TSTP Solution File: GEO046-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO046-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 06:21:52 EDT 2022
% Result : Unsatisfiable 0.54s 0.75s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 21 unt; 6 nHn; 42 RR)
% Number of literals : 73 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
equal(extension(u,v,w,w),v),
file('GEO046-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,extension(v,w,x,y))
| between(v,w,u) ),
file('GEO046-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ between(u,v,w)
| equal(u,v)
| equal(extension(u,v,v,w),w) ),
file('GEO046-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO046-3.p',unknown),
[] ).
cnf(34,axiom,
( ~ between(u,v,w)
| ~ between(u,x,v)
| between(x,v,w) ),
file('GEO046-3.p',unknown),
[] ).
cnf(35,axiom,
( ~ between(u,v,w)
| ~ between(x,u,v)
| equal(u,v)
| between(x,v,w) ),
file('GEO046-3.p',unknown),
[] ).
cnf(36,axiom,
( ~ between(u,v,w)
| ~ between(x,u,v)
| equal(u,v)
| between(x,u,w) ),
file('GEO046-3.p',unknown),
[] ).
cnf(37,axiom,
between(u__dfg,v__dfg,x__dfg),
file('GEO046-3.p',unknown),
[] ).
cnf(38,axiom,
between(v__dfg,w__dfg,x__dfg),
file('GEO046-3.p',unknown),
[] ).
cnf(39,axiom,
~ between(u__dfg,w__dfg,x__dfg),
file('GEO046-3.p',unknown),
[] ).
cnf(43,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO046-3.p',unknown),
[] ).
cnf(65,plain,
~ equal(extension(u__dfg,w__dfg,u,v),x__dfg),
inference(res,[status(thm),theory(equality)],[11,39]),
[iquote('0:Res:11.1,39.0')] ).
cnf(68,plain,
( ~ between(u,w__dfg,x__dfg)
| ~ between(u,u__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[34,39]),
[iquote('0:Res:34.2,39.0')] ).
cnf(90,plain,
~ equal(w__dfg,x__dfg),
inference(spl,[status(thm),theory(equality)],[10,65]),
[iquote('0:SpL:10.0,65.0')] ).
cnf(115,plain,
between(x__dfg,w__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[38,27]),
[iquote('0:Res:38.0,27.0')] ).
cnf(116,plain,
between(x__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[37,27]),
[iquote('0:Res:37.0,27.0')] ).
cnf(120,plain,
between(extension(u,v,w,x),v,u),
inference(res,[status(thm),theory(equality)],[43,27]),
[iquote('0:Res:43.0,27.0')] ).
cnf(142,plain,
~ between(v__dfg,u__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[38,68]),
[iquote('0:Res:38.0,68.0')] ).
cnf(145,plain,
~ between(extension(x__dfg,w__dfg,u,v),u__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[120,68]),
[iquote('0:Res:120.0,68.0')] ).
cnf(375,plain,
( ~ equal(u,v)
| between(w,v,u) ),
inference(spl,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpL:10.0,11.0')] ).
cnf(428,plain,
( ~ equal(u,v)
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[375,27]),
[iquote('0:Res:375.1,27.0')] ).
cnf(454,plain,
( ~ between(x__dfg,u,v__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[116,34]),
[iquote('0:Res:116.0,34.0')] ).
cnf(474,plain,
~ equal(v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[428,142]),
[iquote('0:Res:428.1,142.0')] ).
cnf(501,plain,
( ~ between(x__dfg,w__dfg,u)
| ~ between(u,u__dfg,w__dfg)
| equal(w__dfg,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[20,145]),
[iquote('0:SpL:20.2,145.0')] ).
cnf(504,plain,
( ~ between(x__dfg,w__dfg,u)
| ~ between(u,u__dfg,w__dfg) ),
inference(mrr,[status(thm)],[501,90]),
[iquote('0:MRR:501.2,90.0')] ).
cnf(512,plain,
( ~ between(u,v__dfg,w__dfg)
| equal(w__dfg,v__dfg)
| between(u,v__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[38,36]),
[iquote('0:Res:38.0,36.0')] ).
cnf(548,plain,
( ~ between(u,v__dfg,w__dfg)
| equal(w__dfg,v__dfg)
| between(u,w__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[38,35]),
[iquote('0:Res:38.0,35.0')] ).
