TSTP Solution File: GEO068-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO068-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 06:22:03 EDT 2022
% Result : Unsatisfiable 15.63s 15.84s
% Output : Refutation 15.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 37 ( 21 unt; 3 nHn; 37 RR)
% Number of literals : 68 ( 0 equ; 33 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(x,w,u,v) ),
file('GEO068-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO068-3.p',unknown),
[] ).
cnf(56,axiom,
( ~ between(u,v,w)
| ~ equidistant(u,w,x,y)
| ~ equidistant(v,w,z,y)
| ~ equidistant(u,v,x,z)
| between(x,z,y) ),
file('GEO068-3.p',unknown),
[] ).
cnf(65,axiom,
( ~ between(u,v,w)
| colinear(u,w,v) ),
file('GEO068-3.p',unknown),
[] ).
cnf(66,axiom,
( ~ between(u,v,w)
| colinear(v,u,w) ),
file('GEO068-3.p',unknown),
[] ).
cnf(71,axiom,
( ~ colinear(u,v,w)
| colinear(v,u,w) ),
file('GEO068-3.p',unknown),
[] ).
cnf(77,axiom,
equidistant(u__dfg,v__dfg,u1,v1),
file('GEO068-3.p',unknown),
[] ).
cnf(78,axiom,
equidistant(v__dfg,w__dfg,v1,w1),
file('GEO068-3.p',unknown),
[] ).
cnf(79,axiom,
equidistant(u__dfg,w__dfg,u1,w1),
file('GEO068-3.p',unknown),
[] ).
cnf(80,axiom,
colinear(u__dfg,v__dfg,w__dfg),
file('GEO068-3.p',unknown),
[] ).
cnf(81,axiom,
~ colinear(u1,v1,w1),
file('GEO068-3.p',unknown),
[] ).
cnf(100,axiom,
( ~ between(u,v,w)
| colinear(u,v,w) ),
file('GEO068-3.p',unknown),
[] ).
cnf(103,axiom,
( ~ colinear(u,v,w)
| between(w,u,v)
| between(v,w,u)
| between(u,v,w) ),
file('GEO068-3.p',unknown),
[] ).
cnf(108,plain,
~ between(u1,v1,w1),
inference(res,[status(thm),theory(equality)],[100,81]),
[iquote('0:Res:100.1,81.0')] ).
cnf(109,plain,
~ between(u1,w1,v1),
inference(res,[status(thm),theory(equality)],[65,81]),
[iquote('0:Res:65.1,81.0')] ).
cnf(118,plain,
~ between(v1,u1,w1),
inference(res,[status(thm),theory(equality)],[66,81]),
[iquote('0:Res:66.1,81.0')] ).
cnf(160,plain,
colinear(v__dfg,u__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[80,71]),
[iquote('0:Res:80.0,71.0')] ).
cnf(338,plain,
equidistant(w1,v1,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[78,7]),
[iquote('0:Res:78.0,7.0')] ).
cnf(339,plain,
equidistant(v1,u1,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[77,7]),
[iquote('0:Res:77.0,7.0')] ).
cnf(374,plain,
equidistant(w__dfg,v__dfg,w1,v1),
inference(res,[status(thm),theory(equality)],[338,7]),
[iquote('0:Res:338.0,7.0')] ).
cnf(377,plain,
equidistant(v__dfg,u__dfg,v1,u1),
inference(res,[status(thm),theory(equality)],[339,7]),
[iquote('0:Res:339.0,7.0')] ).
cnf(1213,plain,
( between(w__dfg,v__dfg,u__dfg)
| between(u__dfg,w__dfg,v__dfg)
| between(v__dfg,u__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[160,103]),
[iquote('0:Res:160.0,103.0')] ).
cnf(3639,plain,
( ~ between(u__dfg,u,w__dfg)
| ~ equidistant(u,w__dfg,v,w1)
| ~ equidistant(u__dfg,u,u1,v)
| between(u1,v,w1) ),
inference(res,[status(thm),theory(equality)],[79,56]),
[iquote('0:Res:79.0,56.1')] ).
cnf(3641,plain,
( ~ between(v__dfg,u,w__dfg)
| ~ equidistant(u,w__dfg,v,w1)
| ~ equidistant(v__dfg,u,v1,v)
| between(v1,v,w1) ),
inference(res,[status(thm),theory(equality)],[78,56]),
[iquote('0:Res:78.0,56.1')] ).
