TSTP Solution File: GEO222+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 06:23:38 EDT 2022
% Result : Theorem 0.60s 0.78s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 13 unt; 19 nHn; 38 RR)
% Number of literals : 84 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(u,u),
file('GEO222+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(u,u),
file('GEO222+2.p',unknown),
[] ).
cnf(6,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO222+2.p',unknown),
[] ).
cnf(7,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO222+2.p',unknown),
[] ).
cnf(9,axiom,
convergent_lines(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
file('GEO222+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(u,v) ),
file('GEO222+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ skP0(u,v)
| convergent_lines(v,u) ),
file('GEO222+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ skP0(u,v)
| unorthogonal_lines(v,u) ),
file('GEO222+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ distinct_points(u,v)
| distinct_points(v,w)
| distinct_points(u,w) ),
file('GEO222+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO222+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ skP0(u,v)
| skP0(w,u)
| skP0(w,v) ),
file('GEO222+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| skP0(v,u) ),
file('GEO222+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,u)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO222+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ convergent_lines(u,v)
| ~ apart_point_and_line(w,v)
| distinct_points(w,intersection_point(u,v)) ),
file('GEO222+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ distinct_lines(u,v)
| unorthogonal_lines(v,w)
| unorthogonal_lines(u,w)
| apart_point_and_line(x,v)
| apart_point_and_line(x,u) ),
file('GEO222+2.p',unknown),
[] ).
cnf(29,plain,
distinct_lines(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(32,plain,
convergent_lines(orthogonal_through_point(u,v),u),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(39,plain,
( convergent_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[32,15]),
[iquote('0:Res:32.0,15.0')] ).
cnf(42,plain,
convergent_lines(u,orthogonal_through_point(u,v)),
inference(res,[status(thm),theory(equality)],[39,3]),
[iquote('0:Res:39.1,3.0')] ).
cnf(45,plain,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| skP0(w,v)
| skP0(w,u) ),
inference(res,[status(thm),theory(equality)],[19,18]),
[iquote('0:Res:19.2,18.0')] ).
cnf(69,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)],[23,13]),
[iquote('0:Res:23.2,13.0')] ).
cnf(80,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)],[22,13]),
[iquote('0:Res:22.2,13.0')] ).
cnf(151,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),u)
| unorthogonal_lines(skc2,u)
| apart_point_and_line(v,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
| apart_point_and_line(v,skc2) ),
inference(res,[status(thm),theory(equality)],[29,25]),
[iquote('0:Res:29.0,25.0')] ).
cnf(301,plain,
( ~ apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
| distinct_points(intersection_point(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[9,69]),
[iquote('0:Res:9.0,69.0')] ).
cnf(361,plain,
( ~ apart_point_and_line(u,skc2)
| distinct_points(intersection_point(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[9,80]),
[iquote('0:Res:9.0,80.0')] ).
cnf(783,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),u)
| unorthogonal_lines(skc2,u) ),
inference(spt,[spt(split,[position(s1)])],[151]),
[iquote('1:Spt:151.0,151.1')] ).
cnf(784,plain,
unorthogonal_lines(skc2,orthogonal_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[783,7]),
[iquote('1:Res:783.0,7.0')] ).
cnf(786,plain,
( ~ convergent_lines(skc2,orthogonal_through_point(skc2,skc3))
| skP0(u,orthogonal_through_point(skc2,skc3))
| skP0(u,skc2) ),
inference(res,[status(thm),theory(equality)],[784,45]),
[iquote('1:Res:784.0,45.0')] ).
cnf(787,plain,
( skP0(u,orthogonal_through_point(skc2,skc3))
| skP0(u,skc2) ),
inference(mrr,[status(thm)],[786,42]),
[iquote('1:MRR:786.0,42.0')] ).
cnf(790,plain,
( skP0(u,skc2)
| unorthogonal_lines(orthogonal_through_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[787,12]),
[iquote('1:Res:787.0,12.0')] ).
cnf(801,plain,
skP0(skc2,skc2),
inference(res,[status(thm),theory(equality)],[790,7]),
[iquote('1:Res:790.1,7.0')] ).
cnf(804,plain,
convergent_lines(skc2,skc2),
inference(res,[status(thm),theory(equality)],[801,11]),
[iquote('1:Res:801.0,11.0')] ).
cnf(806,plain,
$false,
inference(mrr,[status(thm)],[804,3]),
[iquote('1:MRR:804.0,3.0')] ).
cnf(808,plain,
( apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
| apart_point_and_line(u,skc2) ),
inference(spt,[spt(split,[position(s2)])],[151]),
[iquote('1:Spt:806.0,151.2,151.3')] ).
cnf(811,plain,
( apart_point_and_line(u,skc2)
| distinct_points(intersection_point(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),v)
| distinct_points(u,v) ),
inference(res,[status(thm),theory(equality)],[808,301]),
[iquote('1:Res:808.0,301.0')] ).
cnf(818,plain,
( distinct_points(intersection_point(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),u)
| distinct_points(v,u) ),
inference(mrr,[status(thm)],[811,361]),
[iquote('1:MRR:811.0,361.0')] ).
cnf(1059,plain,
distinct_points(intersection_point(skc2,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),u),
inference(res,[status(thm),theory(equality)],[818,1]),
[iquote('1:Res:818.1,1.0')] ).
cnf(1063,plain,
$false,
inference(unc,[status(thm)],[1059,1]),
[iquote('1:UnC:1059.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 07:14:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.78
% 0.60/0.78 SPASS V 3.9
% 0.60/0.78 SPASS beiseite: Proof found.
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.78 SPASS derived 1018 clauses, backtracked 6 clauses, performed 1 splits and kept 750 clauses.
% 0.60/0.78 SPASS allocated 86062 KBytes.
% 0.60/0.78 SPASS spent 0:00:00.43 on the problem.
% 0.60/0.78 0:00:00.03 for the input.
% 0.60/0.78 0:00:00.03 for the FLOTTER CNF translation.
% 0.60/0.78 0:00:00.02 for inferences.
% 0.60/0.78 0:00:00.00 for the backtracking.
% 0.60/0.78 0:00:00.32 for the reduction.
% 0.60/0.78
% 0.60/0.78
% 0.60/0.78 Here is a proof with depth 8, length 38 :
% 0.60/0.78 % SZS output start Refutation
% See solution above
% 0.60/0.78 Formulae used in the proof : apart1 apart3 occu1 ooc1 con ceq3 oac1 apart4 apart6 con2 ouo1
% 0.60/0.78
%------------------------------------------------------------------------------