TSTP Solution File: GEO025-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO025-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 06:21:40 EDT 2022
% Result : Unsatisfiable 1.95s 2.15s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 46 ( 29 unt; 1 nHn; 46 RR)
% Number of literals : 87 ( 0 equ; 43 neg)
% Maximal clause size : 8 ( 1 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; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equidistant(u__dfg,v__dfg,u1,v1),
file('GEO025-2.p',unknown),
[] ).
cnf(2,axiom,
equidistant(v__dfg,w__dfg,v1,w1),
file('GEO025-2.p',unknown),
[] ).
cnf(3,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO025-2.p',unknown),
[] ).
cnf(4,axiom,
between(u1,v1,w1),
file('GEO025-2.p',unknown),
[] ).
cnf(5,axiom,
~ equidistant(u__dfg,w__dfg,u1,w1),
file('GEO025-2.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,v,v,u),
file('GEO025-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO025-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO025-2.p',unknown),
[] ).
cnf(9,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO025-2.p',unknown),
[] ).
cnf(10,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO025-2.p',unknown),
[] ).
cnf(11,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('GEO025-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO025-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO025-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO025-2.p',unknown),
[] ).
cnf(25,plain,
( ~ between(u,v,u1)
| ~ between(w,x,u__dfg)
| ~ equidistant(w,x,u,v)
| ~ equidistant(x,w__dfg,v,w1)
| ~ equidistant(w,w__dfg,u,w1)
| ~ equidistant(x,u__dfg,v,u1)
| equal(w,x) ),
inference(res,[status(thm),theory(equality)],[11,5]),
[iquote('0:Res:11.7,5.0')] ).
cnf(27,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(28,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[27,9]),
[iquote('0:SpR:27.0,9.0')] ).
cnf(29,plain,
equidistant(u,u,v,v),
inference(spr,[status(thm),theory(equality)],[27,10]),
[iquote('0:SpR:27.0,10.0')] ).
cnf(31,plain,
( ~ equidistant(v__dfg,w__dfg,u,v)
| equidistant(u,v,v1,w1) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(33,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(41,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.2,12.0')] ).
cnf(56,plain,
equidistant(v1,w1,w__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[2,33]),
[iquote('0:Res:2.0,33.0')] ).
cnf(57,plain,
equidistant(u1,v1,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.0')] ).
cnf(59,plain,
equidistant(u,v,extension(w,x,u,v),x),
inference(res,[status(thm),theory(equality)],[10,33]),
[iquote('0:Res:10.0,33.0')] ).
cnf(65,plain,
equidistant(w__dfg,v__dfg,w1,v1),
inference(res,[status(thm),theory(equality)],[56,33]),
[iquote('0:Res:56.0,33.0')] ).
cnf(68,plain,
equidistant(v__dfg,u__dfg,v1,u1),
inference(res,[status(thm),theory(equality)],[57,33]),
[iquote('0:Res:57.0,33.0')] ).
cnf(111,plain,
equidistant(extension(u,v,v__dfg,w__dfg),v,v1,w1),
inference(res,[status(thm),theory(equality)],[59,31]),
[iquote('0:Res:59.0,31.0')] ).
cnf(117,plain,
equidistant(v1,w1,u,extension(v,u,v__dfg,w__dfg)),
inference(res,[status(thm),theory(equality)],[111,33]),
[iquote('0:Res:111.0,33.0')] ).
cnf(129,plain,
equidistant(u,extension(v,u,v__dfg,w__dfg),w1,v1),
inference(res,[status(thm),theory(equality)],[117,33]),
[iquote('0:Res:117.0,33.0')] ).
cnf(153,plain,
equidistant(w1,v1,extension(u,v,v__dfg,w__dfg),v),
inference(res,[status(thm),theory(equality)],[129,33]),
[iquote('0:Res:129.0,33.0')] ).
cnf(253,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)],[41,13]),
[iquote('0:SpR:41.2,13.2')] ).
cnf(255,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[253]),
[iquote('0:Obv:253.1')] ).
