1')] ).
cnf(20,plain,
( ~ apart_point_and_line(u,skc3)
| distinct_points(u,intersection_point(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.1')] ).
cnf(21,plain,
( ~ distinct_lines(u,v)
| apart_point_and_line(intersection_point(skc3,skc2),u)
| apart_point_and_line(intersection_point(skc3,skc2),v)
| apart_point_and_line(intersection_point(skc2,skc3),v)
| apart_point_and_line(intersection_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(25,plain,
convergent_lines(skc3,skc2),
inference(res,[status(thm),theory(equality)],[17,4]),
[iquote('0:Res:17.1,4.0')] ).
cnf(27,plain,
( distinct_lines(skc3,u)
| distinct_lines(skc2,u) ),
inference(res,[status(thm),theory(equality)],[18,8]),
[iquote('0:Res:18.0,8.0')] ).
cnf(29,plain,
distinct_lines(skc3,skc2),
inference(res,[status(thm),theory(equality)],[27,3]),
[iquote('0:Res:27.1,3.0')] ).
cnf(32,plain,
~ apart_point_and_line(intersection_point(skc2,skc3),skc3),
inference(res,[status(thm),theory(equality)],[20,2]),
[iquote('0:Res:20.1,2.0')] ).
cnf(36,plain,
~ apart_point_and_line(intersection_point(skc2,skc3),skc2),
inference(res,[status(thm),theory(equality)],[19,2]),
[iquote('0:Res:19.1,2.0')] ).
cnf(129,plain,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(intersection_point(u,v),x)
| distinct_points(w,x) ),
inference(res,[status(thm),theory(equality)],[15,7]),
[iquote('0:Res:15.2,7.0')] ).
cnf(154,plain,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(intersection_point(u,v),x)
| distinct_points(w,x) ),
inference(res,[status(thm),theory(equality)],[14,7]),
[iquote('0:Res:14.2,7.0')] ).
cnf(255,plain,
( ~ apart_point_and_line(u,skc2)
| distinct_points(intersection_point(skc3,skc2),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[25,129]),
[iquote('0:Res:25.0,129.0')] ).
cnf(314,plain,
( ~ apart_point_and_line(u,skc3)
| distinct_points(intersection_point(skc3,skc2),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[25,154]),
[iquote('0:Res:25.0,154.0')] ).
cnf(552,plain,
( apart_point_and_line(intersection_point(skc3,skc2),skc3)
| apart_point_and_line(intersection_point(skc3,skc2),skc2)
| apart_point_and_line(intersection_point(skc2,skc3),skc2)
| apart_point_and_line(intersection_point(skc2,skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[29,21]),
[iquote('0:Res:29.0,21.0')] ).
cnf(560,plain,
( apart_point_and_line(intersection_point(skc3,skc2),skc3)
| apart_point_and_line(intersection_point(skc3,skc2),skc2) ),
inference(mrr,[status(thm)],[552,36,32]),
[iquote('0:MRR:552.2,552.3,36.0,32.0')] ).
cnf(590,plain,
apart_point_and_line(intersection_point(skc3,skc2),skc3),
inference(spt,[spt(split,[position(s1)])],[560]),
[iquote('1:Spt:560.0')] ).
cnf(591,plain,
( distinct_points(intersection_point(skc3,skc2),u)
| distinct_points(intersection_point(skc3,skc2),u) ),
inference(res,[status(thm),theory(equality)],[590,314]),
[iquote('1:Res:590.0,314.0')] ).
cnf(597,plain,
distinct_points(intersection_point(skc3,skc2),u),
inference(obv,[status(thm),theory(equality)],[591]),
[iquote('1:Obv:591.0')] ).
cnf(598,plain,
$false,
inference(unc,[status(thm)],[597,2]),
[iquote('1:UnC:597.0,2.0')] ).
cnf(599,plain,
~ apart_point_and_line(intersection_point(skc3,skc2),skc3),
inference(spt,[spt(split,[position(sa)])],[598,590]),
[iquote('1:Spt:598.0,560.0,590.0')] ).
cnf(600,plain,
apart_point_and_line(intersection_point(skc3,skc2),skc2),
inference(spt,[spt(split,[position(s2)])],[560]),
[iquote('1:Spt:598.0,560.1')] ).
cnf(616,plain,
( distinct_points(intersection_point(skc3,skc2),u)
| distinct_points(intersection_point(skc3,skc2),u) ),
inference(res,[status(thm),theory(equality)],[600,255]),
[iquote('1:Res:600.0,255.0')] ).
cnf(622,plain,
distinct_points(intersection_point(skc3,skc2),u),
inference(obv,[status(thm),theory(equality)],[616]),
[iquote('1:Obv:616.0')] ).
cnf(623,plain,
$false,
inference(unc,[status(thm)],[622,2]),
[iquote('1:UnC:622.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 : Fri Jun 17 17:13:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 529 clauses, backtracked 25 clauses, performed 1 splits and kept 337 clauses.
% 0.37/0.55 SPASS allocated 85480 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.37/0.55 0:00:00.03 for the input.
% 0.37/0.55 0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.10 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 6, length 37 :
% 0.37/0.55 % SZS output start Refutation
% See solution above
% 0.37/0.55 Formulae used in the proof : con apart1 apart2 apart3 ceq3 apart4 apart5 apart6 con2 cu1
% 0.37/0.55
%------------------------------------------------------------------------------