TSTP Solution File: GEO032-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO032-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 06:21:44 EDT 2022
% Result : Unsatisfiable 15.45s 15.66s
% Output : Refutation 15.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 38 ( 13 unt; 0 nHn; 38 RR)
% Number of literals : 85 ( 0 equ; 51 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equidistant(u,v,u,v),
file('GEO032-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(v,u,w,x) ),
file('GEO032-3.p',unknown),
[] ).
cnf(10,axiom,
equal(extension(u,v,w,w),v),
file('GEO032-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,extension(v,w,x,y))
| between(v,w,u) ),
file('GEO032-3.p',unknown),
[] ).
cnf(13,axiom,
equidistant(u,reflection(v,u),v,u),
file('GEO032-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(u,v)
| equal(reflection(u,v),v) ),
file('GEO032-3.p',unknown),
[] ).
cnf(17,axiom,
equidistant(u,u,v,v),
file('GEO032-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ between(u,v,w)
| ~ between(x,y,z)
| ~ equidistant(y,z,v,w)
| ~ equidistant(x,y,u,v)
| equidistant(x,z,u,w) ),
file('GEO032-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO032-3.p',unknown),
[] ).
cnf(28,axiom,
between(u,u,v),
file('GEO032-3.p',unknown),
[] ).
cnf(37,axiom,
( ~ between(u,v,w)
| ~ between(x,u,w)
| between(x,v,w) ),
file('GEO032-3.p',unknown),
[] ).
cnf(47,axiom,
( ~ between(u,v,w)
| ~ between(x,y,z)
| ~ equidistant(z,x1,w,x2)
| ~ equidistant(x,x1,u,x2)
| ~ equidistant(x,z,u,w)
| ~ equidistant(x,y,u,v)
| equidistant(y,x1,v,x2) ),
file('GEO032-3.p',unknown),
[] ).
cnf(48,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO032-3.p',unknown),
[] ).
cnf(49,axiom,
between(u1,v1,w1),
file('GEO032-3.p',unknown),
[] ).
cnf(50,axiom,
equidistant(u__dfg,v__dfg,u1,v1),
file('GEO032-3.p',unknown),
[] ).
cnf(51,axiom,
equidistant(u__dfg,w__dfg,u1,w1),
file('GEO032-3.p',unknown),
[] ).
cnf(52,axiom,
~ equidistant(v__dfg,w__dfg,v1,w1),
file('GEO032-3.p',unknown),
[] ).
cnf(54,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO032-3.p',unknown),
[] ).
cnf(84,plain,
( ~ between(u,v1,v)
| ~ between(w,v__dfg,x)
| ~ equidistant(w,x,u,v)
| ~ equidistant(x,w__dfg,v,w1)
| ~ equidistant(w,w__dfg,u,w1)
| ~ equidistant(w,v__dfg,u,v1) ),
inference(res,[status(thm),theory(equality)],[47,52]),
[iquote('0:Res:47.6,52.0')] ).
cnf(108,plain,
( ~ equal(u,v)
| equidistant(v,v,u,v) ),
inference(spr,[status(thm),theory(equality)],[14,13]),
[iquote('0:SpR:14.1,13.0')] ).
cnf(122,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[48,27]),
[iquote('0:Res:48.0,27.0')] ).
cnf(482,plain,
( ~ equal(u,v)
| between(w,v,u) ),
inference(spl,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpL:10.0,11.0')] ).
cnf(503,plain,
( ~ equal(u,v)
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[482,27]),
[iquote('0:Res:482.1,27.0')] ).
cnf(611,plain,
( ~ between(u,w__dfg,u__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[122,37]),
[iquote('0:Res:122.0,37.0')] ).
cnf(834,plain,
( ~ equal(u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[503,611]),
[iquote('0:Res:503.1,611.0')] ).
cnf(869,plain,
( ~ equal(u,w__dfg)
| between(u__dfg,v__dfg,u) ),
inference(res,[status(thm),theory(equality)],[834,27]),
[iquote('0:Res:834.1,27.0')] ).
cnf(870,plain,
( ~ equidistant(u__dfg,w__dfg,u,v)
| equidistant(u,v,u1,w1) ),
inference(res,[status(thm),theory(equality)],[51,54]),
[iquote('0:Res:51.0,54.0')] ).
