TSTP Solution File: GEO059-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO059-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 06:21:58 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 12 unt; 0 nHn; 16 RR)
% Number of literals : 21 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equidistant(v__dfg,u__dfg,v__dfg,reflection(reflection(u__dfg,v__dfg),v__dfg)),
file('GEO059-2.p',unknown),
[] ).
cnf(2,axiom,
equidistant(u,v,v,u),
file('GEO059-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO059-2.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO059-2.p',unknown),
[] ).
cnf(20,axiom,
equal(extension(u,v,u,v),reflection(u,v)),
file('GEO059-2.p',unknown),
[] ).
cnf(21,plain,
( ~ equidistant(u,v,v__dfg,u__dfg)
| ~ equidistant(u,v,v__dfg,reflection(reflection(u__dfg,v__dfg),v__dfg)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.2,1.0')] ).
cnf(26,plain,
equidistant(u,reflection(v,u),v,u),
inference(spr,[status(thm),theory(equality)],[20,6]),
[iquote('0:SpR:20.0,6.0')] ).
cnf(42,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.0')] ).
cnf(46,plain,
equidistant(u,v,u,v),
inference(res,[status(thm),theory(equality)],[2,42]),
[iquote('0:Res:2.0,42.0')] ).
cnf(48,plain,
equidistant(u,v,reflection(u,v),v),
inference(res,[status(thm),theory(equality)],[26,42]),
[iquote('0:Res:26.0,42.0')] ).
cnf(52,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ),
inference(res,[status(thm),theory(equality)],[46,3]),
[iquote('0:Res:46.0,3.0')] ).
cnf(55,plain,
equidistant(reflection(u,v),v,v,u),
inference(res,[status(thm),theory(equality)],[48,42]),
[iquote('0:Res:48.0,42.0')] ).
cnf(59,plain,
equidistant(u,v,u,reflection(v,u)),
inference(res,[status(thm),theory(equality)],[55,42]),
[iquote('0:Res:55.0,42.0')] ).
cnf(66,plain,
~ equidistant(v__dfg,reflection(u__dfg,v__dfg),v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[59,21]),
[iquote('0:Res:59.0,21.1')] ).
cnf(97,plain,
equidistant(u,reflection(v,u),u,v),
inference(res,[status(thm),theory(equality)],[59,52]),
[iquote('0:Res:59.0,52.0')] ).
cnf(104,plain,
$false,
inference(unc,[status(thm)],[97,66]),
[iquote('0:UnC:97.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO059-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.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 : Fri Jun 17 23:53:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 79 clauses, backtracked 0 clauses, performed 0 splits and kept 64 clauses.
% 0.19/0.42 SPASS allocated 63188 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 5, length 16 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : prove_congruence reflexivity_for_equidistance transitivity_for_equidistance segment_construction2 reflection
% 0.19/0.42
%------------------------------------------------------------------------------