%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 : Tue Jul 19 22:01:02 EDT 2022

% Result   : Theorem 5.23s 5.45s
% Output   : Refutation 5.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   7 unt;   0 nHn;  15 RR)
%            Number of literals    :   41 (   0 equ;  32 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc11),
    file('SWC006+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc10),
    file('SWC006+1.p',unknown),
    [] ).

cnf(3,axiom,
    ssList(skc9),
    file('SWC006+1.p',unknown),
    [] ).

cnf(61,axiom,
    equal(app(skc9,skc11),skc7),
    file('SWC006+1.p',unknown),
    [] ).

cnf(70,axiom,
    equal(app(app(skc9,skc10),skc11),skc8),
    file('SWC006+1.p',unknown),
    [] ).

cnf(157,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(w,v),u),app(w,app(v,u))) ),
    file('SWC006+1.p',unknown),
    [] ).

cnf(185,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(u,v),w),skc8)
    | ~ equal(app(u,w),skc7) ),
    file('SWC006+1.p',unknown),
    [] ).

cnf(200,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(w,u),skc7)
    | ~ equal(app(w,app(v,u)),skc8) ),
    inference(rew,[status(thm),theory(equality)],[157,185]),
    [iquote('0:Rew:157.3,185.3')] ).

cnf(9940,plain,
    ( ~ ssList(skc11)
    | ~ ssList(skc10)
    | ~ ssList(skc9)
    | equal(app(skc9,app(skc10,skc11)),skc8) ),
    inference(spr,[status(thm),theory(equality)],[70,157]),
    [iquote('0:SpR:70.0,157.3')] ).

cnf(9958,plain,
    equal(app(skc9,app(skc10,skc11)),skc8),
    inference(ssi,[status(thm)],[9940,3,2,1]),
    [iquote('0:SSi:9940.2,9940.1,9940.0,3.0,2.0,1.0')] ).

cnf(11039,plain,
    ( ~ ssList(skc11)
    | ~ ssList(skc10)
    | ~ ssList(skc9)
    | ~ equal(app(skc9,skc11),skc7)
    | ~ equal(skc8,skc8) ),
    inference(spl,[status(thm),theory(equality)],[9958,200]),
    [iquote('0:SpL:9958.0,200.4')] ).

cnf(11051,plain,
    ( ~ ssList(skc11)
    | ~ ssList(skc10)
    | ~ ssList(skc9)
    | ~ equal(app(skc9,skc11),skc7) ),
    inference(obv,[status(thm),theory(equality)],[11039]),
    [iquote('0:Obv:11039.4')] ).

cnf(11052,plain,
    ( ~ ssList(skc11)
    | ~ ssList(skc10)
    | ~ ssList(skc9)
    | ~ equal(skc7,skc7) ),
    inference(rew,[status(thm),theory(equality)],[61,11051]),
    [iquote('0:Rew:61.0,11051.3')] ).

cnf(11053,plain,
    ( ~ ssList(skc11)
    | ~ ssList(skc10)
    | ~ ssList(skc9) ),
    inference(obv,[status(thm),theory(equality)],[11052]),
    [iquote('0:Obv:11052.3')] ).

cnf(11054,plain,
    $false,
    inference(ssi,[status(thm)],[11053,3,2,1]),
    [iquote('0:SSi:11053.2,11053.1,11053.0,3.0,2.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n010.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 : Sun Jun 12 19:23:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 5.23/5.45  
% 5.23/5.45  SPASS V 3.9 
% 5.23/5.45  SPASS beiseite: Proof found.
% 5.23/5.45  % SZS status Theorem
% 5.23/5.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 5.23/5.45  SPASS derived 7151 clauses, backtracked 1988 clauses, performed 30 splits and kept 4653 clauses.
% 5.23/5.45  SPASS allocated 107654 KBytes.
% 5.23/5.45  SPASS spent	0:00:04.70 on the problem.
% 5.23/5.45  		0:00:00.04 for the input.
% 5.23/5.45  		0:00:00.07 for the FLOTTER CNF translation.
% 5.23/5.45  		0:00:00.07 for inferences.
% 5.23/5.45  		0:00:00.08 for the backtracking.
% 5.23/5.45  		0:00:04.26 for the reduction.
% 5.23/5.45  
% 5.23/5.45  
% 5.23/5.45  Here is a proof with depth 2, length 15 :
% 5.23/5.45  % SZS output start Refutation
% See solution above
% 5.23/5.45  Formulae used in the proof : co1 ax82
% 5.23/5.45  
%------------------------------------------------------------------------------