%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO042-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 06:21:49 EDT 2022
% Result : Unsatisfiable 0.48s 0.65s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 19 RR)
% Number of literals : 35 ( 0 equ; 17 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,x__dfg),
file('GEO042-2.p',unknown),
[] ).
cnf(2,axiom,
between(v__dfg,w__dfg,x__dfg),
file('GEO042-2.p',unknown),
[] ).
cnf(3,axiom,
~ between(u__dfg,v__dfg,w__dfg),
file('GEO042-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO042-2.p',unknown),
[] ).
cnf(7,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO042-2.p',unknown),
[] ).
cnf(8,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO042-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO042-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO042-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO042-2.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(616,plain,
( ~ between(v__dfg,u,x__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,545]),
[iquote('0:Res:1.0,545.0')] ).
cnf(635,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[2,616]),
[iquote('0:Res:2.0,616.0')] ).
cnf(639,plain,
( ~ between(v__dfg,u,u__dfg)
| between(u,v__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[635,545]),
[iquote('0:Res:635.0,545.0')] ).
cnf(680,plain,
between(u__dfg,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[30,639]),
[iquote('0:Res:30.0,639.0')] ).
cnf(683,plain,
$false,
inference(mrr,[status(thm)],[680,3]),
[iquote('0:MRR:680.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO042-2 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 20:00:49 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.48/0.65
% 0.48/0.65 SPASS V 3.9
% 0.48/0.65 SPASS beiseite: Proof found.
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.65 SPASS derived 575 clauses, backtracked 0 clauses, performed 1 splits and kept 297 clauses.
% 0.48/0.65 SPASS allocated 63965 KBytes.
% 0.48/0.65 SPASS spent 0:00:00.28 on the problem.
% 0.48/0.65 0:00:00.04 for the input.
% 0.48/0.65 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.65 0:00:00.01 for inferences.
% 0.48/0.65 0:00:00.00 for the backtracking.
% 0.48/0.65 0:00:00.20 for the reduction.
% 0.48/0.65
% 0.48/0.65
% 0.48/0.65 Here is a proof with depth 6, length 19 :
% 0.48/0.65 % SZS output start Refutation
% See solution above
% 0.48/0.65 Formulae used in the proof : v_between_u_and_x w_between_v_and_x prove_v_between_u_and_w identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.48/0.65
%------------------------------------------------------------------------------