TSTP Solution File: GEO200+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 06:23:19 EDT 2022
% Result : Theorem 0.38s 0.61s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 15 unt; 13 nHn; 34 RR)
% Number of literals : 69 ( 0 equ; 16 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 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,
distinct_points(skc2,skc3),
file('GEO200+2.p',unknown),
[] ).
cnf(2,axiom,
~ distinct_points(u,u),
file('GEO200+2.p',unknown),
[] ).
cnf(5,axiom,
distinct_lines(line_connecting(skc2,skc3),line_connecting(skc3,skc2)),
file('GEO200+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO200+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(w,line_connecting(u,v))
| distinct_points(w,u) ),
file('GEO200+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ distinct_points(u,v)
| ~ apart_point_and_line(w,line_connecting(u,v))
| distinct_points(w,v) ),
file('GEO200+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('GEO200+2.p',unknown),
[] ).
cnf(17,plain,
( ~ distinct_lines(u,v)
| apart_point_and_line(skc3,u)
| apart_point_and_line(skc3,v)
| apart_point_and_line(skc2,v)
| apart_point_and_line(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.0,16.0')] ).
cnf(18,plain,
( distinct_points(skc3,u)
| distinct_points(skc2,u) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(24,plain,
( apart_point_and_line(skc3,line_connecting(skc2,skc3))
| apart_point_and_line(skc3,line_connecting(skc3,skc2))
| apart_point_and_line(skc2,line_connecting(skc3,skc2))
| apart_point_and_line(skc2,line_connecting(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[5,17]),
[iquote('0:Res:5.0,17.0')] ).
cnf(25,plain,
distinct_points(skc3,skc2),
inference(res,[status(thm),theory(equality)],[18,2]),
[iquote('0:Res:18.1,2.0')] ).
cnf(33,plain,
( distinct_points(skc3,u)
| distinct_points(u,v)
| distinct_points(skc2,v) ),
inference(res,[status(thm),theory(equality)],[18,7]),
[iquote('0:Res:18.1,7.0')] ).
cnf(39,plain,
( distinct_points(skc3,u)
| distinct_points(u,skc2) ),
inference(res,[status(thm),theory(equality)],[33,2]),
[iquote('0:Res:33.2,2.0')] ).
cnf(41,plain,
( distinct_points(u,skc2)
| distinct_points(u,v)
| distinct_points(skc3,v) ),
inference(res,[status(thm),theory(equality)],[39,7]),
[iquote('0:Res:39.0,7.0')] ).
cnf(51,plain,
( distinct_points(u,skc2)
| distinct_points(u,skc3) ),
inference(res,[status(thm),theory(equality)],[41,2]),
[iquote('0:Res:41.2,2.0')] ).
cnf(57,plain,
( distinct_points(u,skc3)
| distinct_points(skc2,v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[51,7]),
[iquote('0:Res:51.0,7.0')] ).
cnf(64,plain,
( distinct_points(u,skc3)
| distinct_points(skc2,u) ),
inference(res,[status(thm),theory(equality)],[57,2]),
[iquote('0:Res:57.2,2.0')] ).
cnf(923,plain,
apart_point_and_line(skc3,line_connecting(skc2,skc3)),
inference(spt,[spt(split,[position(s1)])],[24]),
[iquote('1:Spt:24.0')] ).
cnf(929,plain,
( ~ distinct_points(skc2,skc3)
| distinct_points(skc3,skc3) ),
inference(res,[status(thm),theory(equality)],[923,13]),
[iquote('1:Res:923.0,13.1')] ).
cnf(931,plain,
$false,
inference(mrr,[status(thm)],[929,64,2]),
[iquote('1:MRR:929.0,929.1,64.1,2.0')] ).
cnf(932,plain,
~ apart_point_and_line(skc3,line_connecting(skc2,skc3)),
inference(spt,[spt(split,[position(sa)])],[931,923]),
[iquote('1:Spt:931.0,24.0,923.0')] ).
