TSTP Solution File: GEO010-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 06:21:31 EDT 2022
% Result : Unsatisfiable 0.21s 0.58s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 61 ( 29 unt; 8 nHn; 61 RR)
% Number of literals : 121 ( 0 equ; 57 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
colinear(a,b,c),
file('GEO010-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
file('GEO010-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO010-2.p',unknown),
[] ).
cnf(6,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO010-2.p',unknown),
[] ).
cnf(7,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO010-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO010-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO010-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO010-2.p',unknown),
[] ).
cnf(21,axiom,
( ~ between(u,v,w)
| colinear(u,v,w) ),
file('GEO010-2.p',unknown),
[] ).
cnf(22,axiom,
( ~ between(u,v,w)
| colinear(w,u,v) ),
file('GEO010-2.p',unknown),
[] ).
cnf(23,axiom,
( ~ between(u,v,w)
| colinear(v,w,u) ),
file('GEO010-2.p',unknown),
[] ).
cnf(24,axiom,
( ~ colinear(u,v,w)
| between(w,u,v)
| between(v,w,u)
| between(u,v,w) ),
file('GEO010-2.p',unknown),
[] ).
cnf(29,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.0,5.0')] ).
cnf(30,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[29,6]),
[iquote('0:SpR:29.0,6.0')] ).
cnf(40,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(res,[status(thm),theory(equality)],[1,24]),
[iquote('0:Res:1.0,24.0')] ).
cnf(48,plain,
( between(b,c,a)
| between(a,b,c)
| colinear(c,a,b) ),
inference(res,[status(thm),theory(equality)],[40,21]),
[iquote('0:Res:40.0,21.0')] ).
cnf(49,plain,
( between(b,c,a)
| between(a,b,c)
| colinear(b,c,a) ),
inference(res,[status(thm),theory(equality)],[40,22]),
[iquote('0:Res:40.0,22.0')] ).
cnf(51,plain,
colinear(c,a,b),
inference(mrr,[status(thm)],[48,23,22]),
[iquote('0:MRR:48.0,48.1,23.0,22.0')] ).
cnf(52,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[2,51]),
[iquote('0:MRR:2.1,51.0')] ).
cnf(53,plain,
colinear(b,c,a),
inference(mrr,[status(thm)],[49,21,23]),
[iquote('0:MRR:49.0,49.1,21.0,23.0')] ).
cnf(54,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[52,53]),
[iquote('0:MRR:52.1,53.0')] ).
cnf(66,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.2,9.0')] ).
cnf(67,plain,
( ~ between(u,v,w)
| ~ between(x,y,w)
| colinear(v,inner_pasch(x,y,w,v,u),x) ),
inference(res,[status(thm),theory(equality)],[11,21]),
[iquote('0:Res:11.2,21.0')] ).
cnf(87,plain,
( ~ between(u,v,w)
| ~ between(x,u,w)
| equal(inner_pasch(x,u,w,v,u),u) ),
inference(res,[status(thm),theory(equality)],[10,9]),
[iquote('0:Res:10.2,9.0')] ).
cnf(518,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)],[66,10]),
[iquote('0:SpR:66.2,10.2')] ).
cnf(520,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[518]),
[iquote('0:Obv:518.1')] ).
cnf(525,plain,
( ~ between(a,u,b)
| between(b,c,a)
| between(a,b,c)
| between(u,a,c) ),
inference(res,[status(thm),theory(equality)],[40,520]),
[iquote('0:Res:40.0,520.0')] ).
cnf(565,plain,
( ~ between(u,v,w)
| ~ between(x,u,w)
| ~ between(u,v,w)
| ~ between(x,u,w)
| colinear(v,u,x) ),
inference(spr,[status(thm),theory(equality)],[87,67]),
[iquote('0:SpR:87.2,67.2')] ).
cnf(569,plain,
( ~ between(u,v,w)
| ~ between(x,u,w)
| colinear(v,u,x) ),
inference(obv,[status(thm),theory(equality)],[565]),
[iquote('0:Obv:565.1')] ).
cnf(606,plain,
( ~ between(u,v,w)
| colinear(w,v,u) ),
inference(res,[status(thm),theory(equality)],[30,569]),
[iquote('0:Res:30.0,569.0')] ).
cnf(621,plain,
( between(b,c,a)
| between(a,b,c)
| colinear(b,a,c) ),
inference(res,[status(thm),theory(equality)],[40,606]),
[iquote('0:Res:40.0,606.0')] ).
cnf(632,plain,
between(b,c,a),
inference(spt,[spt(split,[position(s1)])],[621]),
[iquote('1:Spt:621.0')] ).
cnf(633,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[632,606]),
[iquote('1:Res:632.0,606.0')] ).
cnf(636,plain,
( ~ between(c,u,a)
| between(u,c,b) ),
inference(res,[status(thm),theory(equality)],[632,520]),
[iquote('1:Res:632.0,520.0')] ).
cnf(640,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,a,c) ),
inference(mrr,[status(thm)],[54,633]),
[iquote('1:MRR:54.2,633.0')] ).
cnf(646,plain,
between(a,c,b),
inference(res,[status(thm),theory(equality)],[30,636]),
[iquote('1:Res:30.0,636.0')] ).
cnf(655,plain,
colinear(b,a,c),
inference(res,[status(thm),theory(equality)],[646,22]),
[iquote('1:Res:646.0,22.0')] ).
