TSTP Solution File: GEO002-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO002-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 06:21:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 8 unt; 0 nHn; 18 RR)
% Number of literals : 36 ( 0 equ; 21 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 : 9 ( 9 usr; 7 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ between(a,a,b),
file('GEO002-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO002-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,u,v) ),
file('GEO002-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO002-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO002-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO002-1.p',unknown),
[] ).
cnf(14,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO002-1.p',unknown),
[] ).
cnf(15,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO002-1.p',unknown),
[] ).
cnf(22,plain,
( ~ between(a,a,u)
| ~ between(a,b,u) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.2,1.0')] ).
cnf(35,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[15,6]),
[iquote('0:Res:15.0,6.0')] ).
cnf(37,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[35,14]),
[iquote('0:SpR:35.0,14.0')] ).
cnf(44,plain,
~ between(a,a,extension(a,b,u,v)),
inference(res,[status(thm),theory(equality)],[14,22]),
[iquote('0:Res:14.0,22.1')] ).
cnf(60,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| equal(outer_pasch(x,u,u,w,v),u) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.2,2.0')] ).
cnf(638,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)],[60,9]),
[iquote('0:SpR:60.2,9.2')] ).
cnf(640,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[638]),
[iquote('0:Obv:638.1')] ).
cnf(643,plain,
( ~ between(u,v,w)
| between(w,v,u) ),
inference(res,[status(thm),theory(equality)],[37,640]),
[iquote('0:Res:37.0,640.0')] ).
cnf(650,plain,
between(u,u,v),
inference(res,[status(thm),theory(equality)],[37,643]),
[iquote('0:Res:37.0,643.0')] ).
cnf(656,plain,
$false,
inference(unc,[status(thm)],[650,44]),
[iquote('0:UnC:650.0,44.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO002-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 14:03:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 550 clauses, backtracked 0 clauses, performed 1 splits and kept 270 clauses.
% 0.19/0.55 SPASS allocated 63832 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.55 0:00:00.04 for the input.
% 0.19/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.01 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.13 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 4, length 18 :
% 0.19/0.55 % SZS output start Refutation
% See solution above
% 0.19/0.55 Formulae used in the proof : prove_a_between_a_and_b identity_for_betweeness transitivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2
% 0.19/0.55
%------------------------------------------------------------------------------