TSTP Solution File: GEO037-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO037-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 18 unt; 0 nHn; 27 RR)
% Number of literals : 38 ( 0 equ; 13 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; 13 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,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('GEO037-2.p',unknown),
[] ).
cnf(2,axiom,
equidistant(u,v,v,u),
file('GEO037-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO037-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO037-2.p',unknown),
[] ).
cnf(5,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO037-2.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO037-2.p',unknown),
[] ).
cnf(13,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('GEO037-2.p',unknown),
[] ).
cnf(20,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)],[1,5]),
[iquote('0:MRR:1.1,5.0')] ).
cnf(22,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.0,4.0')] ).
cnf(23,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[22,5]),
[iquote('0:SpR:22.0,5.0')] ).
cnf(26,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.0')] ).
cnf(27,plain,
( ~ equidistant(u,extension(v,u,w,x),y,z)
| equidistant(y,z,w,x) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.0,3.0')] ).
cnf(31,plain,
equidistant(u,v,u,v),
inference(res,[status(thm),theory(equality)],[2,26]),
[iquote('0:Res:2.0,26.0')] ).
cnf(32,plain,
equidistant(u,v,extension(w,x,u,v),x),
inference(res,[status(thm),theory(equality)],[6,26]),
[iquote('0:Res:6.0,26.0')] ).
cnf(36,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ),
inference(res,[status(thm),theory(equality)],[31,3]),
[iquote('0:Res:31.0,3.0')] ).
cnf(39,plain,
equidistant(extension(u,v,w,x),v,x,w),
inference(res,[status(thm),theory(equality)],[32,26]),
[iquote('0:Res:32.0,26.0')] ).
cnf(43,plain,
equidistant(u,v,w,extension(x,w,v,u)),
inference(res,[status(thm),theory(equality)],[39,26]),
[iquote('0:Res:39.0,26.0')] ).
cnf(47,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,y,extension(z,y,v,u)) ),
inference(res,[status(thm),theory(equality)],[43,3]),
[iquote('0:Res:43.0,3.0')] ).
cnf(87,plain,
equidistant(u,extension(v,u,extension(w,x,y,z),x),y,z),
inference(res,[status(thm),theory(equality)],[43,27]),
[iquote('0:Res:43.0,27.0')] ).
cnf(96,plain,
equidistant(u,v,w,extension(x,w,extension(y,z,u,v),z)),
inference(res,[status(thm),theory(equality)],[87,36]),
[iquote('0:Res:87.0,36.0')] ).
cnf(286,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)],[47,20]),
[iquote('0:Res:47.1,20.0')] ).
cnf(288,plain,
equal(extension(u__dfg,v__dfg,lower_dimension_point_1,lower_dimension_point_2),v__dfg),
inference(mrr,[status(thm)],[286,43]),
[iquote('0:MRR:286.0,43.0')] ).
cnf(306,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,u,extension(v,u,v__dfg,v__dfg)),
inference(spr,[status(thm),theory(equality)],[288,96]),
[iquote('0:SpR:288.0,96.0')] ).
cnf(327,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,u,u),
inference(rew,[status(thm),theory(equality)],[22,306]),
[iquote('0:Rew:22.0,306.0')] ).
cnf(355,plain,
equal(lower_dimension_point_2,lower_dimension_point_1),
inference(res,[status(thm),theory(equality)],[327,4]),
[iquote('0:Res:327.0,4.0')] ).
cnf(361,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1),
inference(rew,[status(thm),theory(equality)],[355,13]),
[iquote('0:Rew:355.0,13.0')] ).
cnf(377,plain,
$false,
inference(mrr,[status(thm)],[361,23]),
[iquote('0:MRR:361.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO037-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 : Fri Jun 17 20:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 301 clauses, backtracked 0 clauses, performed 0 splits and kept 164 clauses.
% 0.18/0.46 SPASS allocated 63502 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.46 0:00:00.03 for the input.
% 0.18/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.01 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.05 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 8, length 27 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : prove_lengthen reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction1 segment_construction2 lower_dimension3
% 0.18/0.46
%------------------------------------------------------------------------------