cnf(3644,plain,
( ~ between(u__dfg,u,v__dfg)
| ~ equidistant(u,v__dfg,v,v1)
| ~ equidistant(u__dfg,u,u1,v)
| between(u1,v,v1) ),
inference(res,[status(thm),theory(equality)],[77,56]),
[iquote('0:Res:77.0,56.1')] ).
cnf(15280,plain,
( ~ between(u__dfg,w__dfg,v__dfg)
| ~ equidistant(u__dfg,w__dfg,u1,w1)
| between(u1,w1,v1) ),
inference(res,[status(thm),theory(equality)],[374,3644]),
[iquote('0:Res:374.0,3644.1')] ).
cnf(15308,plain,
~ between(u__dfg,w__dfg,v__dfg),
inference(mrr,[status(thm)],[15280,79,109]),
[iquote('0:MRR:15280.1,15280.2,79.0,109.0')] ).
cnf(15309,plain,
( between(w__dfg,v__dfg,u__dfg)
| between(v__dfg,u__dfg,w__dfg) ),
inference(mrr,[status(thm)],[1213,15308]),
[iquote('0:MRR:1213.1,15308.0')] ).
cnf(15326,plain,
between(w__dfg,v__dfg,u__dfg),
inference(spt,[spt(split,[position(s1)])],[15309]),
[iquote('1:Spt:15309.0')] ).
cnf(15345,plain,
between(u__dfg,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[15326,27]),
[iquote('1:Res:15326.0,27.0')] ).
cnf(15358,plain,
( ~ between(v__dfg,u__dfg,w__dfg)
| ~ equidistant(v__dfg,u__dfg,v1,u1)
| between(v1,u1,w1) ),
inference(res,[status(thm),theory(equality)],[79,3641]),
[iquote('0:Res:79.0,3641.1')] ).
cnf(15397,plain,
~ between(v__dfg,u__dfg,w__dfg),
inference(mrr,[status(thm)],[15358,377,118]),
[iquote('0:MRR:15358.1,15358.2,377.0,118.0')] ).
cnf(15458,plain,
( ~ between(u__dfg,v__dfg,w__dfg)
| ~ equidistant(u__dfg,v__dfg,u1,v1)
| between(u1,v1,w1) ),
inference(res,[status(thm),theory(equality)],[78,3639]),
[iquote('0:Res:78.0,3639.1')] ).
cnf(15495,plain,
$false,
inference(mrr,[status(thm)],[15458,15345,77,108]),
[iquote('1:MRR:15458.0,15458.1,15458.2,15345.0,77.0,108.0')] ).
cnf(15506,plain,
~ between(w__dfg,v__dfg,u__dfg),
inference(spt,[spt(split,[position(sa)])],[15495,15326]),
[iquote('1:Spt:15495.0,15309.0,15326.0')] ).
cnf(15507,plain,
between(v__dfg,u__dfg,w__dfg),
inference(spt,[spt(split,[position(s2)])],[15309]),
[iquote('1:Spt:15495.0,15309.1')] ).
cnf(15508,plain,
$false,
inference(mrr,[status(thm)],[15507,15397]),
[iquote('1:MRR:15507.0,15397.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO068-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 10:42:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 15.63/15.84
% 15.63/15.84 SPASS V 3.9
% 15.63/15.84 SPASS beiseite: Proof found.
% 15.63/15.84 % SZS status Theorem
% 15.63/15.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.63/15.84 SPASS derived 13632 clauses, backtracked 26 clauses, performed 1 splits and kept 6517 clauses.
% 15.63/15.84 SPASS allocated 75203 KBytes.
% 15.63/15.84 SPASS spent 0:0:15.28 on the problem.
% 15.63/15.84 0:00:00.04 for the input.
% 15.63/15.84 0:00:00.00 for the FLOTTER CNF translation.
% 15.63/15.84 0:00:00.18 for inferences.
% 15.63/15.84 0:00:00.01 for the backtracking.
% 15.63/15.84 0:0:14.93 for the reduction.
% 15.63/15.84
% 15.63/15.84
% 15.63/15.84 Here is a proof with depth 4, length 37 :
% 15.63/15.84 % SZS output start Refutation
% See solution above
% 15.63/15.84 Formulae used in the proof : d4_4 t1 b11 c2_2 c2_3 t10_5 u_to_v_equals_u1_to_v1 v_to_w_equals_v1_to_w1 u_to_w_equals_u1_to_w1 uvw_colinear prove_u1v1w1_colinear colinearity1 colinearity4
% 15.63/15.84
%------------------------------------------------------------------------------