cnf(933,plain,
( apart_point_and_line(skc3,line_connecting(skc3,skc2))
| apart_point_and_line(skc2,line_connecting(skc3,skc2))
| apart_point_and_line(skc2,line_connecting(skc2,skc3)) ),
inference(spt,[spt(split,[position(s2)])],[24]),
[iquote('1:Spt:931.0,24.1,24.2,24.3')] ).
cnf(964,plain,
apart_point_and_line(skc3,line_connecting(skc3,skc2)),
inference(spt,[spt(split,[position(s2s1)])],[933]),
[iquote('2:Spt:933.0')] ).
cnf(967,plain,
( ~ distinct_points(skc3,skc2)
| distinct_points(skc3,skc3) ),
inference(res,[status(thm),theory(equality)],[964,12]),
[iquote('2:Res:964.0,12.1')] ).
cnf(969,plain,
$false,
inference(mrr,[status(thm)],[967,51,2]),
[iquote('2:MRR:967.0,967.1,51.0,2.0')] ).
cnf(970,plain,
~ apart_point_and_line(skc3,line_connecting(skc3,skc2)),
inference(spt,[spt(split,[position(s2sa)])],[969,964]),
[iquote('2:Spt:969.0,933.0,964.0')] ).
cnf(971,plain,
( apart_point_and_line(skc2,line_connecting(skc3,skc2))
| apart_point_and_line(skc2,line_connecting(skc2,skc3)) ),
inference(spt,[spt(split,[position(s2s2)])],[933]),
[iquote('2:Spt:969.0,933.1,933.2')] ).
cnf(1002,plain,
apart_point_and_line(skc2,line_connecting(skc3,skc2)),
inference(spt,[spt(split,[position(s2s2s1)])],[971]),
[iquote('3:Spt:971.0')] ).
cnf(1006,plain,
( ~ distinct_points(skc3,skc2)
| distinct_points(skc2,skc2) ),
inference(res,[status(thm),theory(equality)],[1002,13]),
[iquote('3:Res:1002.0,13.1')] ).
cnf(1007,plain,
$false,
inference(mrr,[status(thm)],[1006,25,2]),
[iquote('3:MRR:1006.0,1006.1,25.0,2.0')] ).
cnf(1008,plain,
~ apart_point_and_line(skc2,line_connecting(skc3,skc2)),
inference(spt,[spt(split,[position(s2s2sa)])],[1007,1002]),
[iquote('3:Spt:1007.0,971.0,1002.0')] ).
cnf(1009,plain,
apart_point_and_line(skc2,line_connecting(skc2,skc3)),
inference(spt,[spt(split,[position(s2s2s2)])],[971]),
[iquote('3:Spt:1007.0,971.1')] ).
cnf(1019,plain,
( ~ distinct_points(skc2,skc3)
| distinct_points(skc2,skc2) ),
inference(res,[status(thm),theory(equality)],[1009,12]),
[iquote('3:Res:1009.0,12.1')] ).
cnf(1022,plain,
$false,
inference(mrr,[status(thm)],[1019,64,2]),
[iquote('3:MRR:1019.0,1019.1,64.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 08:45:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.38/0.61
% 0.38/0.61 SPASS V 3.9
% 0.38/0.61 SPASS beiseite: Proof found.
% 0.38/0.61 % SZS status Theorem
% 0.38/0.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.61 SPASS derived 821 clauses, backtracked 107 clauses, performed 3 splits and kept 365 clauses.
% 0.38/0.61 SPASS allocated 85776 KBytes.
% 0.38/0.61 SPASS spent 0:00:00.26 on the problem.
% 0.38/0.61 0:00:00.03 for the input.
% 0.38/0.61 0:00:00.03 for the FLOTTER CNF translation.
% 0.38/0.61 0:00:00.02 for inferences.
% 0.38/0.61 0:00:00.00 for the backtracking.
% 0.38/0.61 0:00:00.15 for the reduction.
% 0.38/0.61
% 0.38/0.61
% 0.38/0.61 Here is a proof with depth 7, length 34 :
% 0.38/0.61 % SZS output start Refutation
% See solution above
% 0.38/0.61 Formulae used in the proof : con apart1 apart4 con1 cu1
% 0.38/0.61
%------------------------------------------------------------------------------