%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 2.64s 2.83s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 43 ( 17 unt; 23 nHn; 43 RR)
% Number of literals : 89 ( 0 equ; 18 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ distinct_lines(u,u),
file('GEO223+1.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(u,u),
file('GEO223+1.p',unknown),
[] ).
cnf(4,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO223+1.p',unknown),
[] ).
cnf(5,axiom,
~ apart_point_and_line(u,parallel_through_point(v,u)),
file('GEO223+1.p',unknown),
[] ).
cnf(6,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO223+1.p',unknown),
[] ).
cnf(7,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO223+1.p',unknown),
[] ).
cnf(8,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO223+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ skP0(u,v)
| convergent_lines(v,u) ),
file('GEO223+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ skP0(u,v)
| unorthogonal_lines(v,u) ),
file('GEO223+1.p',unknown),
[] ).
cnf(11,axiom,
distinct_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
file('GEO223+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO223+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ convergent_lines(u,v)
| distinct_lines(v,w)
| convergent_lines(u,w) ),
file('GEO223+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ skP0(u,v)
| skP0(w,u)
| skP0(w,v) ),
file('GEO223+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| skP0(v,u) ),
file('GEO223+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ distinct_lines(u,v)
| convergent_lines(u,v)
| apart_point_and_line(w,v)
| apart_point_and_line(w,u) ),
file('GEO223+1.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('GEO223+1.p',unknown),
[] ).
cnf(27,plain,
( apart_point_and_line(u,parallel_through_point(skc2,skc3))
| apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
| unorthogonal_lines(parallel_through_point(skc2,skc3),v)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),v) ),
inference(res,[status(thm),theory(equality)],[11,25]),
[iquote('0:Res:11.0,25.0')] ).
cnf(28,plain,
( apart_point_and_line(u,parallel_through_point(skc2,skc3))
| apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
| convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
inference(res,[status(thm),theory(equality)],[11,24]),
[iquote('0:Res:11.0,24.0')] ).
cnf(31,plain,
( apart_point_and_line(u,parallel_through_point(skc2,skc3))
| apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
inference(spt,[spt(split,[position(s1)])],[28]),
[iquote('1:Spt:28.0,28.1')] ).
cnf(32,plain,
apart_point_and_line(skc3,parallel_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[31,8]),
[iquote('1:Res:31.1,8.0')] ).
cnf(33,plain,
$false,
inference(mrr,[status(thm)],[32,5]),
[iquote('1:MRR:32.0,5.0')] ).
cnf(34,plain,
convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
inference(spt,[spt(split,[position(s2)])],[28]),
[iquote('1:Spt:33.0,28.2')] ).
cnf(35,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(37,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[35,21]),
[iquote('0:Res:35.0,21.0')] ).
cnf(46,plain,
( distinct_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(orthogonal_through_point(u,x),w) ),
inference(res,[status(thm),theory(equality)],[37,14]),
[iquote('0:Res:37.1,14.0')] ).
cnf(54,plain,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| skP0(w,v)
| skP0(w,u) ),
inference(res,[status(thm),theory(equality)],[23,22]),
[iquote('0:Res:23.2,22.0')] ).
cnf(78,plain,
( distinct_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),x)
| convergent_lines(x,y)
| convergent_lines(v,y) ),
inference(res,[status(thm),theory(equality)],[46,14]),
[iquote('0:Res:46.1,14.0')] ).
cnf(220,plain,
( unorthogonal_lines(parallel_through_point(skc2,skc3),u)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),u) ),
inference(spt,[spt(split,[position(s2s1)])],[27]),
[iquote('2:Spt:27.2,27.3')] ).
cnf(221,plain,
unorthogonal_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[220,7]),
[iquote('2:Res:220.1,7.0')] ).
cnf(223,plain,
( ~ convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(skc2,skc3))
| skP0(u,orthogonal_through_point(skc2,skc3))
| skP0(u,parallel_through_point(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[221,54]),
[iquote('2:Res:221.0,54.0')] ).
