TSTP Solution File: GEO056-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO056-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 06:21:57 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 9 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(v__dfg,u__dfg),
file('GEO056-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(reflection(u__dfg,v__dfg),v__dfg),
file('GEO056-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO056-2.p',unknown),
[] ).
cnf(7,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO056-2.p',unknown),
[] ).
cnf(21,axiom,
equal(extension(u,v,u,v),reflection(u,v)),
file('GEO056-2.p',unknown),
[] ).
cnf(22,plain,
~ equal(reflection(u__dfg,u__dfg),u__dfg),
inference(rew,[status(thm),theory(equality)],[1,2]),
[iquote('0:Rew:1.0,2.0')] ).
cnf(34,plain,
~ equidistant(u__dfg,reflection(u__dfg,u__dfg),u,u),
inference(res,[status(thm),theory(equality)],[5,22]),
[iquote('0:Res:5.1,22.0')] ).
cnf(41,plain,
equidistant(u,reflection(v,u),v,u),
inference(spr,[status(thm),theory(equality)],[21,7]),
[iquote('0:SpR:21.0,7.0')] ).
cnf(43,plain,
$false,
inference(unc,[status(thm)],[41,34]),
[iquote('0:UnC:41.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO056-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n003.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 16:54:27 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.19/0.42 SPASS allocated 63135 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 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 1, length 9 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : u_equals_v prove_v_equals_reflection identity_for_equidistance segment_construction2 reflection
% 0.19/0.42
%------------------------------------------------------------------------------