TSTP Solution File: GEO030-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO030-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 06:21:42 EDT 2022

% Result   : Unsatisfiable 1.31s 1.48s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   23 (  12 unt;   3 nHn;  23 RR)
%            Number of literals    :   53 (   0 equ;  30 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :   13 (  13 usr;  12 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    between(u__dfg,v__dfg,w__dfg),
    file('GEO030-2.p',unknown),
    [] ).

cnf(2,axiom,
    equidistant(u__dfg,w__dfg,u__dfg,w1),
    file('GEO030-2.p',unknown),
    [] ).

cnf(3,axiom,
    equidistant(v__dfg,w__dfg,v__dfg,w1),
    file('GEO030-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(v__dfg,u__dfg),
    file('GEO030-2.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(w1,w__dfg),
    file('GEO030-2.p',unknown),
    [] ).

cnf(6,axiom,
    equidistant(u,v,v,u),
    file('GEO030-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equidistant(u,v,w,x)
    | ~ equidistant(u,v,y,z)
    | equidistant(y,z,w,x) ),
    file('GEO030-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO030-2.p',unknown),
    [] ).

cnf(10,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO030-2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,z)
    | ~ equidistant(y,x1,v,x2)
    | ~ equidistant(x,x1,u,x2)
    | ~ equidistant(y,z,v,w)
    | ~ equidistant(x,y,u,v)
    | equal(x,y)
    | equidistant(z,x1,w,x2) ),
    file('GEO030-2.p',unknown),
    [] ).

cnf(35,plain,
    ~ equidistant(w__dfg,w1,u,u),
    inference(res,[status(thm),theory(equality)],[8,5]),
    [iquote('0:Res:8.1,5.0')] ).

cnf(39,plain,
    equal(extension(u,v,w,w),v),
    inference(res,[status(thm),theory(equality)],[10,8]),
    [iquote('0:Res:10.0,8.0')] ).

cnf(41,plain,
    equidistant(u,u,v,v),
    inference(spr,[status(thm),theory(equality)],[39,10]),
    [iquote('0:SpR:39.0,10.0')] ).

cnf(46,plain,
    ( ~ equidistant(u,v,w,x)
    | equidistant(w,x,v,u) ),
    inference(res,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Res:6.0,7.0')] ).

cnf(49,plain,
    ( ~ equidistant(u,u,v,w)
    | equidistant(v,w,x,x) ),
    inference(res,[status(thm),theory(equality)],[41,7]),
    [iquote('0:Res:41.0,7.0')] ).

cnf(70,plain,
    equidistant(u,v,u,v),
    inference(res,[status(thm),theory(equality)],[6,46]),
    [iquote('0:Res:6.0,46.0')] ).

cnf(185,plain,
    ( ~ between(u,v__dfg,v)
    | ~ between(w,v__dfg,x)
    | ~ equidistant(w,w__dfg,u,w1)
    | ~ equidistant(v__dfg,x,v__dfg,v)
    | ~ equidistant(w,v__dfg,u,v__dfg)
    | equal(w,v__dfg)
    | equidistant(x,w__dfg,v,w1) ),
    inference(res,[status(thm),theory(equality)],[3,11]),
    [iquote('0:Res:3.0,11.2')] ).

cnf(667,plain,
    ( ~ between(u__dfg,v__dfg,u)
    | ~ between(u__dfg,v__dfg,v)
    | ~ equidistant(v__dfg,v,v__dfg,u)
    | ~ equidistant(u__dfg,v__dfg,u__dfg,v__dfg)
    | equal(v__dfg,u__dfg)
    | equidistant(v,w__dfg,u,w1) ),
    inference(res,[status(thm),theory(equality)],[2,185]),
    [iquote('0:Res:2.0,185.2')] ).

cnf(684,plain,
    ( ~ between(u__dfg,v__dfg,u)
    | ~ between(u__dfg,v__dfg,v)
    | ~ equidistant(v__dfg,v,v__dfg,u)
    | equidistant(v,w__dfg,u,w1) ),
    inference(mrr,[status(thm)],[667,70,4]),
    [iquote('0:MRR:667.3,667.4,70.0,4.0')] ).

cnf(1670,plain,
    ( ~ between(u__dfg,v__dfg,u)
    | ~ between(u__dfg,v__dfg,u)
    | equidistant(u,w__dfg,u,w1) ),
    inference(res,[status(thm),theory(equality)],[70,684]),
    [iquote('0:Res:70.0,684.2')] ).

cnf(1681,plain,
    ( ~ between(u__dfg,v__dfg,u)
    | equidistant(u,w__dfg,u,w1) ),
    inference(obv,[status(thm),theory(equality)],[1670]),
    [iquote('0:Obv:1670.0')] ).

cnf(1773,plain,
    ( ~ between(u__dfg,v__dfg,w__dfg)
    | equidistant(w__dfg,w1,u,u) ),
    inference(res,[status(thm),theory(equality)],[1681,49]),
    [iquote('0:Res:1681.1,49.0')] ).

cnf(1774,plain,
    $false,
    inference(mrr,[status(thm)],[1773,1,35]),
    [iquote('0:MRR:1773.0,1773.1,1.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : GEO030-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09  % Command  : run_spass %d %s
% 0.09/0.27  % Computer : n032.cluster.edu
% 0.09/0.27  % Model    : x86_64 x86_64
% 0.09/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27  % Memory   : 8042.1875MB
% 0.09/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Fri Jun 17 16:36:31 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 1.31/1.48  
% 1.31/1.48  SPASS V 3.9 
% 1.31/1.48  SPASS beiseite: Proof found.
% 1.31/1.48  % SZS status Theorem
% 1.31/1.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.31/1.48  SPASS derived 1679 clauses, backtracked 0 clauses, performed 0 splits and kept 1090 clauses.
% 1.31/1.48  SPASS allocated 65812 KBytes.
% 1.31/1.48  SPASS spent	0:00:01.17 on the problem.
% 1.31/1.48  		0:00:00.03 for the input.
% 1.31/1.48  		0:00:00.00 for the FLOTTER CNF translation.
% 1.31/1.48  		0:00:00.04 for inferences.
% 1.31/1.48  		0:00:00.00 for the backtracking.
% 1.31/1.48  		0:00:01.07 for the reduction.
% 1.31/1.48  
% 1.31/1.48  
% 1.31/1.48  Here is a proof with depth 4, length 23 :
% 1.31/1.48  % SZS output start Refutation
% See solution above
% 1.31/1.48  Formulae used in the proof : v_between_u_and_w u_to_w_equals_u_to_w1 v_to_w_equals_v_to_w1 u_not_v prove_w_is_w1 reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction2 outer_five_segment
% 1.31/1.48  
%------------------------------------------------------------------------------