TSTP Solution File: GEO053-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO053-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 06:21:55 EDT 2022
% Result : Unsatisfiable 2.06s 2.24s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 11 unt; 4 nHn; 25 RR)
% Number of literals : 51 ( 0 equ; 27 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
equal(extension(u,v,w,w),v),
file('GEO053-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,extension(v,w,x,y))
| between(v,w,u) ),
file('GEO053-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ between(u,v,w)
| ~ between(u,v,x)
| ~ equidistant(v,x,v,w)
| equal(x,w)
| equal(u,v) ),
file('GEO053-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO053-3.p',unknown),
[] ).
cnf(36,axiom,
( ~ between(u,v,w)
| ~ between(x,u,v)
| equal(u,v)
| between(x,u,w) ),
file('GEO053-3.p',unknown),
[] ).
cnf(42,axiom,
~ equal(extension(u,v,lower_dimension_point_1,lower_dimension_point_2),v),
file('GEO053-3.p',unknown),
[] ).
cnf(50,axiom,
( ~ between(u,v,w)
| ~ equidistant(w,v,w,x)
| ~ equidistant(u,v,u,x)
| equal(v,x) ),
file('GEO053-3.p',unknown),
[] ).
cnf(63,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO053-3.p',unknown),
[] ).
cnf(64,axiom,
equidistant(u__dfg,v__dfg,u__dfg,w__dfg),
file('GEO053-3.p',unknown),
[] ).
cnf(65,axiom,
~ equal(w__dfg,v__dfg),
file('GEO053-3.p',unknown),
[] ).
cnf(69,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO053-3.p',unknown),
[] ).
cnf(197,plain,
between(extension(u,v,w,x),v,u),
inference(res,[status(thm),theory(equality)],[69,27]),
[iquote('0:Res:69.0,27.0')] ).
cnf(620,plain,
( ~ equal(u,v)
| between(w,v,u) ),
inference(spl,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpL:10.0,11.0')] ).
cnf(627,plain,
( ~ equal(u,v)
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[620,27]),
[iquote('0:Res:620.1,27.0')] ).
cnf(943,plain,
( ~ between(u,u__dfg,v__dfg)
| equal(v__dfg,u__dfg)
| between(u,u__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[63,36]),
[iquote('0:Res:63.0,36.0')] ).
cnf(1662,plain,
( ~ between(u,v__dfg,u__dfg)
| ~ equidistant(u,v__dfg,u,w__dfg)
| equal(w__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[64,50]),
[iquote('0:Res:64.0,50.1')] ).
cnf(1684,plain,
( ~ between(u,v__dfg,u__dfg)
| ~ equidistant(u,v__dfg,u,w__dfg) ),
inference(mrr,[status(thm)],[1662,65]),
[iquote('0:MRR:1662.2,65.0')] ).
cnf(2166,plain,
( ~ between(u,u__dfg,w__dfg)
| ~ between(u,u__dfg,v__dfg)
| equal(w__dfg,v__dfg)
| equal(u,u__dfg) ),
inference(res,[status(thm),theory(equality)],[64,19]),
[iquote('0:Res:64.0,19.2')] ).
cnf(2188,plain,
( ~ between(u,u__dfg,w__dfg)
| ~ between(u,u__dfg,v__dfg)
| equal(u,u__dfg) ),
inference(mrr,[status(thm)],[2166,65]),
[iquote('0:MRR:2166.2,65.0')] ).
cnf(4007,plain,
~ between(u__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[64,1684]),
[iquote('0:Res:64.0,1684.1')] ).
cnf(4010,plain,
~ equal(v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[627,4007]),
[iquote('0:Res:627.1,4007.0')] ).
cnf(4034,plain,
( ~ between(u,u__dfg,v__dfg)
| between(u,u__dfg,w__dfg) ),
inference(mrr,[status(thm)],[943,4010]),
[iquote('0:MRR:943.1,4010.0')] ).
cnf(4120,plain,
( ~ between(u,u__dfg,v__dfg)
| equal(u,u__dfg) ),
inference(mrr,[status(thm)],[2188,4034]),
[iquote('0:MRR:2188.0,4034.1')] ).
cnf(4134,plain,
equal(extension(v__dfg,u__dfg,u,v),u__dfg),
inference(res,[status(thm),theory(equality)],[197,4120]),
[iquote('0:Res:197.0,4120.0')] ).
cnf(4144,plain,
$false,
inference(unc,[status(thm)],[4134,42]),
[iquote('0:UnC:4134.0,42.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO053-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 16:14:58 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.06/2.24
% 2.06/2.24 SPASS V 3.9
% 2.06/2.24 SPASS beiseite: Proof found.
% 2.06/2.24 % SZS status Theorem
% 2.06/2.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.06/2.24 SPASS derived 3719 clauses, backtracked 0 clauses, performed 0 splits and kept 2048 clauses.
% 2.06/2.24 SPASS allocated 66358 KBytes.
% 2.06/2.24 SPASS spent 0:00:01.87 on the problem.
% 2.06/2.24 0:00:00.04 for the input.
% 2.06/2.24 0:00:00.00 for the FLOTTER CNF translation.
% 2.06/2.24 0:00:00.04 for inferences.
% 2.06/2.24 0:00:00.00 for the backtracking.
% 2.06/2.24 0:00:01.74 for the reduction.
% 2.06/2.24
% 2.06/2.24
% 2.06/2.24 Here is a proof with depth 3, length 25 :
% 2.06/2.24 % SZS output start Refutation
% See solution above
% 2.06/2.24 Formulae used in the proof : e1 b0 d9 t1 b7 e3_1 d15 v_between_u_and_w u_to_v_equals_u_to_w prove_v_equals_w segment_construction1
% 2.06/2.24
%------------------------------------------------------------------------------