cnf(656,plain,
colinear(c,b,a),
inference(res,[status(thm),theory(equality)],[646,23]),
[iquote('1:Res:646.0,23.0')] ).
cnf(657,plain,
~ colinear(c,b,a),
inference(mrr,[status(thm)],[640,655]),
[iquote('1:MRR:640.1,655.0')] ).
cnf(658,plain,
$false,
inference(mrr,[status(thm)],[657,656]),
[iquote('1:MRR:657.0,656.0')] ).
cnf(659,plain,
~ between(b,c,a),
inference(spt,[spt(split,[position(sa)])],[658,632]),
[iquote('1:Spt:658.0,621.0,632.0')] ).
cnf(660,plain,
( between(a,b,c)
| colinear(b,a,c) ),
inference(spt,[spt(split,[position(s2)])],[621]),
[iquote('1:Spt:658.0,621.1,621.2')] ).
cnf(663,plain,
( ~ between(a,u,b)
| between(a,b,c)
| between(u,a,c) ),
inference(mrr,[status(thm)],[525,659]),
[iquote('1:MRR:525.1,659.0')] ).
cnf(665,plain,
between(a,b,c),
inference(spt,[spt(split,[position(s2s1)])],[660]),
[iquote('2:Spt:660.0')] ).
cnf(666,plain,
colinear(c,b,a),
inference(res,[status(thm),theory(equality)],[665,606]),
[iquote('2:Res:665.0,606.0')] ).
cnf(669,plain,
( ~ between(b,u,c)
| between(u,b,a) ),
inference(res,[status(thm),theory(equality)],[665,520]),
[iquote('2:Res:665.0,520.0')] ).
cnf(673,plain,
( ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[54,666]),
[iquote('2:MRR:54.0,666.0')] ).
cnf(679,plain,
between(c,b,a),
inference(res,[status(thm),theory(equality)],[30,669]),
[iquote('2:Res:30.0,669.0')] ).
cnf(688,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[679,22]),
[iquote('2:Res:679.0,22.0')] ).
cnf(689,plain,
colinear(b,a,c),
inference(res,[status(thm),theory(equality)],[679,23]),
[iquote('2:Res:679.0,23.0')] ).
cnf(690,plain,
~ colinear(b,a,c),
inference(mrr,[status(thm)],[673,688]),
[iquote('2:MRR:673.1,688.0')] ).
cnf(691,plain,
$false,
inference(mrr,[status(thm)],[690,689]),
[iquote('2:MRR:690.0,689.0')] ).
cnf(692,plain,
~ between(a,b,c),
inference(spt,[spt(split,[position(s2sa)])],[691,665]),
[iquote('2:Spt:691.0,660.0,665.0')] ).
cnf(693,plain,
colinear(b,a,c),
inference(spt,[spt(split,[position(s2s2)])],[660]),
[iquote('2:Spt:691.0,660.1')] ).
cnf(696,plain,
( ~ between(a,u,b)
| between(u,a,c) ),
inference(mrr,[status(thm)],[663,692]),
[iquote('2:MRR:663.1,692.0')] ).
cnf(698,plain,
( ~ colinear(c,b,a)
| ~ colinear(a,c,b) ),
inference(mrr,[status(thm)],[54,693]),
[iquote('2:MRR:54.1,693.0')] ).
cnf(707,plain,
between(b,a,c),
inference(res,[status(thm),theory(equality)],[30,696]),
[iquote('2:Res:30.0,696.0')] ).
cnf(716,plain,
colinear(c,b,a),
inference(res,[status(thm),theory(equality)],[707,22]),
[iquote('2:Res:707.0,22.0')] ).
cnf(717,plain,
colinear(a,c,b),
inference(res,[status(thm),theory(equality)],[707,23]),
[iquote('2:Res:707.0,23.0')] ).
cnf(718,plain,
~ colinear(a,c,b),
inference(mrr,[status(thm)],[698,716]),
[iquote('2:MRR:698.0,716.0')] ).
cnf(719,plain,
$false,
inference(mrr,[status(thm)],[718,717]),
[iquote('2:MRR:718.0,717.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GEO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 02:59:39 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.58
% 0.21/0.58 SPASS V 3.9
% 0.21/0.58 SPASS beiseite: Proof found.
% 0.21/0.58 % SZS status Theorem
% 0.21/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.58 SPASS derived 598 clauses, backtracked 14 clauses, performed 2 splits and kept 347 clauses.
% 0.21/0.58 SPASS allocated 63881 KBytes.
% 0.21/0.58 SPASS spent 0:00:00.21 on the problem.
% 0.21/0.58 0:00:00.04 for the input.
% 0.21/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.58 0:00:00.01 for inferences.
% 0.21/0.58 0:00:00.00 for the backtracking.
% 0.21/0.58 0:00:00.13 for the reduction.
% 0.21/0.58
% 0.21/0.58
% 0.21/0.58 Here is a proof with depth 9, length 61 :
% 0.21/0.58 % SZS output start Refutation
% See solution above
% 0.21/0.58 Formulae used in the proof : abc_colinear prove_colinear_in_all_orders identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2 colinearity1 colinearity2 colinearity3 colinearity4
% 0.21/0.58
%------------------------------------------------------------------------------