cnf(549,plain,
( ~ between(u,u__dfg,v__dfg)
| equal(v__dfg,u__dfg)
| between(u,v__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[37,35]),
[iquote('0:Res:37.0,35.0')] ).
cnf(561,plain,
( ~ between(u,u__dfg,v__dfg)
| between(u,v__dfg,x__dfg) ),
inference(mrr,[status(thm)],[549,474]),
[iquote('0:MRR:549.1,474.0')] ).
cnf(687,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[115,454]),
[iquote('0:Res:115.0,454.0')] ).
cnf(699,plain,
between(u__dfg,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[687,27]),
[iquote('0:Res:687.0,27.0')] ).
cnf(1183,plain,
( ~ between(u,u__dfg,v__dfg)
| between(x__dfg,v__dfg,u) ),
inference(res,[status(thm),theory(equality)],[561,27]),
[iquote('0:Res:561.1,27.0')] ).
cnf(1467,plain,
equal(w__dfg,v__dfg),
inference(spt,[spt(split,[position(s1)])],[512]),
[iquote('1:Spt:512.1')] ).
cnf(1562,plain,
( ~ between(x__dfg,w__dfg,u)
| ~ between(u,u__dfg,v__dfg) ),
inference(rew,[status(thm),theory(equality)],[1467,504]),
[iquote('1:Rew:1467.0,504.1')] ).
cnf(1666,plain,
( ~ between(x__dfg,v__dfg,u)
| ~ between(u,u__dfg,v__dfg) ),
inference(rew,[status(thm),theory(equality)],[1467,1562]),
[iquote('1:Rew:1467.0,1562.0')] ).
cnf(1667,plain,
~ between(u,u__dfg,v__dfg),
inference(mrr,[status(thm)],[1666,1183]),
[iquote('1:MRR:1666.0,1183.1')] ).
cnf(1668,plain,
$false,
inference(unc,[status(thm)],[1667,120]),
[iquote('1:UnC:1667.0,120.0')] ).
cnf(1718,plain,
~ equal(w__dfg,v__dfg),
inference(spt,[spt(split,[position(sa)])],[1668,1467]),
[iquote('1:Spt:1668.0,512.1,1467.0')] ).
cnf(1719,plain,
( ~ between(u,v__dfg,w__dfg)
| between(u,v__dfg,x__dfg) ),
inference(spt,[spt(split,[position(s2)])],[512]),
[iquote('1:Spt:1668.0,512.0,512.2')] ).
cnf(1730,plain,
( ~ between(u,v__dfg,w__dfg)
| between(u,w__dfg,x__dfg) ),
inference(mrr,[status(thm)],[548,1718]),
[iquote('1:MRR:548.1,1718.0')] ).
cnf(1891,plain,
~ between(u__dfg,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[1730,39]),
[iquote('1:Res:1730.1,39.0')] ).
cnf(1902,plain,
$false,
inference(mrr,[status(thm)],[1891,699]),
[iquote('1:MRR:1891.0,699.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GEO046-3 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n023.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Fri Jun 17 17:18:34 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.54/0.75
% 0.54/0.75 SPASS V 3.9
% 0.54/0.75 SPASS beiseite: Proof found.
% 0.54/0.75 % SZS status Theorem
% 0.54/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.75 SPASS derived 1601 clauses, backtracked 204 clauses, performed 2 splits and kept 893 clauses.
% 0.54/0.75 SPASS allocated 64511 KBytes.
% 0.54/0.75 SPASS spent 0:00:00.45 on the problem.
% 0.54/0.75 0:00:00.02 for the input.
% 0.54/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.54/0.75 0:00:00.02 for inferences.
% 0.54/0.75 0:00:00.00 for the backtracking.
% 0.54/0.75 0:00:00.38 for the reduction.
% 0.54/0.75
% 0.54/0.75
% 0.54/0.75 Here is a proof with depth 4, length 42 :
% 0.54/0.75 % SZS output start Refutation
% See solution above
% 0.54/0.75 Formulae used in the proof : e1 b0 d10_1 t1 b5 b6 b7 v_between_u_and_x w_between_v_and_x prove_w_between_u_and_x segment_construction1
% 0.54/0.75
%------------------------------------------------------------------------------