%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 17 unt; 2 nHn; 29 RR)
% Number of literals : 48 ( 0 equ; 20 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('GEO006-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(d,c),
file('GEO006-2.p',unknown),
[] ).
cnf(4,axiom,
between(a,c,d),
file('GEO006-2.p',unknown),
[] ).
cnf(5,axiom,
( between(a,d,c)
| between(c,a,d) ),
file('GEO006-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO006-2.p',unknown),
[] ).
cnf(9,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO006-2.p',unknown),
[] ).
cnf(10,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO006-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO006-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO006-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO006-2.p',unknown),
[] ).
cnf(25,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(26,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[25,9]),
[iquote('0:SpR:25.0,9.0')] ).
cnf(40,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.2,12.0')] ).
cnf(477,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(spr,[status(thm),theory(equality)],[40,13]),
[iquote('0:SpR:40.2,13.2')] ).
cnf(479,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[477]),
[iquote('0:Obv:477.1')] ).
cnf(481,plain,
( ~ between(c,u,d)
| between(u,c,a) ),
inference(res,[status(thm),theory(equality)],[4,479]),
[iquote('0:Res:4.0,479.0')] ).
cnf(490,plain,
( between(a,d,c)
| between(a,c,a) ),
inference(res,[status(thm),theory(equality)],[5,481]),
[iquote('0:Res:5.1,481.0')] ).
cnf(491,plain,
between(d,c,a),
inference(res,[status(thm),theory(equality)],[26,481]),
[iquote('0:Res:26.0,481.0')] ).
cnf(494,plain,
( ~ between(c,u,a)
| between(u,c,d) ),
inference(res,[status(thm),theory(equality)],[491,479]),
[iquote('0:Res:491.0,479.0')] ).
cnf(495,plain,
between(a,d,c),
inference(spt,[spt(split,[position(s1)])],[490]),
[iquote('1:Spt:490.0')] ).
cnf(496,plain,
( ~ between(d,u,c)
| between(u,d,a) ),
inference(res,[status(thm),theory(equality)],[495,479]),
[iquote('1:Res:495.0,479.0')] ).
cnf(507,plain,
between(c,d,a),
inference(res,[status(thm),theory(equality)],[26,496]),
[iquote('1:Res:26.0,496.0')] ).
cnf(511,plain,
between(d,c,d),
inference(res,[status(thm),theory(equality)],[507,494]),
[iquote('1:Res:507.0,494.0')] ).
cnf(512,plain,
equal(d,c),
inference(res,[status(thm),theory(equality)],[511,12]),
[iquote('1:Res:511.0,12.0')] ).
cnf(514,plain,
$false,
inference(mrr,[status(thm)],[512,3]),
[iquote('1:MRR:512.0,3.0')] ).
cnf(515,plain,
~ between(a,d,c),
inference(spt,[spt(split,[position(sa)])],[514,495]),
[iquote('1:Spt:514.0,490.0,495.0')] ).
cnf(516,plain,
between(a,c,a),
inference(spt,[spt(split,[position(s2)])],[490]),
[iquote('1:Spt:514.0,490.1')] ).
cnf(519,plain,
equal(c,a),
inference(res,[status(thm),theory(equality)],[516,12]),
[iquote('1:Res:516.0,12.0')] ).
cnf(521,plain,
$false,
inference(mrr,[status(thm)],[519,1]),
[iquote('1:MRR:519.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 21:15:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 423 clauses, backtracked 4 clauses, performed 1 splits and kept 245 clauses.
% 0.18/0.51 SPASS allocated 63712 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.10 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 9, length 29 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : a_not_c c_not_d c_between_a_and_d prove_not_between_others identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.18/0.51
%------------------------------------------------------------------------------