TSTP Solution File: GEO058-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 22 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 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,
equal(reflection(u__dfg,v__dfg),v__dfg),
file('GEO058-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(u__dfg,v__dfg),
file('GEO058-2.p',unknown),
[] ).
cnf(3,axiom,
equidistant(u,v,v,u),
file('GEO058-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO058-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO058-2.p',unknown),
[] ).
cnf(7,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO058-2.p',unknown),
[] ).
cnf(21,axiom,
equal(extension(u,v,u,v),reflection(u,v)),
file('GEO058-2.p',unknown),
[] ).
cnf(26,plain,
~ equidistant(u__dfg,v__dfg,u,u),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
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(42,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.0,5.0')] ).
cnf(43,plain,
equidistant(v__dfg,v__dfg,u__dfg,v__dfg),
inference(spr,[status(thm),theory(equality)],[1,41]),
[iquote('0:SpR:1.0,41.0')] ).
cnf(45,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(48,plain,
( ~ equidistant(v__dfg,v__dfg,u,v)
| equidistant(u,v,u__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[43,4]),
[iquote('0:Res:43.0,4.0')] ).
cnf(56,plain,
equidistant(u,u,v,v),
inference(spr,[status(thm),theory(equality)],[42,7]),
[iquote('0:SpR:42.0,7.0')] ).
cnf(62,plain,
equidistant(u,u,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[56,48]),
[iquote('0:Res:56.0,48.0')] ).
cnf(77,plain,
equidistant(u__dfg,v__dfg,u,u),
inference(res,[status(thm),theory(equality)],[62,45]),
[iquote('0:Res:62.0,45.0')] ).
cnf(79,plain,
$false,
inference(mrr,[status(thm)],[77,26]),
[iquote('0:MRR:77.0,26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 15:01:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 57 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.18/0.41 SPASS allocated 63173 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 5, length 17 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : v_equals_reflection prove_u_equals_v reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction2 reflection
% 0.18/0.41
%------------------------------------------------------------------------------