TSTP Solution File: GEO002-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO002-2 : 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 06:21:25 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 7 unt; 0 nHn; 15 RR)
% Number of literals : 30 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ between(a,a,b),
file('GEO002-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO002-2.p',unknown),
[] ).
cnf(5,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO002-2.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO002-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO002-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO002-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO002-2.p',unknown),
[] ).
cnf(30,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.0,4.0')] ).
cnf(33,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[30,5]),
[iquote('0:SpR:30.0,5.0')] ).
cnf(43,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.2,8.0')] ).
cnf(469,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)],[43,9]),
[iquote('0:SpR:43.2,9.2')] ).
cnf(471,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[469]),
[iquote('0:Obv:469.1')] ).
cnf(503,plain,
( ~ between(u,v,u)
| between(v,u,w) ),
inference(res,[status(thm),theory(equality)],[33,471]),
[iquote('0:Res:33.0,471.0')] ).
cnf(509,plain,
between(u,u,v),
inference(res,[status(thm),theory(equality)],[33,503]),
[iquote('0:Res:33.0,503.0')] ).
cnf(512,plain,
$false,
inference(unc,[status(thm)],[509,1]),
[iquote('0:UnC:509.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO002-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 05:56:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.52
% 0.18/0.52 SPASS V 3.9
% 0.18/0.52 SPASS beiseite: Proof found.
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52 SPASS derived 423 clauses, backtracked 0 clauses, performed 1 splits and kept 235 clauses.
% 0.18/0.52 SPASS allocated 63733 KBytes.
% 0.18/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.18/0.52 0:00:00.04 for the input.
% 0.18/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.52 0:00:00.01 for inferences.
% 0.18/0.52 0:00:00.00 for the backtracking.
% 0.18/0.52 0:00:00.10 for the reduction.
% 0.18/0.52
% 0.18/0.52
% 0.18/0.52 Here is a proof with depth 4, length 15 :
% 0.18/0.52 % SZS output start Refutation
% See solution above
% 0.18/0.52 Formulae used in the proof : prove_a_between_a_and_b identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.18/0.52
%------------------------------------------------------------------------------