%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC179-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 22:02:16 EDT 2022

% Result   : Unsatisfiable 0.67s 0.89s
% Output   : Refutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   21 (  13 unt;   7 nHn;  21 RR)
%            Number of literals    :   42 (   0 equ;  14 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC179-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC179-1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ duplicatefreeP(sk1),
    file('SWC179-1.p',unknown),
    [] ).

cnf(18,axiom,
    ( equal(cons(sk5,nil),sk3)
    | equal(nil,sk3) ),
    file('SWC179-1.p',unknown),
    [] ).

cnf(23,axiom,
    duplicatefreeP(nil),
    file('SWC179-1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC179-1.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ ssList(u)
    | duplicatefreeP(u)
    | ssItem(v) ),
    file('SWC179-1.p',unknown),
    [] ).

cnf(198,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(hd(v),hd(u))
    | ~ equal(tl(v),tl(u))
    | equal(v,u)
    | equal(nil,v)
    | equal(nil,u) ),
    file('SWC179-1.p',unknown),
    [] ).

cnf(215,plain,
    ( equal(nil,sk1)
    | equal(cons(sk5,nil),sk1) ),
    inference(rew,[status(thm),theory(equality)],[6,18]),
    [iquote('0:Rew:6.0,18.1,6.0,18.0')] ).

cnf(479,plain,
    ( duplicatefreeP(sk1)
    | ssItem(u) ),
    inference(res,[status(thm),theory(equality)],[1,93]),
    [iquote('0:Res:1.0,93.0')] ).

cnf(494,plain,
    ( ~ ssList(u)
    | ~ equal(hd(u),hd(sk1))
    | ~ equal(tl(u),tl(sk1))
    | equal(u,sk1)
    | equal(nil,u)
    | equal(nil,sk1) ),
    inference(res,[status(thm),theory(equality)],[1,198]),
    [iquote('0:Res:1.0,198.1')] ).

cnf(569,plain,
    ssItem(u),
    inference(mrr,[status(thm)],[479,7]),
    [iquote('0:MRR:479.0,7.0')] ).

cnf(578,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[86,569]),
    [iquote('0:MRR:86.0,569.0')] ).

cnf(782,plain,
    equal(nil,sk1),
    inference(spt,[spt(split,[position(s1)])],[494]),
    [iquote('1:Spt:494.5')] ).

cnf(859,plain,
    duplicatefreeP(sk1),
    inference(rew,[status(thm),theory(equality)],[782,23]),
    [iquote('1:Rew:782.0,23.0')] ).

cnf(891,plain,
    $false,
    inference(mrr,[status(thm)],[859,7]),
    [iquote('1:MRR:859.0,7.0')] ).

cnf(1196,plain,
    ~ equal(nil,sk1),
    inference(spt,[spt(split,[position(sa)])],[891,782]),
    [iquote('1:Spt:891.0,494.5,782.0')] ).

cnf(1197,plain,
    ( ~ ssList(u)
    | ~ equal(hd(u),hd(sk1))
    | ~ equal(tl(u),tl(sk1))
    | equal(u,sk1)
    | equal(nil,u) ),
    inference(spt,[spt(split,[position(s2)])],[494]),
    [iquote('1:Spt:891.0,494.0,494.1,494.2,494.3,494.4')] ).

cnf(1204,plain,
    equal(cons(sk5,nil),sk1),
    inference(mrr,[status(thm)],[215,1196]),
    [iquote('1:MRR:215.0,1196.0')] ).

cnf(1454,plain,
    duplicatefreeP(sk1),
    inference(spr,[status(thm),theory(equality)],[1204,578]),
    [iquote('1:SpR:1204.0,578.0')] ).

cnf(1462,plain,
    $false,
    inference(mrr,[status(thm)],[1454,7]),
    [iquote('1:MRR:1454.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWC179-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.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 10:37:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.67/0.89  
% 0.67/0.89  SPASS V 3.9 
% 0.67/0.89  SPASS beiseite: Proof found.
% 0.67/0.89  % SZS status Theorem
% 0.67/0.89  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.67/0.89  SPASS derived 909 clauses, backtracked 533 clauses, performed 21 splits and kept 1343 clauses.
% 0.67/0.89  SPASS allocated 77052 KBytes.
% 0.67/0.89  SPASS spent	0:00:00.54 on the problem.
% 0.67/0.89  		0:00:00.04 for the input.
% 0.67/0.89  		0:00:00.00 for the FLOTTER CNF translation.
% 0.67/0.89  		0:00:00.00 for inferences.
% 0.67/0.89  		0:00:00.01 for the backtracking.
% 0.67/0.89  		0:00:00.30 for the reduction.
% 0.67/0.89  
% 0.67/0.89  
% 0.67/0.89  Here is a proof with depth 2, length 21 :
% 0.67/0.89  % SZS output start Refutation
% See solution above
% 0.67/0.89  Formulae used in the proof : co1_1 co1_6 co1_7 co1_18 clause2 clause65 clause72 clause177
% 0.67/0.89  
%------------------------------------------------------------------------------