%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC381-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 22:03:42 EDT 2022

% Result   : Unsatisfiable 1.82s 2.00s
% Output   : Refutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   21 (   8 unt;   2 nHn;  21 RR)
%            Number of literals    :   40 (   0 equ;  23 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC381-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC381-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ssItem(sk5)
    | neq(sk2,nil) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ ssItem(u)
    | ~ equal(cons(u,nil),sk1)
    | ~ memberP(sk2,u)
    | ~ neq(sk4,nil) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ neq(sk4,nil)
    | ssItem(sk5) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ neq(sk4,nil)
    | equal(cons(sk5,nil),sk3) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ neq(sk4,nil)
    | memberP(sk4,sk5) ),
    file('SWC381-1.p',unknown),
    [] ).

cnf(204,plain,
    ( ~ neq(sk2,nil)
    | ssItem(sk5) ),
    inference(rew,[status(thm),theory(equality)],[5,14]),
    [iquote('0:Rew:5.0,14.0')] ).

cnf(205,plain,
    ssItem(sk5),
    inference(mrr,[status(thm)],[204,10]),
    [iquote('0:MRR:204.0,10.1')] ).

cnf(207,plain,
    neq(sk2,nil),
    inference(obv,[status(thm),theory(equality)],[7]),
    [iquote('0:Obv:7.0')] ).

cnf(208,plain,
    ( ~ neq(sk2,nil)
    | memberP(sk2,sk5) ),
    inference(rew,[status(thm),theory(equality)],[5,16]),
    [iquote('0:Rew:5.0,16.1,5.0,16.0')] ).

cnf(209,plain,
    memberP(sk2,sk5),
    inference(mrr,[status(thm)],[208,207]),
    [iquote('0:MRR:208.0,207.0')] ).

cnf(210,plain,
    ( ~ neq(sk2,nil)
    | equal(cons(sk5,nil),sk1) ),
    inference(rew,[status(thm),theory(equality)],[6,15,5]),
    [iquote('0:Rew:6.0,15.1,5.0,15.0')] ).

cnf(211,plain,
    equal(cons(sk5,nil),sk1),
    inference(mrr,[status(thm)],[210,207]),
    [iquote('0:MRR:210.0,207.0')] ).

cnf(212,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,nil),sk1)
    | ~ memberP(sk2,u)
    | ~ neq(sk2,nil) ),
    inference(rew,[status(thm),theory(equality)],[5,13]),
    [iquote('0:Rew:5.0,13.3')] ).

cnf(213,plain,
    ( ~ ssItem(u)
    | ~ memberP(sk2,u)
    | ~ equal(cons(u,nil),sk1) ),
    inference(mrr,[status(thm)],[212,207]),
    [iquote('0:MRR:212.3,207.0')] ).

cnf(4290,plain,
    ( ~ ssItem(sk5)
    | ~ memberP(sk2,sk5)
    | ~ equal(sk1,sk1) ),
    inference(spl,[status(thm),theory(equality)],[211,213]),
    [iquote('0:SpL:211.0,213.2')] ).

cnf(4293,plain,
    ( ~ ssItem(sk5)
    | ~ memberP(sk2,sk5) ),
    inference(obv,[status(thm),theory(equality)],[4290]),
    [iquote('0:Obv:4290.2')] ).

cnf(4294,plain,
    ~ memberP(sk2,sk5),
    inference(ssi,[status(thm)],[4293,205]),
    [iquote('0:SSi:4293.0,205.0')] ).

cnf(4295,plain,
    $false,
    inference(mrr,[status(thm)],[4294,209]),
    [iquote('0:MRR:4294.0,209.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC381-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.15/0.35  % Computer : n026.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Sun Jun 12 06:16:50 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 1.82/2.00  
% 1.82/2.00  SPASS V 3.9 
% 1.82/2.00  SPASS beiseite: Proof found.
% 1.82/2.00  % SZS status Theorem
% 1.82/2.00  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.82/2.00  SPASS derived 3346 clauses, backtracked 2634 clauses, performed 70 splits and kept 4935 clauses.
% 1.82/2.00  SPASS allocated 78463 KBytes.
% 1.82/2.00  SPASS spent	0:00:01.61 on the problem.
% 1.82/2.00  		0:00:00.04 for the input.
% 1.82/2.00  		0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.00  		0:00:00.01 for inferences.
% 1.82/2.00  		0:00:00.03 for the backtracking.
% 1.82/2.00  		0:00:01.35 for the reduction.
% 1.82/2.00  
% 1.82/2.00  
% 1.82/2.00  Here is a proof with depth 1, length 21 :
% 1.82/2.00  % SZS output start Refutation
% See solution above
% 1.82/2.00  Formulae used in the proof : co1_5 co1_6 co1_7 co1_10 co1_13 co1_14 co1_15 co1_16
% 1.82/2.00  
%------------------------------------------------------------------------------