TSTP Solution File: GEO007-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO007-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 06:21:29 EDT 2022
% Result : Unsatisfiable 0.76s 0.99s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 27 unt; 9 nHn; 49 RR)
% Number of literals : 91 ( 0 equ; 39 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 : 11 ( 11 usr; 9 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(c,a),
file('GEO007-1.p',unknown),
[] ).
cnf(2,axiom,
between(d,a,c),
file('GEO007-1.p',unknown),
[] ).
cnf(3,axiom,
between(e,a,c),
file('GEO007-1.p',unknown),
[] ).
cnf(4,axiom,
~ between(d,e,a),
file('GEO007-1.p',unknown),
[] ).
cnf(5,axiom,
~ between(e,d,a),
file('GEO007-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO007-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,u,v) ),
file('GEO007-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ between(u,v,w)
| ~ between(u,v,x)
| equal(u,v)
| between(u,w,x)
| between(u,x,w) ),
file('GEO007-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO007-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(x,outer_pasch(y,x,u,w,v),u) ),
file('GEO007-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ between(u,v,w)
| ~ between(x,y,v)
| between(w,y,outer_pasch(y,x,u,w,v)) ),
file('GEO007-1.p',unknown),
[] ).
cnf(18,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO007-1.p',unknown),
[] ).
cnf(19,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO007-1.p',unknown),
[] ).
cnf(26,plain,
( ~ between(d,a,u)
| ~ between(e,d,u) ),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.2,5.0')] ).
cnf(36,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[19,10]),
[iquote('0:Res:19.0,10.0')] ).
cnf(37,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[36,18]),
[iquote('0:SpR:36.0,18.0')] ).
cnf(40,plain,
( ~ between(u,e,c)
| between(u,e,a) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.0,7.0')] ).
cnf(56,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(100,plain,
( ~ between(e,a,u)
| equal(e,a)
| between(e,c,u)
| between(e,u,c) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(101,plain,
( ~ between(d,a,u)
| equal(d,a)
| between(d,c,u)
| between(d,u,c) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(574,plain,
equal(e,a),
inference(spt,[spt(split,[position(s1)])],[100]),
[iquote('1:Spt:100.1')] ).
cnf(578,plain,
~ between(d,a,a),
inference(rew,[status(thm),theory(equality)],[574,4]),
[iquote('1:Rew:574.0,4.0')] ).
cnf(601,plain,
$false,
inference(mrr,[status(thm)],[578,37]),
[iquote('1:MRR:578.0,37.0')] ).
cnf(620,plain,
~ equal(e,a),
inference(spt,[spt(split,[position(sa)])],[601,574]),
[iquote('1:Spt:601.0,100.1,574.0')] ).
cnf(621,plain,
( ~ between(e,a,u)
| between(e,c,u)
| between(e,u,c) ),
inference(spt,[spt(split,[position(s2)])],[100]),
[iquote('1:Spt:601.0,100.0,100.2,100.3')] ).
cnf(705,plain,
equal(d,a),
inference(spt,[spt(split,[position(s2s1)])],[101]),
[iquote('2:Spt:101.1')] ).
cnf(710,plain,
~ between(e,a,a),
inference(rew,[status(thm),theory(equality)],[705,5]),
[iquote('2:Rew:705.0,5.0')] ).
cnf(734,plain,
$false,
inference(mrr,[status(thm)],[710,37]),
[iquote('2:MRR:710.0,37.0')] ).
cnf(758,plain,
~ equal(d,a),
inference(spt,[spt(split,[position(s2sa)])],[734,705]),
[iquote('2:Spt:734.0,101.1,705.0')] ).
cnf(759,plain,
( ~ between(d,a,u)
| between(d,c,u)
| between(d,u,c) ),
inference(spt,[spt(split,[position(s2s2)])],[101]),
[iquote('2:Spt:734.0,101.0,101.2,101.3')] ).
cnf(878,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)],[56,13]),
[iquote('0:SpR:56.2,13.2')] ).
cnf(880,plain,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(w,x,u) ),
inference(obv,[status(thm),theory(equality)],[878]),
[iquote('0:Obv:878.1')] ).
cnf(882,plain,
( ~ between(e,u,a)
| between(c,u,e) ),
inference(res,[status(thm),theory(equality)],[3,880]),
[iquote('0:Res:3.0,880.0')] ).
