%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO040-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 06:21:48 EDT 2022

% Result   : Unsatisfiable 2.78s 2.98s
% Output   : Refutation 2.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   4 unt;   0 nHn;  12 RR)
%            Number of literals    :   28 (   0 equ;  17 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(29,axiom,
    between(u__dfg,v__dfg,w__dfg),
    file('GEO040-3.p',unknown),
    [] ).

cnf(30,axiom,
    between(v__dfg,u__dfg,w__dfg),
    file('GEO040-3.p',unknown),
    [] ).

cnf(31,axiom,
    ~ equal(v__dfg,u__dfg),
    file('GEO040-3.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO040-3.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(y,inner_pasch(x,y,w,v,u),u) ),
    file('GEO040-3.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(v,inner_pasch(x,y,w,v,u),x) ),
    file('GEO040-3.p',unknown),
    [] ).

cnf(600,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | equal(inner_pasch(v,x,w,v,u),v) ),
    inference(res,[status(thm),theory(equality)],[40,38]),
    [iquote('0:Res:40.2,38.0')] ).

cnf(617,plain,
    ( ~ between(u,v,w)
    | ~ between(x,u,w)
    | equal(inner_pasch(x,u,w,v,u),u) ),
    inference(res,[status(thm),theory(equality)],[39,38]),
    [iquote('0:Res:39.2,38.0')] ).

cnf(2599,plain,
    ( ~ between(u,v,w)
    | ~ between(v,u,w)
    | ~ between(u,v,w)
    | ~ between(v,u,w)
    | equal(u,v) ),
    inference(spr,[status(thm),theory(equality)],[617,600]),
    [iquote('0:SpR:617.2,600.2')] ).

cnf(2600,plain,
    ( ~ between(u,v,w)
    | ~ between(v,u,w)
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[2599]),
    [iquote('0:Obv:2599.1')] ).

cnf(8374,plain,
    ( ~ between(u__dfg,v__dfg,w__dfg)
    | equal(v__dfg,u__dfg) ),
    inference(res,[status(thm),theory(equality)],[30,2600]),
    [iquote('0:Res:30.0,2600.0')] ).

cnf(8426,plain,
    $false,
    inference(mrr,[status(thm)],[8374,29,31]),
    [iquote('0:MRR:8374.0,8374.1,29.0,31.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO040-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n014.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jun 18 17:08:48 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 2.78/2.98  
% 2.78/2.98  SPASS V 3.9 
% 2.78/2.98  SPASS beiseite: Proof found.
% 2.78/2.98  % SZS status Theorem
% 2.78/2.98  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.78/2.98  SPASS derived 6791 clauses, backtracked 0 clauses, performed 0 splits and kept 1814 clauses.
% 2.78/2.98  SPASS allocated 69296 KBytes.
% 2.78/2.98  SPASS spent	0:00:02.58 on the problem.
% 2.78/2.98  		0:00:00.04 for the input.
% 2.78/2.98  		0:00:00.00 for the FLOTTER CNF translation.
% 2.78/2.98  		0:00:00.08 for inferences.
% 2.78/2.98  		0:00:00.00 for the backtracking.
% 2.78/2.98  		0:00:02.43 for the reduction.
% 2.78/2.98  
% 2.78/2.98  
% 2.78/2.98  Here is a proof with depth 3, length 12 :
% 2.78/2.98  % SZS output start Refutation
% See solution above
% 2.78/2.98  Formulae used in the proof : v_between_u_and_w u_between_v_and_w prove_u_is_v identity_for_betweeness inner_pasch1 inner_pasch2
% 2.78/2.98  
%------------------------------------------------------------------------------