TSTP Solution File: GEO002-4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 06:21:26 EDT 2022

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   23 (   8 unt;   0 nHn;  23 RR)
%            Number of literals    :   50 (   0 equ;  34 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    :   10 (  10 usr;   8 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,u,w)
    | between(x,u,v) ),
    file('GEO002-4.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ equidistant(u,v,w,w)
    | equalish(u,v) ),
    file('GEO002-4.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,v)
    | between(x,outer_pasch(y,x,u,w,v),u) ),
    file('GEO002-4.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,v)
    | between(w,y,outer_pasch(y,x,u,w,v)) ),
    file('GEO002-4.p',unknown),
    [] ).

cnf(5,axiom,
    between(u,v,extension(u,v,w,x)),
    file('GEO002-4.p',unknown),
    [] ).

cnf(6,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO002-4.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equalish(u,v)
    | ~ between(w,x,u)
    | between(w,x,v) ),
    file('GEO002-4.p',unknown),
    [] ).

cnf(8,axiom,
    ~ between(a,a,b),
    file('GEO002-4.p',unknown),
    [] ).

cnf(9,plain,
    ( ~ between(a,a,u)
    | ~ between(a,b,u) ),
    inference(res,[status(thm),theory(equality)],[1,8]),
    [iquote('0:Res:1.2,8.0')] ).

cnf(12,plain,
    equalish(u,extension(v,u,w,w)),
    inference(res,[status(thm),theory(equality)],[6,2]),
    [iquote('0:Res:6.0,2.0')] ).

cnf(19,plain,
    ( ~ between(u,v,extension(v,w,x,y))
    | between(u,v,w) ),
    inference(res,[status(thm),theory(equality)],[5,1]),
    [iquote('0:Res:5.0,1.0')] ).

cnf(21,plain,
    between(u,u,u),
    inference(res,[status(thm),theory(equality)],[5,19]),
    [iquote('0:Res:5.0,19.0')] ).

cnf(26,plain,
    ( ~ equalish(u,v)
    | between(u,u,v) ),
    inference(res,[status(thm),theory(equality)],[21,7]),
    [iquote('0:Res:21.0,7.1')] ).

cnf(27,plain,
    ( ~ between(u,v,w)
    | ~ between(x,y,v)
    | ~ between(z,x,u)
    | between(z,x,outer_pasch(y,x,u,w,v)) ),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.2,1.0')] ).

cnf(33,plain,
    ( ~ equalish(u,v)
    | ~ between(w,u,v)
    | between(w,u,u) ),
    inference(res,[status(thm),theory(equality)],[26,1]),
    [iquote('0:Res:26.1,1.0')] ).

cnf(38,plain,
    ( ~ between(u,v,a)
    | ~ between(w,a,v)
    | ~ between(a,b,outer_pasch(a,w,u,a,v)) ),
    inference(res,[status(thm),theory(equality)],[4,9]),
    [iquote('0:Res:4.2,9.0')] ).

cnf(60,plain,
    ( ~ equalish(u,extension(v,u,w,x))
    | between(v,u,u) ),
    inference(res,[status(thm),theory(equality)],[5,33]),
    [iquote('0:Res:5.0,33.1')] ).

cnf(70,plain,
    between(u,v,v),
    inference(res,[status(thm),theory(equality)],[12,60]),
    [iquote('0:Res:12.0,60.0')] ).

cnf(136,plain,
    ( ~ between(u,v,a)
    | ~ between(b,a,v)
    | ~ between(a,b,u)
    | ~ between(u,v,a)
    | ~ between(b,a,v) ),
    inference(res,[status(thm),theory(equality)],[27,38]),
    [iquote('0:Res:27.3,38.2')] ).

cnf(137,plain,
    ( ~ between(a,b,u)
    | ~ between(u,v,a)
    | ~ between(b,a,v) ),
    inference(obv,[status(thm),theory(equality)],[136]),
    [iquote('0:Obv:136.1')] ).

cnf(385,plain,
    ( ~ between(b,u,a)
    | ~ between(b,a,u) ),
    inference(res,[status(thm),theory(equality)],[70,137]),
    [iquote('0:Res:70.0,137.0')] ).

cnf(393,plain,
    ~ between(b,a,a),
    inference(res,[status(thm),theory(equality)],[70,385]),
    [iquote('0:Res:70.0,385.0')] ).

cnf(402,plain,
    $false,
    inference(mrr,[status(thm)],[393,70]),
    [iquote('0:MRR:393.0,70.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO002-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n012.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 09:07:08 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  
% 0.20/0.55  SPASS V 3.9 
% 0.20/0.55  SPASS beiseite: Proof found.
% 0.20/0.55  % SZS status Theorem
% 0.20/0.55  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.55  SPASS derived 386 clauses, backtracked 0 clauses, performed 0 splits and kept 279 clauses.
% 0.20/0.55  SPASS allocated 63590 KBytes.
% 0.20/0.55  SPASS spent	0:00:00.19 on the problem.
% 0.20/0.55  		0:00:00.04 for the input.
% 0.20/0.55  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55  		0:00:00.01 for inferences.
% 0.20/0.55  		0:00:00.00 for the backtracking.
% 0.20/0.55  		0:00:00.12 for the reduction.
% 0.20/0.55  
% 0.20/0.55  
% 0.20/0.55  Here is a proof with depth 8, length 23 :
% 0.20/0.55  % SZS output start Refutation
% See solution above
% 0.20/0.55  Formulae used in the proof : transitivity_for_betweeness identity_for_equidistance outer_pasch1 outer_pasch2 segment_construction1 segment_construction2 between_substitution3 prove_a_between_a_and_b
% 0.20/0.55  
%------------------------------------------------------------------------------