TSTP Solution File: GEO223+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 06:23:39 EDT 2022
% Result : Theorem 3.18s 3.39s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 16 unt; 20 nHn; 39 RR)
% Number of literals : 80 ( 0 equ; 16 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(3,axiom,
~ convergent_lines(u,u),
file('GEO223+2.p',unknown),
[] ).
cnf(4,axiom,
~ convergent_lines(parallel_through_point(u,v),u),
file('GEO223+2.p',unknown),
[] ).
cnf(5,axiom,
~ apart_point_and_line(u,parallel_through_point(v,u)),
file('GEO223+2.p',unknown),
[] ).
cnf(6,axiom,
( unorthogonal_lines(u,v)
| convergent_lines(u,v) ),
file('GEO223+2.p',unknown),
[] ).
cnf(7,axiom,
~ unorthogonal_lines(orthogonal_through_point(u,v),u),
file('GEO223+2.p',unknown),
[] ).
cnf(8,axiom,
~ apart_point_and_line(u,orthogonal_through_point(v,u)),
file('GEO223+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ skP0(u,v)
| convergent_lines(v,u) ),
file('GEO223+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ skP0(u,v)
| unorthogonal_lines(v,u) ),
file('GEO223+2.p',unknown),
[] ).
cnf(12,axiom,
distinct_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
file('GEO223+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(u,w) ),
file('GEO223+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ skP0(u,v)
| skP0(w,u)
| skP0(w,v) ),
file('GEO223+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ unorthogonal_lines(u,v)
| ~ convergent_lines(u,v)
| skP0(v,u) ),
file('GEO223+2.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+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('GEO223+2.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)],[12,25]),
[iquote('0:Res:12.0,25.0')] ).
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)],[12,24]),
[iquote('0:Res:12.0,24.0')] ).
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(43,plain,
( convergent_lines(u,v)
| convergent_lines(orthogonal_through_point(u,w),v) ),
inference(res,[status(thm),theory(equality)],[35,15]),
[iquote('0:Res:35.0,15.0')] ).
cnf(46,plain,
( convergent_lines(u,v)
| convergent_lines(v,w)
| convergent_lines(orthogonal_through_point(u,x),w) ),
inference(res,[status(thm),theory(equality)],[43,15]),
[iquote('0:Res:43.1,15.0')] ).
cnf(52,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(67,plain,
( convergent_lines(u,v)
| convergent_lines(orthogonal_through_point(w,x),v)
| convergent_lines(u,y)
| convergent_lines(w,y) ),
inference(res,[status(thm),theory(equality)],[46,15]),
[iquote('0:Res:46.0,15.0')] ).
cnf(438,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(439,plain,
unorthogonal_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[438,7]),
[iquote('2:Res:438.1,7.0')] ).
cnf(441,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)],[439,52]),
[iquote('2:Res:439.0,52.0')] ).
cnf(3112,plain,
( convergent_lines(u,v)
| convergent_lines(orthogonal_through_point(w,x),v)
| convergent_lines(u,w) ),
inference(res,[status(thm),theory(equality)],[67,3]),
[iquote('0:Res:67.3,3.0')] ).
cnf(3776,plain,
( convergent_lines(parallel_through_point(u,v),w)
| convergent_lines(orthogonal_through_point(u,x),w) ),
inference(res,[status(thm),theory(equality)],[3112,4]),
[iquote('0:Res:3112.2,4.0')] ).
cnf(3799,plain,
convergent_lines(parallel_through_point(u,v),orthogonal_through_point(u,w)),
inference(res,[status(thm),theory(equality)],[3776,3]),
[iquote('0:Res:3776.1,3.0')] ).
cnf(3808,plain,
( skP0(u,orthogonal_through_point(skc2,skc3))
| skP0(u,parallel_through_point(skc2,skc3)) ),
inference(mrr,[status(thm)],[441,3799]),
[iquote('2:MRR:441.0,3799.0')] ).
cnf(3881,plain,
( skP0(u,orthogonal_through_point(skc2,skc3))
| convergent_lines(parallel_through_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[3808,10]),
[iquote('2:Res:3808.1,10.0')] ).
cnf(3885,plain,
( convergent_lines(parallel_through_point(skc2,skc3),u)
| unorthogonal_lines(orthogonal_through_point(skc2,skc3),u) ),
inference(res,[status(thm),theory(equality)],[3881,11]),
[iquote('2:Res:3881.0,11.0')] ).
cnf(3935,plain,
convergent_lines(parallel_through_point(skc2,skc3),skc2),
inference(res,[status(thm),theory(equality)],[3885,7]),
[iquote('2:Res:3885.1,7.0')] ).
cnf(3937,plain,
$false,
inference(mrr,[status(thm)],[3935,4]),
[iquote('2:MRR:3935.0,4.0')] ).
cnf(3938,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:3937.0,27.0,27.1')] ).
cnf(3942,plain,
apart_point_and_line(skc3,parallel_through_point(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[3938,8]),
[iquote('2:Res:3938.1,8.0')] ).
cnf(3953,plain,
$false,
inference(mrr,[status(thm)],[3942,5]),
[iquote('2:MRR:3942.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 06:33:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.18/3.39
% 3.18/3.39 SPASS V 3.9
% 3.18/3.39 SPASS beiseite: Proof found.
% 3.18/3.39 % SZS status Theorem
% 3.18/3.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.18/3.39 SPASS derived 3831 clauses, backtracked 13 clauses, performed 3 splits and kept 2734 clauses.
% 3.18/3.39 SPASS allocated 88916 KBytes.
% 3.18/3.39 SPASS spent 0:00:03.02 on the problem.
% 3.18/3.39 0:00:00.04 for the input.
% 3.18/3.39 0:00:00.03 for the FLOTTER CNF translation.
% 3.18/3.39 0:00:00.09 for inferences.
% 3.18/3.39 0:00:00.01 for the backtracking.
% 3.18/3.39 0:00:02.81 for the reduction.
% 3.18/3.39
% 3.18/3.39
% 3.18/3.39 Here is a proof with depth 7, length 39 :
% 3.18/3.39 % SZS output start Refutation
% See solution above
% 3.18/3.39 Formulae used in the proof : apart3 cp1 cp2 occu1 ooc1 ooc2 oac1 con apart6 cup1 ouo1
% 3.18/3.39
%------------------------------------------------------------------------------