cnf(876,plain,
( ~ equidistant(u,u,v,w)
| equidistant(v,w,x,x) ),
inference(res,[status(thm),theory(equality)],[17,54]),
[iquote('0:Res:17.0,54.0')] ).
cnf(1484,plain,
( ~ between(u,v,w)
| ~ between(x,v,w)
| ~ equidistant(x,v,u,v)
| equidistant(x,w,u,w) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.2')] ).
cnf(2861,plain,
( ~ equal(u,v)
| equidistant(u,v,w,w) ),
inference(res,[status(thm),theory(equality)],[108,876]),
[iquote('0:Res:108.1,876.0')] ).
cnf(9159,plain,
( ~ equal(u,v)
| ~ between(u,v,w)
| ~ between(v,v,w)
| equidistant(v,w,u,w) ),
inference(res,[status(thm),theory(equality)],[108,1484]),
[iquote('0:Res:108.1,1484.2')] ).
cnf(9174,plain,
( ~ equal(u,v)
| equidistant(v,w,u,w) ),
inference(mrr,[status(thm)],[9159,503,28]),
[iquote('0:MRR:9159.1,9159.2,503.1,28.0')] ).
cnf(10711,plain,
( ~ equal(u,v)
| equidistant(w,v,u,w) ),
inference(res,[status(thm),theory(equality)],[9174,3]),
[iquote('0:Res:9174.1,3.0')] ).
cnf(11321,plain,
( ~ equal(u,w__dfg)
| equidistant(u,u__dfg,u1,w1) ),
inference(res,[status(thm),theory(equality)],[10711,870]),
[iquote('0:Res:10711.1,870.0')] ).
cnf(11334,plain,
( ~ equal(u,w__dfg)
| equidistant(u__dfg,u,u1,w1) ),
inference(res,[status(thm),theory(equality)],[11321,3]),
[iquote('0:Res:11321.1,3.0')] ).
cnf(14940,plain,
( ~ equal(u,w__dfg)
| ~ between(u1,v1,w1)
| ~ between(u__dfg,v__dfg,u)
| ~ equidistant(u,w__dfg,w1,w1)
| ~ equidistant(u__dfg,w__dfg,u1,w1)
| ~ equidistant(u__dfg,v__dfg,u1,v1) ),
inference(res,[status(thm),theory(equality)],[11334,84]),
[iquote('0:Res:11334.1,84.2')] ).
cnf(15197,plain,
~ equal(u,w__dfg),
inference(mrr,[status(thm)],[14940,49,869,2861,51,50]),
[iquote('0:MRR:14940.1,14940.2,14940.3,14940.4,14940.5,49.0,869.1,2861.1,51.0,50.0')] ).
cnf(15198,plain,
$false,
inference(unc,[status(thm)],[15197,10]),
[iquote('0:UnC:15197.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO032-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 04:20:46 EDT 2022
% 0.11/0.33 % CPUTime :
% 15.45/15.66
% 15.45/15.66 SPASS V 3.9
% 15.45/15.66 SPASS beiseite: Proof found.
% 15.45/15.66 % SZS status Theorem
% 15.45/15.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.45/15.66 SPASS derived 13158 clauses, backtracked 1316 clauses, performed 2 splits and kept 7335 clauses.
% 15.45/15.66 SPASS allocated 75685 KBytes.
% 15.45/15.66 SPASS spent 0:0:15.19 on the problem.
% 15.45/15.66 0:00:00.04 for the input.
% 15.45/15.66 0:00:00.00 for the FLOTTER CNF translation.
% 15.45/15.66 0:00:00.16 for inferences.
% 15.45/15.66 0:00:00.31 for the backtracking.
% 15.45/15.66 0:0:14.59 for the reduction.
% 15.45/15.66
% 15.45/15.66
% 15.45/15.66 Here is a proof with depth 6, length 38 :
% 15.45/15.66 % SZS output start Refutation
% See solution above
% 15.45/15.66 Formulae used in the proof : d1 d3 e1 b0 r2_2 r3_1 d7 d8 t1 t2 b8 d12 v_between_u_and_w v1_between_u1_and_w1 u_to_v_equals_u1_to_v1 u_to_w_equals_u1_to_w1 v_to_w_equals_v1_to_w1 transitivity_for_equidistance
% 15.45/15.66
%------------------------------------------------------------------------------