TSTP Solution File: GEO001-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO001-1 : 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 06:21:24 EDT 2022
% Result : Unsatisfiable 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 7 unt; 0 nHn; 18 RR)
% Number of literals : 37 ( 0 equ; 22 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(a,b,c),
file('GEO001-1.p',unknown),
[] ).
cnf(2,axiom,
~ between(c,b,a),
file('GEO001-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO001-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,u,v) ),
file('GEO001-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO001-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO001-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO001-1.p',unknown),
[] ).
cnf(15,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO001-1.p',unknown),
[] ).
cnf(16,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO001-1.p',unknown),
[] ).
cnf(23,plain,
( ~ between(b,a,u)
| ~ between(c,b,u) ),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.2,2.0')] ).
cnf(33,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.0,7.0')] ).
cnf(34,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[33,15]),
[iquote('0:SpR:33.0,15.0')] ).
cnf(65,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| equal(outer_pasch(x,u,u,w,v),u) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.2,3.0')] ).
cnf(861,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)],[65,10]),
[iquote('0:SpR:65.2,10.2')] ).
cnf(863,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[861]),
[iquote('0:Obv:861.1')] ).
cnf(910,plain,
( ~ between(a,u,b)
| between(c,u,a) ),
inference(res,[status(thm),theory(equality)],[1,863]),
[iquote('0:Res:1.0,863.0')] ).
cnf(914,plain,
( ~ between(a,b,b)
| ~ between(b,a,a) ),
inference(res,[status(thm),theory(equality)],[910,23]),
[iquote('0:Res:910.1,23.1')] ).
cnf(918,plain,
$false,
inference(mrr,[status(thm)],[914,34]),
[iquote('0:MRR:914.0,914.1,34.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO001-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 13:14:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 739 clauses, backtracked 29 clauses, performed 2 splits and kept 369 clauses.
% 0.47/0.64 SPASS allocated 64063 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.47/0.64 0:00:00.04 for the input.
% 0.47/0.64 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.02 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.21 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 4, length 18 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : b_between_a_and_c prove_b_between_c_and_a identity_for_betweeness transitivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2
% 0.47/0.64
%------------------------------------------------------------------------------