TSTP Solution File: GEO053-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO053-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 06:21:55 EDT 2022
% Result : Unsatisfiable 153.05s 153.24s
% Output : Refutation 153.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 53 ( 23 unt; 7 nHn; 53 RR)
% Number of literals : 132 ( 0 equ; 76 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO053-2.p',unknown),
[] ).
cnf(2,axiom,
equidistant(u__dfg,v__dfg,u__dfg,w__dfg),
file('GEO053-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(w__dfg,v__dfg),
file('GEO053-2.p',unknown),
[] ).
cnf(4,axiom,
equidistant(u,v,v,u),
file('GEO053-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO053-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO053-2.p',unknown),
[] ).
cnf(7,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO053-2.p',unknown),
[] ).
cnf(8,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO053-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,z)
| ~ equidistant(y,x1,v,x2)
| ~ equidistant(x,x1,u,x2)
| ~ equidistant(y,z,v,w)
| ~ equidistant(x,y,u,v)
| equal(x,y)
| equidistant(z,x1,w,x2) ),
file('GEO053-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO053-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO053-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO053-2.p',unknown),
[] ).
cnf(37,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.0,6.0')] ).
cnf(38,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[37,7]),
[iquote('0:SpR:37.0,7.0')] ).
cnf(43,plain,
( ~ equidistant(u__dfg,v__dfg,u,v)
| equidistant(u,v,u__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(44,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.0,5.0')] ).
cnf(47,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[12,10]),
[iquote('0:Res:12.2,10.0')] ).
cnf(49,plain,
equidistant(v__dfg,u__dfg,u__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[4,43]),
[iquote('0:Res:4.0,43.0')] ).
cnf(54,plain,
( ~ between(u,v,w)
| ~ between(x,u,w)
| equal(inner_pasch(x,u,w,v,u),u) ),
inference(res,[status(thm),theory(equality)],[11,10]),
[iquote('0:Res:11.2,10.0')] ).
cnf(62,plain,
equidistant(u__dfg,w__dfg,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[49,44]),
[iquote('0:Res:49.0,44.0')] ).
cnf(67,plain,
equidistant(u__dfg,v__dfg,w__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[62,44]),
[iquote('0:Res:62.0,44.0')] ).
cnf(73,plain,
equidistant(w__dfg,u__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[67,44]),
[iquote('0:Res:67.0,44.0')] ).
cnf(169,plain,
( ~ between(u,u__dfg,v)
| ~ between(w,u__dfg,x)
| ~ equidistant(w,v__dfg,u,w__dfg)
| ~ equidistant(u__dfg,x,u__dfg,v)
| ~ equidistant(w,u__dfg,u,u__dfg)
| equal(w,u__dfg)
| equidistant(x,v__dfg,v,w__dfg) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.0,9.2')] ).
cnf(177,plain,
( ~ between(u,v,w)
| ~ between(x,y,z)
| ~ equidistant(x,v,u,y)
| ~ equidistant(y,z,v,w)
| ~ equidistant(x,y,u,v)
| equal(x,y)
| equidistant(z,v,w,y) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.2')] ).
cnf(259,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)],[47,11]),
[iquote('0:SpR:47.2,11.2')] ).
cnf(261,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[259]),
[iquote('0:Obv:259.1')] ).
cnf(285,plain,
( ~ between(u,v,w)
| ~ between(v,u,w)
| ~ between(u,v,w)
| ~ between(v,u,w)
| equal(u,v) ),
inference(spr,[status(thm),theory(equality)],[54,47]),
[iquote('0:SpR:54.2,47.2')] ).
cnf(286,plain,
( ~ between(u,v,w)
| ~ between(v,u,w)
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[285]),
[iquote('0:Obv:285.1')] ).
cnf(511,plain,
( ~ between(v__dfg,u__dfg,w__dfg)
| equal(v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,286]),
[iquote('0:Res:1.0,286.0')] ).
cnf(650,plain,
( ~ between(v__dfg,u__dfg,u)
| ~ between(w__dfg,u__dfg,v)
| ~ equidistant(u__dfg,v,u__dfg,u)
| ~ equidistant(w__dfg,u__dfg,v__dfg,u__dfg)
| equal(w__dfg,u__dfg)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[4,169]),
[iquote('0:Res:4.0,169.2')] ).
cnf(664,plain,
( ~ between(v__dfg,u__dfg,u)
| ~ between(w__dfg,u__dfg,v)
| ~ equidistant(u__dfg,v,u__dfg,u)
| equal(w__dfg,u__dfg)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(mrr,[status(thm)],[650,73]),
[iquote('0:MRR:650.3,73.0')] ).
cnf(694,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,w__dfg,v)
| ~ equidistant(w__dfg,v,v__dfg,u)
| ~ equidistant(u__dfg,w__dfg,u__dfg,v__dfg)
| equal(w__dfg,u__dfg)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[2,177]),
[iquote('0:Res:2.0,177.2')] ).
cnf(769,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,w__dfg,v)
| ~ equidistant(w__dfg,v,v__dfg,u)
| equal(w__dfg,u__dfg)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(mrr,[status(thm)],[694,62]),
[iquote('0:MRR:694.3,62.0')] ).
cnf(1340,plain,
( ~ between(v__dfg,u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,261]),
[iquote('0:Res:1.0,261.0')] ).
cnf(1343,plain,
( ~ between(u,v,extension(w,u,x,y))
| between(v,u,w) ),
inference(res,[status(thm),theory(equality)],[7,261]),
[iquote('0:Res:7.0,261.0')] ).
