TSTP Solution File: GEO018-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO018-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 06:21:37 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equidistant(u__dfg,v__dfg,w__dfg,x__dfg),
file('GEO018-2.p',unknown),
[] ).
cnf(2,axiom,
~ equidistant(v__dfg,u__dfg,x__dfg,w__dfg),
file('GEO018-2.p',unknown),
[] ).
cnf(3,axiom,
equidistant(u,v,v,u),
file('GEO018-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO018-2.p',unknown),
[] ).
cnf(21,plain,
( ~ equidistant(u,v,x__dfg,w__dfg)
| ~ equidistant(u,v,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.2,2.0')] ).
cnf(30,plain,
~ equidistant(w__dfg,x__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[3,21]),
[iquote('0:Res:3.0,21.0')] ).
cnf(33,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[3,4]),
[iquote('0:Res:3.0,4.0')] ).
cnf(45,plain,
equidistant(w__dfg,x__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.0')] ).
cnf(51,plain,
$false,
inference(mrr,[status(thm)],[45,30]),
[iquote('0:MRR:45.0,30.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO018-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 13:41:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 30 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.20/0.41 SPASS allocated 63141 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 2, length 9 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : u_to_v_equals_w_to_x prove_symmetry reflexivity_for_equidistance transitivity_for_equidistance
% 0.20/0.41
%------------------------------------------------------------------------------