cnf(884,plain,
( ~ between(u,v,w)
| between(w,v,u) ),
inference(res,[status(thm),theory(equality)],[37,880]),
[iquote('0:Res:37.0,880.0')] ).
cnf(890,plain,
( ~ between(d,u,a)
| between(c,u,d) ),
inference(res,[status(thm),theory(equality)],[2,880]),
[iquote('0:Res:2.0,880.0')] ).
cnf(891,plain,
between(c,a,e),
inference(res,[status(thm),theory(equality)],[37,882]),
[iquote('0:Res:37.0,882.0')] ).
cnf(894,plain,
( ~ between(c,a,u)
| equal(c,a)
| between(c,e,u)
| between(c,u,e) ),
inference(res,[status(thm),theory(equality)],[891,8]),
[iquote('0:Res:891.0,8.0')] ).
cnf(896,plain,
( ~ between(c,a,u)
| between(c,e,u)
| between(c,u,e) ),
inference(mrr,[status(thm)],[894,1]),
[iquote('0:MRR:894.1,1.0')] ).
cnf(897,plain,
between(c,a,d),
inference(res,[status(thm),theory(equality)],[37,890]),
[iquote('0:Res:37.0,890.0')] ).
cnf(1263,plain,
( between(c,e,d)
| between(c,d,e) ),
inference(res,[status(thm),theory(equality)],[897,896]),
[iquote('0:Res:897.0,896.0')] ).
cnf(1276,plain,
( between(c,d,e)
| between(d,e,c) ),
inference(res,[status(thm),theory(equality)],[1263,884]),
[iquote('0:Res:1263.0,884.0')] ).
cnf(1281,plain,
between(c,d,e),
inference(spt,[spt(split,[position(s2s2s1)])],[1276]),
[iquote('3:Spt:1276.0')] ).
cnf(1283,plain,
between(e,d,c),
inference(res,[status(thm),theory(equality)],[1281,884]),
[iquote('3:Res:1281.0,884.0')] ).
cnf(1294,plain,
~ between(d,a,c),
inference(res,[status(thm),theory(equality)],[1283,26]),
[iquote('3:Res:1283.0,26.1')] ).
cnf(1297,plain,
$false,
inference(mrr,[status(thm)],[1294,2]),
[iquote('3:MRR:1294.0,2.0')] ).
cnf(1298,plain,
~ between(c,d,e),
inference(spt,[spt(split,[position(s2s2sa)])],[1297,1281]),
[iquote('3:Spt:1297.0,1276.0,1281.0')] ).
cnf(1299,plain,
between(d,e,c),
inference(spt,[spt(split,[position(s2s2s2)])],[1276]),
[iquote('3:Spt:1297.0,1276.1')] ).
cnf(1312,plain,
between(d,e,a),
inference(res,[status(thm),theory(equality)],[1299,40]),
[iquote('3:Res:1299.0,40.0')] ).
cnf(1313,plain,
$false,
inference(mrr,[status(thm)],[1312,4]),
[iquote('3:MRR:1312.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO007-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 02:08:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.76/0.99
% 0.76/0.99 SPASS V 3.9
% 0.76/0.99 SPASS beiseite: Proof found.
% 0.76/0.99 % SZS status Theorem
% 0.76/0.99 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.99 SPASS derived 1086 clauses, backtracked 65 clauses, performed 5 splits and kept 683 clauses.
% 0.76/0.99 SPASS allocated 64821 KBytes.
% 0.76/0.99 SPASS spent 0:00:00.63 on the problem.
% 0.76/0.99 0:00:00.04 for the input.
% 0.76/0.99 0:00:00.00 for the FLOTTER CNF translation.
% 0.76/0.99 0:00:00.03 for inferences.
% 0.76/0.99 0:00:00.00 for the backtracking.
% 0.76/0.99 0:00:00.54 for the reduction.
% 0.76/0.99
% 0.76/0.99
% 0.76/0.99 Here is a proof with depth 10, length 49 :
% 0.76/0.99 % SZS output start Refutation
% See solution above
% 0.76/0.99 Formulae used in the proof : a_not_c a_between_a_and_c a_between_a_and_e e_not_between_d_and_a prove_d_between_e_and_a identity_for_betweeness transitivity_for_betweeness connectivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2
% 0.76/0.99
%------------------------------------------------------------------------------