cnf(3133,plain,
( convergent_lines(orthogonal_through_point(u,v),w)
| convergent_lines(w,x)
| convergent_lines(u,x) ),
inference(res,[status(thm),theory(equality)],[78,2]),
[iquote('0:Res:78.0,2.0')] ).
cnf(3173,plain,
( convergent_lines(orthogonal_through_point(u,v),w)
| convergent_lines(w,u) ),
inference(res,[status(thm),theory(equality)],[3133,3]),
[iquote('0:Res:3133.2,3.0')] ).
cnf(3321,plain,
( convergent_lines(u,v)
| convergent_lines(u,w)
| convergent_lines(orthogonal_through_point(v,x),w) ),
inference(res,[status(thm),theory(equality)],[3173,14]),
[iquote('0:Res:3173.0,14.0')] ).
cnf(3542,plain,
( convergent_lines(parallel_through_point(u,v),w)
| convergent_lines(orthogonal_through_point(u,x),w) ),
inference(res,[status(thm),theory(equality)],[3321,4]),
[iquote('0:Res:3321.0,4.0')] ).
cnf(3586,plain,
convergent_lines(parallel_through_point(u,v),orthogonal_through_point(u,w)),
inference(res,[status(thm),theory(equality)],[3542,3]),
[iquote('0:Res:3542.1,3.0')] ).
cnf(3592,plain,
( skP0(u,orthogonal_through_point(skc2,skc3))
| skP0(u,parallel_through_point(skc2,skc3)) ),
inference(mrr,[status(thm)],[223,3586]),
[iquote('2:MRR:223.0,3586.0')] ).
cnf(3617,plain,
( skP0(u,orthogonal_through_point(skc2,skc3))
| convergent_lines(parallel_through_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[3592,9]),
[iquote('2:Res:3592.1,9.0')] ).
cnf(3621,plain,
( convergent_lines(parallel_through_point(skc2,skc3),u)
| unorthogonal_lines(orthogonal_through_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[3617,10]),
[iquote('2:Res:3617.0,10.0')] ).
cnf(3874,plain,
convergent_lines(parallel_through_point(skc2,skc3),skc2),
inference(res,[status(thm),theory(equality)],[3621,7]),
[iquote('2:Res:3621.1,7.0')] ).
cnf(3876,plain,
$false,
inference(mrr,[status(thm)],[3874,4]),
[iquote('2:MRR:3874.0,4.0')] ).
cnf(3877,plain,
( apart_point_and_line(u,parallel_through_point(skc2,skc3))
| apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
inference(spt,[spt(split,[position(s2s2)])],[27]),
[iquote('2:Spt:3876.0,27.0,27.1')] ).
cnf(3879,plain,
apart_point_and_line(skc3,parallel_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[3877,8]),
[iquote('2:Res:3877.1,8.0')] ).
cnf(3884,plain,
$false,
inference(mrr,[status(thm)],[3879,5]),
[iquote('2:MRR:3879.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 11:40:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.64/2.83
% 2.64/2.83 SPASS V 3.9
% 2.64/2.83 SPASS beiseite: Proof found.
% 2.64/2.83 % SZS status Theorem
% 2.64/2.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/2.83 SPASS derived 3719 clauses, backtracked 9 clauses, performed 3 splits and kept 2585 clauses.
% 2.64/2.83 SPASS allocated 88318 KBytes.
% 2.64/2.83 SPASS spent 0:00:02.47 on the problem.
% 2.64/2.83 0:00:00.03 for the input.
% 2.64/2.83 0:00:00.04 for the FLOTTER CNF translation.
% 2.64/2.83 0:00:00.09 for inferences.
% 2.64/2.83 0:00:00.01 for the backtracking.
% 2.64/2.83 0:00:02.27 for the reduction.
% 2.64/2.83
% 2.64/2.83
% 2.64/2.83 Here is a proof with depth 9, length 43 :
% 2.64/2.83 % SZS output start Refutation
% See solution above
% 2.64/2.83 Formulae used in the proof : apart2 apart3 cp1 cp2 occu1 ooc1 ooc2 oac1 con ax6 ceq3 cup1 ouo1
% 2.64/2.83
%------------------------------------------------------------------------------