TSTP Solution File: GEO037-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 06:21:46 EDT 2022
% Result : Unsatisfiable 54.49s 54.72s
% Output : Refutation 54.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 17 unt; 0 nHn; 32 RR)
% Number of literals : 50 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(v,u,x,w) ),
file('GEO037-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(x,w,u,v) ),
file('GEO037-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(y,z,u,v)
| equidistant(y,z,w,x) ),
file('GEO037-3.p',unknown),
[] ).
cnf(13,axiom,
equidistant(u,reflection(v,u),v,u),
file('GEO037-3.p',unknown),
[] ).
cnf(17,axiom,
equidistant(u,u,v,v),
file('GEO037-3.p',unknown),
[] ).
cnf(24,axiom,
equal(reflection(reflection(u,v),v),u),
file('GEO037-3.p',unknown),
[] ).
cnf(39,axiom,
~ equal(lower_dimension_point_2,lower_dimension_point_1),
file('GEO037-3.p',unknown),
[] ).
cnf(42,axiom,
( ~ equidistant(v__dfg,extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),x__dfg,extension(w__dfg,x__dfg,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u__dfg,v__dfg,extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2))
| equal(extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),v__dfg) ),
file('GEO037-3.p',unknown),
[] ).
cnf(44,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO037-3.p',unknown),
[] ).
cnf(45,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO037-3.p',unknown),
[] ).
cnf(46,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO037-3.p',unknown),
[] ).
cnf(47,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO037-3.p',unknown),
[] ).
cnf(64,plain,
( ~ equidistant(v__dfg,extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),x__dfg,extension(w__dfg,x__dfg,lower_dimension_point_1,lower_dimension_point_2))
| equal(extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),v__dfg) ),
inference(mrr,[status(thm)],[42,46]),
[iquote('0:MRR:42.1,46.0')] ).
cnf(72,plain,
equidistant(u,v,reflection(v,u),u),
inference(spr,[status(thm),theory(equality)],[24,13]),
[iquote('0:SpR:24.0,13.0')] ).
cnf(126,plain,
equidistant(u,v,u,reflection(v,u)),
inference(res,[status(thm),theory(equality)],[13,7]),
[iquote('0:Res:13.0,7.0')] ).
cnf(129,plain,
equidistant(u,reflection(v,u),u,v),
inference(res,[status(thm),theory(equality)],[72,7]),
[iquote('0:Res:72.0,7.0')] ).
cnf(131,plain,
equidistant(u,v,w,extension(x,w,v,u)),
inference(res,[status(thm),theory(equality)],[47,7]),
[iquote('0:Res:47.0,7.0')] ).
cnf(154,plain,
equidistant(u,v,v,reflection(u,v)),
inference(res,[status(thm),theory(equality)],[129,7]),
[iquote('0:Res:129.0,7.0')] ).
cnf(183,plain,
equidistant(extension(u,v,w,x),v,x,w),
inference(res,[status(thm),theory(equality)],[47,5]),
[iquote('0:Res:47.0,5.0')] ).
cnf(705,plain,
( ~ equidistant(u,u,v,w)
| equidistant(v,w,x,x) ),
inference(res,[status(thm),theory(equality)],[17,44]),
[iquote('0:Res:17.0,44.0')] ).
cnf(709,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,y,extension(z,y,v,u)) ),
inference(res,[status(thm),theory(equality)],[131,44]),
[iquote('0:Res:131.0,44.0')] ).
cnf(799,plain,
( ~ equidistant(u,v,w,x)
| equidistant(u,v,w,reflection(x,w)) ),
inference(res,[status(thm),theory(equality)],[126,9]),
[iquote('0:Res:126.0,9.0')] ).
cnf(805,plain,
( ~ equidistant(u,v,w,x)
| equidistant(u,v,x,reflection(w,x)) ),
inference(res,[status(thm),theory(equality)],[154,9]),
[iquote('0:Res:154.0,9.0')] ).
cnf(17740,plain,
( ~ equidistant(u,u,v,w)
| equidistant(v,reflection(w,v),x,x) ),
inference(res,[status(thm),theory(equality)],[799,705]),
[iquote('0:Res:799.1,705.0')] ).
cnf(22544,plain,
( ~ equidistant(u,u,v,w)
| equidistant(w,reflection(reflection(v,w),w),x,x) ),
inference(res,[status(thm),theory(equality)],[805,17740]),
[iquote('0:Res:805.1,17740.0')] ).
cnf(22711,plain,
( ~ equidistant(u,u,v,w)
| equidistant(w,v,x,x) ),
inference(rew,[status(thm),theory(equality)],[24,22544]),
[iquote('0:Rew:24.0,22544.1')] ).
cnf(26484,plain,
( ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,v__dfg,extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2))
| equal(extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),v__dfg) ),
inference(res,[status(thm),theory(equality)],[709,64]),
[iquote('0:Res:709.1,64.0')] ).
cnf(26489,plain,
equal(extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),v__dfg),
inference(mrr,[status(thm)],[26484,131]),
[iquote('0:MRR:26484.0,131.0')] ).
cnf(26494,plain,
equidistant(v__dfg,v__dfg,lower_dimension_point_2,lower_dimension_point_1),
inference(spr,[status(thm),theory(equality)],[26489,183]),
[iquote('0:SpR:26489.0,183.0')] ).
cnf(26592,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,u,u),
inference(res,[status(thm),theory(equality)],[26494,22711]),
[iquote('0:Res:26494.0,22711.0')] ).
cnf(26648,plain,
equal(lower_dimension_point_2,lower_dimension_point_1),
inference(res,[status(thm),theory(equality)],[26592,45]),
[iquote('0:Res:26592.0,45.0')] ).
cnf(26670,plain,
$false,
inference(mrr,[status(thm)],[26648,39]),
[iquote('0:MRR:26648.0,39.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 04:43:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 54.49/54.72
% 54.49/54.72 SPASS V 3.9
% 54.49/54.72 SPASS beiseite: Proof found.
% 54.49/54.72 % SZS status Theorem
% 54.49/54.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.49/54.72 SPASS derived 22033 clauses, backtracked 0 clauses, performed 0 splits and kept 8732 clauses.
% 54.49/54.72 SPASS allocated 84370 KBytes.
% 54.49/54.72 SPASS spent 0:0:53.69 on the problem.
% 54.49/54.72 0:00:00.04 for the input.
% 54.49/54.72 0:00:00.00 for the FLOTTER CNF translation.
% 54.49/54.72 0:00:00.32 for inferences.
% 54.49/54.72 0:00:00.00 for the backtracking.
% 54.49/54.72 0:0:53.19 for the reduction.
% 54.49/54.72
% 54.49/54.72
% 54.49/54.72 Here is a proof with depth 7, length 32 :
% 54.49/54.72 % SZS output start Refutation
% See solution above
% 54.49/54.72 Formulae used in the proof : d4_2 d4_4 d5 r2_2 d7 r6 e2_1 prove_lengthen transitivity_for_equidistance identity_for_equidistance segment_construction1 segment_construction2
% 54.49/54.72
%------------------------------------------------------------------------------