TSTP Solution File: GEO006-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO006-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 06:21:28 EDT 2022
% Result : Unsatisfiable 0.10s 0.42s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 15 unt; 2 nHn; 29 RR)
% Number of literals : 51 ( 0 equ; 23 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(c,a),
file('GEO006-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(d,c),
file('GEO006-1.p',unknown),
[] ).
cnf(4,axiom,
between(a,c,d),
file('GEO006-1.p',unknown),
[] ).
cnf(5,axiom,
( between(a,d,c)
| between(c,a,d) ),
file('GEO006-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO006-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,u,v) ),
file('GEO006-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO006-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO006-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO006-1.p',unknown),
[] ).
cnf(18,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO006-1.p',unknown),
[] ).
cnf(19,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO006-1.p',unknown),
[] ).
cnf(27,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[19,10]),
[iquote('0:Res:19.0,10.0')] ).
cnf(28,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[27,18]),
[iquote('0:SpR:27.0,18.0')] ).
cnf(31,plain,
( ~ between(u,a,d)
| between(u,a,c) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.0')] ).
cnf(37,plain,
( between(a,d,c)
| between(c,a,c) ),
inference(res,[status(thm),theory(equality)],[5,31]),
[iquote('0:Res:5.1,31.0')] ).
cnf(38,plain,
between(a,d,c),
inference(spt,[spt(split,[position(s1)])],[37]),
[iquote('1:Spt:37.0')] ).
cnf(53,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| equal(outer_pasch(x,u,u,w,v),u) ),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.2,6.0')] ).
cnf(522,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(spr,[status(thm),theory(equality)],[53,13]),
[iquote('0:SpR:53.2,13.2')] ).
cnf(524,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[522]),
[iquote('0:Obv:522.1')] ).
cnf(529,plain,
( ~ between(u,v,w)
| between(w,v,u) ),
inference(res,[status(thm),theory(equality)],[28,524]),
[iquote('0:Res:28.0,524.0')] ).
cnf(542,plain,
between(d,c,a),
inference(res,[status(thm),theory(equality)],[4,529]),
[iquote('0:Res:4.0,529.0')] ).
cnf(543,plain,
between(c,d,a),
inference(res,[status(thm),theory(equality)],[38,529]),
[iquote('1:Res:38.0,529.0')] ).
cnf(565,plain,
( ~ between(u,d,a)
| between(u,d,c) ),
inference(res,[status(thm),theory(equality)],[542,7]),
[iquote('0:Res:542.0,7.0')] ).
cnf(674,plain,
( ~ between(c,d,a)
| equal(d,c) ),
inference(res,[status(thm),theory(equality)],[565,6]),
[iquote('0:Res:565.1,6.0')] ).
cnf(681,plain,
$false,
inference(mrr,[status(thm)],[674,543,3]),
[iquote('1:MRR:674.0,674.1,543.0,3.0')] ).
cnf(683,plain,
~ between(a,d,c),
inference(spt,[spt(split,[position(sa)])],[681,38]),
[iquote('1:Spt:681.0,37.0,38.0')] ).
cnf(684,plain,
between(c,a,c),
inference(spt,[spt(split,[position(s2)])],[37]),
[iquote('1:Spt:681.0,37.1')] ).
cnf(688,plain,
equal(c,a),
inference(res,[status(thm),theory(equality)],[684,6]),
[iquote('1:Res:684.0,6.0')] ).
cnf(694,plain,
$false,
inference(mrr,[status(thm)],[688,1]),
[iquote('1:MRR:688.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO006-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Fri Jun 17 15:47:17 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.10/0.42
% 0.10/0.42 SPASS V 3.9
% 0.10/0.42 SPASS beiseite: Proof found.
% 0.10/0.42 % SZS status Theorem
% 0.10/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 SPASS derived 575 clauses, backtracked 6 clauses, performed 1 splits and kept 347 clauses.
% 0.10/0.42 SPASS allocated 63937 KBytes.
% 0.10/0.42 SPASS spent 0:00:00.15 on the problem.
% 0.10/0.42 0:00:00.02 for the input.
% 0.10/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.10/0.42 0:00:00.01 for inferences.
% 0.10/0.42 0:00:00.00 for the backtracking.
% 0.10/0.42 0:00:00.11 for the reduction.
% 0.10/0.42
% 0.10/0.42
% 0.10/0.42 Here is a proof with depth 6, length 29 :
% 0.10/0.42 % SZS output start Refutation
% See solution above
% 0.10/0.42 Formulae used in the proof : a_not_c c_not_d c_between_a_and_d prove_not_between_others identity_for_betweeness transitivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2
% 0.10/0.42
%------------------------------------------------------------------------------