cnf(1357,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[38,1340]),
[iquote('0:Res:38.0,1340.0')] ).
cnf(1363,plain,
( ~ between(v__dfg,w__dfg,u__dfg)
| equal(w__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[1357,286]),
[iquote('0:Res:1357.0,286.0')] ).
cnf(1364,plain,
~ between(v__dfg,w__dfg,u__dfg),
inference(mrr,[status(thm)],[1363,3]),
[iquote('0:MRR:1363.1,3.0')] ).
cnf(1369,plain,
equal(w__dfg,u__dfg),
inference(spt,[spt(split,[position(s1)])],[664]),
[iquote('1:Spt:664.3')] ).
cnf(1371,plain,
~ equal(v__dfg,u__dfg),
inference(rew,[status(thm),theory(equality)],[1369,3]),
[iquote('1:Rew:1369.0,3.0')] ).
cnf(1430,plain,
( ~ between(v__dfg,u__dfg,u__dfg)
| equal(v__dfg,u__dfg) ),
inference(rew,[status(thm),theory(equality)],[1369,511]),
[iquote('1:Rew:1369.0,511.0')] ).
cnf(2043,plain,
equal(v__dfg,u__dfg),
inference(mrr,[status(thm)],[1430,38]),
[iquote('1:MRR:1430.0,38.0')] ).
cnf(2044,plain,
$false,
inference(mrr,[status(thm)],[2043,1371]),
[iquote('1:MRR:2043.0,1371.0')] ).
cnf(2895,plain,
~ equal(w__dfg,u__dfg),
inference(spt,[spt(split,[position(sa)])],[2044,1369]),
[iquote('1:Spt:2044.0,664.3,1369.0')] ).
cnf(2896,plain,
( ~ between(v__dfg,u__dfg,u)
| ~ between(w__dfg,u__dfg,v)
| ~ equidistant(u__dfg,v,u__dfg,u)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(spt,[spt(split,[position(s2)])],[664]),
[iquote('1:Spt:2044.0,664.0,664.1,664.2,664.4')] ).
cnf(2897,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,w__dfg,v)
| ~ equidistant(w__dfg,v,v__dfg,u)
| equidistant(v,v__dfg,u,w__dfg) ),
inference(mrr,[status(thm)],[769,2895]),
[iquote('1:MRR:769.3,2895.0')] ).
cnf(3605,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,w__dfg,extension(v,w__dfg,v__dfg,u))
| equidistant(extension(v,w__dfg,v__dfg,u),v__dfg,u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[8,2897]),
[iquote('1:Res:8.0,2897.2')] ).
cnf(4632,plain,
between(extension(u,v,w,x),v,u),
inference(res,[status(thm),theory(equality)],[38,1343]),
[iquote('0:Res:38.0,1343.0')] ).
cnf(7513,plain,
( ~ between(u__dfg,v__dfg,w__dfg)
| ~ between(u__dfg,w__dfg,extension(u,w__dfg,v__dfg,w__dfg))
| equal(extension(u,w__dfg,v__dfg,w__dfg),v__dfg) ),
inference(res,[status(thm),theory(equality)],[3605,6]),
[iquote('1:Res:3605.2,6.0')] ).
cnf(7520,plain,
( ~ between(u__dfg,w__dfg,extension(u,w__dfg,v__dfg,w__dfg))
| equal(extension(u,w__dfg,v__dfg,w__dfg),v__dfg) ),
inference(mrr,[status(thm)],[7513,1]),
[iquote('1:MRR:7513.0,1.0')] ).
cnf(33432,plain,
equal(extension(u__dfg,w__dfg,v__dfg,w__dfg),v__dfg),
inference(res,[status(thm),theory(equality)],[7,7520]),
[iquote('1:Res:7.0,7520.0')] ).
cnf(33437,plain,
between(v__dfg,w__dfg,u__dfg),
inference(spr,[status(thm),theory(equality)],[33432,4632]),
[iquote('1:SpR:33432.0,4632.0')] ).
cnf(33750,plain,
$false,
inference(mrr,[status(thm)],[33437,1364]),
[iquote('1:MRR:33437.0,1364.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : GEO053-2 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jun 18 13:23:40 EDT 2022
% 0.21/0.37 % CPUTime :
% 153.05/153.24
% 153.05/153.24 SPASS V 3.9
% 153.05/153.24 SPASS beiseite: Proof found.
% 153.05/153.24 % SZS status Theorem
% 153.05/153.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.05/153.24 SPASS derived 28482 clauses, backtracked 2951 clauses, performed 2 splits and kept 13556 clauses.
% 153.05/153.24 SPASS allocated 102455 KBytes.
% 153.05/153.24 SPASS spent 0:2:31.81 on the problem.
% 153.05/153.24 0:00:00.04 for the input.
% 153.05/153.24 0:00:00.00 for the FLOTTER CNF translation.
% 153.05/153.24 0:00:00.71 for inferences.
% 153.05/153.24 0:00:01.65 for the backtracking.
% 153.05/153.24 0:2:29.08 for the reduction.
% 153.05/153.24
% 153.05/153.24
% 153.05/153.24 Here is a proof with depth 6, length 53 :
% 153.05/153.24 % SZS output start Refutation
% See solution above
% 153.05/153.24 Formulae used in the proof : v_between_u_and_w u_to_v_equals_u_to_w prove_v_equals_w reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction1 segment_construction2 outer_five_segment identity_for_betweeness inner_pasch1 inner_pasch2
% 153.05/153.24
%------------------------------------------------------------------------------