TSTP Solution File: GEO043-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO043-2 : 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 06:21:50 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 21 RR)
% Number of literals : 38 ( 0 equ; 18 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO043-2.p',unknown),
[] ).
cnf(2,axiom,
between(u__dfg,w__dfg,x__dfg),
file('GEO043-2.p',unknown),
[] ).
cnf(3,axiom,
~ between(v__dfg,w__dfg,x__dfg),
file('GEO043-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO043-2.p',unknown),
[] ).
cnf(7,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO043-2.p',unknown),
[] ).
cnf(8,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO043-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO043-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO043-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO043-2.p',unknown),
[] ).
cnf(29,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.0,6.0')] ).
cnf(30,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[29,7]),
[iquote('0:SpR:29.0,7.0')] ).
cnf(53,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[12,10]),
[iquote('0:Res:12.2,10.0')] ).
cnf(543,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)],[53,11]),
[iquote('0:SpR:53.2,11.2')] ).
cnf(545,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[543]),
[iquote('0:Obv:543.1')] ).
cnf(615,plain,
( ~ between(w__dfg,u,x__dfg)
| between(u,w__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[2,545]),
[iquote('0:Res:2.0,545.0')] ).
cnf(616,plain,
( ~ between(v__dfg,u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,545]),
[iquote('0:Res:1.0,545.0')] ).
cnf(624,plain,
between(x__dfg,w__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[30,615]),
[iquote('0:Res:30.0,615.0')] ).
cnf(634,plain,
( ~ between(w__dfg,u,u__dfg)
| between(u,w__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[624,545]),
[iquote('0:Res:624.0,545.0')] ).
cnf(635,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[30,616]),
[iquote('0:Res:30.0,616.0')] ).
cnf(642,plain,
between(v__dfg,w__dfg,x__dfg),
inference(res,[status(thm),theory(equality)],[635,634]),
[iquote('0:Res:635.0,634.0')] ).
cnf(643,plain,
$false,
inference(mrr,[status(thm)],[642,3]),
[iquote('0:MRR:642.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO043-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % 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 16:16:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.54
% 0.19/0.54 SPASS V 3.9
% 0.19/0.54 SPASS beiseite: Proof found.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.54 SPASS derived 537 clauses, backtracked 0 clauses, performed 1 splits and kept 261 clauses.
% 0.19/0.54 SPASS allocated 63817 KBytes.
% 0.19/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.19/0.54 0:00:00.04 for the input.
% 0.19/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.54 0:00:00.01 for inferences.
% 0.19/0.54 0:00:00.00 for the backtracking.
% 0.19/0.54 0:00:00.12 for the reduction.
% 0.19/0.54
% 0.19/0.54
% 0.19/0.54 Here is a proof with depth 6, length 21 :
% 0.19/0.54 % SZS output start Refutation
% See solution above
% 0.19/0.54 Formulae used in the proof : v_between_u_and_w w_between_u_and_x prove_w_between_v_and_x identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.19/0.54
%------------------------------------------------------------------------------