TSTP Solution File: GEO048-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO048-2 : 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 06:21:52 EDT 2022
% Result : Unsatisfiable 0.48s 0.69s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 12 unt; 0 nHn; 24 RR)
% Number of literals : 44 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 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('GEO048-2.p',unknown),
[] ).
cnf(2,axiom,
between(u1,v1,w__dfg),
file('GEO048-2.p',unknown),
[] ).
cnf(3,axiom,
between(u__dfg,x__dfg,u1),
file('GEO048-2.p',unknown),
[] ).
cnf(5,axiom,
~ between(v__dfg,inner_pasch(v1,inner_pasch(u__dfg,x__dfg,u1,v1,w__dfg),u__dfg,v__dfg,w__dfg),v1),
file('GEO048-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO048-2.p',unknown),
[] ).
cnf(9,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO048-2.p',unknown),
[] ).
cnf(10,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO048-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO048-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO048-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO048-2.p',unknown),
[] ).
cnf(25,plain,
( ~ between(w__dfg,v__dfg,u__dfg)
| ~ between(v1,inner_pasch(u__dfg,x__dfg,u1,v1,w__dfg),u__dfg) ),
inference(res,[status(thm),theory(equality)],[14,5]),
[iquote('0:Res:14.2,5.0')] ).
cnf(38,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(39,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[38,9]),
[iquote('0:SpR:38.0,9.0')] ).
cnf(52,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(54,plain,
( ~ between(w__dfg,v1,u1)
| ~ between(u__dfg,x__dfg,u1)
| ~ between(w__dfg,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[14,25]),
[iquote('0:Res:14.2,25.1')] ).
cnf(55,plain,
( ~ between(w__dfg,v1,u1)
| ~ between(w__dfg,v__dfg,u__dfg) ),
inference(mrr,[status(thm)],[54,3]),
[iquote('0:MRR:54.1,3.0')] ).
cnf(462,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)],[52,13]),
[iquote('0:SpR:52.2,13.2')] ).
cnf(464,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[462]),
[iquote('0:Obv:462.1')] ).
cnf(530,plain,
( ~ between(v1,u,w__dfg)
| between(u,v1,u1) ),
inference(res,[status(thm),theory(equality)],[2,464]),
[iquote('0:Res:2.0,464.0')] ).
cnf(531,plain,
( ~ between(v__dfg,u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,464]),
[iquote('0:Res:1.0,464.0')] ).
cnf(550,plain,
between(w__dfg,v1,u1),
inference(res,[status(thm),theory(equality)],[39,530]),
[iquote('0:Res:39.0,530.0')] ).
cnf(553,plain,
~ between(w__dfg,v__dfg,u__dfg),
inference(mrr,[status(thm)],[55,550]),
[iquote('0:MRR:55.0,550.0')] ).
cnf(590,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[39,531]),
[iquote('0:Res:39.0,531.0')] ).
cnf(593,plain,
$false,
inference(mrr,[status(thm)],[590,553]),
[iquote('0:MRR:590.0,553.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO048-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 18:09:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.48/0.69
% 0.48/0.69 SPASS V 3.9
% 0.48/0.69 SPASS beiseite: Proof found.
% 0.48/0.69 % SZS status Theorem
% 0.48/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.69 SPASS derived 497 clauses, backtracked 0 clauses, performed 2 splits and kept 303 clauses.
% 0.48/0.69 SPASS allocated 64029 KBytes.
% 0.48/0.69 SPASS spent 0:00:00.33 on the problem.
% 0.48/0.69 0:00:00.04 for the input.
% 0.48/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.69 0:00:00.02 for inferences.
% 0.48/0.69 0:00:00.00 for the backtracking.
% 0.48/0.69 0:00:00.25 for the reduction.
% 0.48/0.69
% 0.48/0.69
% 0.48/0.69 Here is a proof with depth 4, length 24 :
% 0.48/0.69 % SZS output start Refutation
% See solution above
% 0.48/0.69 Formulae used in the proof : v_between_u_and_w v1_between_u1_and_w x_between_u_and_u1 prove_conclusion2 identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.48/0.69
%------------------------------------------------------------------------------