cnf(468,plain,
( ~ between(w1,v1,u1)
| ~ between(w__dfg,v__dfg,u__dfg)
| ~ equidistant(v__dfg,w__dfg,v1,w1)
| ~ equidistant(w__dfg,w__dfg,w1,w1)
| ~ equidistant(v__dfg,u__dfg,v1,u1)
| equal(w__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[65,25]),
[iquote('0:Res:65.0,25.2')] ).
cnf(508,plain,
( ~ between(w1,v1,u1)
| ~ between(w__dfg,v__dfg,u__dfg)
| equal(w__dfg,v__dfg) ),
inference(mrr,[status(thm)],[468,2,29,68]),
[iquote('0:MRR:468.2,468.3,468.4,2.0,29.0,68.0')] ).
cnf(834,plain,
( ~ between(v1,u,w1)
| between(u,v1,u1) ),
inference(res,[status(thm),theory(equality)],[4,255]),
[iquote('0:Res:4.0,255.0')] ).
cnf(835,plain,
( ~ between(v__dfg,u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[3,255]),
[iquote('0:Res:3.0,255.0')] ).
cnf(845,plain,
between(w1,v1,u1),
inference(res,[status(thm),theory(equality)],[28,834]),
[iquote('0:Res:28.0,834.0')] ).
cnf(849,plain,
( ~ between(w__dfg,v__dfg,u__dfg)
| equal(w__dfg,v__dfg) ),
inference(mrr,[status(thm)],[508,845]),
[iquote('0:MRR:508.0,845.0')] ).
cnf(865,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[28,835]),
[iquote('0:Res:28.0,835.0')] ).
cnf(869,plain,
equal(w__dfg,v__dfg),
inference(mrr,[status(thm)],[849,865]),
[iquote('0:MRR:849.0,865.0')] ).
cnf(872,plain,
~ equidistant(u__dfg,v__dfg,u1,w1),
inference(rew,[status(thm),theory(equality)],[869,5]),
[iquote('0:Rew:869.0,5.0')] ).
cnf(883,plain,
equidistant(w1,v1,extension(u,v,v__dfg,v__dfg),v),
inference(rew,[status(thm),theory(equality)],[869,153]),
[iquote('0:Rew:869.0,153.0')] ).
cnf(1181,plain,
equidistant(w1,v1,u,u),
inference(rew,[status(thm),theory(equality)],[27,883]),
[iquote('0:Rew:27.0,883.0')] ).
cnf(1571,plain,
equal(w1,v1),
inference(res,[status(thm),theory(equality)],[1181,8]),
[iquote('0:Res:1181.0,8.0')] ).
cnf(1584,plain,
~ equidistant(u__dfg,v__dfg,u1,v1),
inference(rew,[status(thm),theory(equality)],[1571,872]),
[iquote('0:Rew:1571.0,872.0')] ).
cnf(1726,plain,
$false,
inference(mrr,[status(thm)],[1584,1]),
[iquote('0:MRR:1584.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO025-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 14:06:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.95/2.15
% 1.95/2.15 SPASS V 3.9
% 1.95/2.15 SPASS beiseite: Proof found.
% 1.95/2.15 % SZS status Theorem
% 1.95/2.15 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/2.15 SPASS derived 1286 clauses, backtracked 0 clauses, performed 0 splits and kept 898 clauses.
% 1.95/2.15 SPASS allocated 65869 KBytes.
% 1.95/2.15 SPASS spent 0:00:01.77 on the problem.
% 1.95/2.15 0:00:00.04 for the input.
% 1.95/2.15 0:00:00.00 for the FLOTTER CNF translation.
% 1.95/2.15 0:00:00.04 for inferences.
% 1.95/2.15 0:00:00.00 for the backtracking.
% 1.95/2.15 0:00:01.66 for the reduction.
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Here is a proof with depth 7, length 46 :
% 1.95/2.15 % SZS output start Refutation
% See solution above
% 1.95/2.15 Formulae used in the proof : u_to_v_equals_u1_to_v1 v_to_w_equals_v1_to_w1 v_between_u_and_w v1_between_u1_and_w1 prove_equal_sums reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction1 segment_construction2 outer_five_segment identity_for_betweeness inner_pasch1 inner_pasch2
% 1.95/2.15
%------------------------------------------------------------------------------