TSTP Solution File: GEO002-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 06:21:26 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 8 unt; 0 nHn; 23 RR)
% Number of literals : 50 ( 0 equ; 34 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 : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,u,v) ),
file('GEO002-4.p',unknown),
[] ).
cnf(2,axiom,
( ~ equidistant(u,v,w,w)
| equalish(u,v) ),
file('GEO002-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO002-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO002-4.p',unknown),
[] ).
cnf(5,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO002-4.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO002-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ equalish(u,v)
| ~ between(w,x,u)
| between(w,x,v) ),
file('GEO002-4.p',unknown),
[] ).
cnf(8,axiom,
~ between(a,a,b),
file('GEO002-4.p',unknown),
[] ).
cnf(9,plain,
( ~ between(a,a,u)
| ~ between(a,b,u) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.2,8.0')] ).
cnf(12,plain,
equalish(u,extension(v,u,w,w)),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.0,2.0')] ).
cnf(19,plain,
( ~ between(u,v,extension(v,w,x,y))
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.0,1.0')] ).
cnf(21,plain,
between(u,u,u),
inference(res,[status(thm),theory(equality)],[5,19]),
[iquote('0:Res:5.0,19.0')] ).
cnf(26,plain,
( ~ equalish(u,v)
| between(u,u,v) ),
inference(res,[status(thm),theory(equality)],[21,7]),
[iquote('0:Res:21.0,7.1')] ).
cnf(27,plain,
( ~ between(u,v,w)
| ~ between(x,y,v)
| ~ between(z,x,u)
| between(z,x,outer_pasch(y,x,u,w,v)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.2,1.0')] ).
cnf(33,plain,
( ~ equalish(u,v)
| ~ between(w,u,v)
| between(w,u,u) ),
inference(res,[status(thm),theory(equality)],[26,1]),
[iquote('0:Res:26.1,1.0')] ).
cnf(38,plain,
( ~ between(u,v,a)
| ~ between(w,a,v)
| ~ between(a,b,outer_pasch(a,w,u,a,v)) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.2,9.0')] ).
cnf(60,plain,
( ~ equalish(u,extension(v,u,w,x))
| between(v,u,u) ),
inference(res,[status(thm),theory(equality)],[5,33]),
[iquote('0:Res:5.0,33.1')] ).
cnf(70,plain,
between(u,v,v),
inference(res,[status(thm),theory(equality)],[12,60]),
[iquote('0:Res:12.0,60.0')] ).
cnf(136,plain,
( ~ between(u,v,a)
| ~ between(b,a,v)
| ~ between(a,b,u)
| ~ between(u,v,a)
| ~ between(b,a,v) ),
inference(res,[status(thm),theory(equality)],[27,38]),
[iquote('0:Res:27.3,38.2')] ).
cnf(137,plain,
( ~ between(a,b,u)
| ~ between(u,v,a)
| ~ between(b,a,v) ),
inference(obv,[status(thm),theory(equality)],[136]),
[iquote('0:Obv:136.1')] ).
cnf(385,plain,
( ~ between(b,u,a)
| ~ between(b,a,u) ),
inference(res,[status(thm),theory(equality)],[70,137]),
[iquote('0:Res:70.0,137.0')] ).
cnf(393,plain,
~ between(b,a,a),
inference(res,[status(thm),theory(equality)],[70,385]),
[iquote('0:Res:70.0,385.0')] ).
cnf(402,plain,
$false,
inference(mrr,[status(thm)],[393,70]),
[iquote('0:MRR:393.0,70.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 09:07:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 386 clauses, backtracked 0 clauses, performed 0 splits and kept 279 clauses.
% 0.20/0.55 SPASS allocated 63590 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.55 0:00:00.04 for the input.
% 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.01 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.12 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 8, length 23 :
% 0.20/0.55 % SZS output start Refutation
% See solution above
% 0.20/0.55 Formulae used in the proof : transitivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2 between_substitution3 prove_a_between_a_and_b
% 0.20/0.55
%------------------------------------------------------------------------------