%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC094-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 22:01:40 EDT 2022

% Result   : Unsatisfiable 2.80s 2.98s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   25 (  16 unt;   0 nHn;  25 RR)
%            Number of literals    :   50 (   0 equ;  32 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 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(sk1),
    file('SWC094-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC094-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC094-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(sk4,sk3),
    file('SWC094-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(u,v),w),sk1)
    | ~ equal(app(u,w),sk2) ),
    file('SWC094-1.p',unknown),
    [] ).

cnf(9,axiom,
    equalelemsP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(10,axiom,
    duplicatefreeP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderedP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(12,axiom,
    totalorderedP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(13,axiom,
    strictorderP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(14,axiom,
    totalorderP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(15,axiom,
    cyclefreeP(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(16,axiom,
    ssList(nil),
    file('SWC094-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC094-1.p',unknown),
    [] ).

cnf(157,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(u,v),w),app(u,app(v,w))) ),
    file('SWC094-1.p',unknown),
    [] ).

cnf(196,plain,
    equal(sk4,sk1),
    inference(rew,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Rew:6.0,7.0')] ).

cnf(197,plain,
    equal(sk2,sk1),
    inference(rew,[status(thm),theory(equality)],[5,196]),
    [iquote('0:Rew:5.0,196.0')] ).

cnf(202,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(w,u),sk1)
    | ~ equal(app(w,app(v,u)),sk1) ),
    inference(rew,[status(thm),theory(equality)],[197,8,157]),
    [iquote('0:Rew:197.0,8.4,157.3,8.3')] ).

cnf(286,plain,
    equal(app(nil,sk1),sk1),
    inference(res,[status(thm),theory(equality)],[1,82]),
    [iquote('0:Res:1.0,82.0')] ).

cnf(4438,plain,
    ( ~ ssList(u)
    | ~ ssList(u)
    | ~ ssList(nil)
    | ~ ssList(v)
    | ~ equal(app(v,u),sk1)
    | ~ equal(app(v,u),sk1) ),
    inference(spl,[status(thm),theory(equality)],[82,202]),
    [iquote('0:SpL:82.1,202.4')] ).

cnf(4468,plain,
    ( ~ ssList(u)
    | ~ ssList(nil)
    | ~ ssList(v)
    | ~ equal(app(v,u),sk1) ),
    inference(obv,[status(thm),theory(equality)],[4438]),
    [iquote('0:Obv:4438.4')] ).

cnf(4469,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(v,u),sk1) ),
    inference(ssi,[status(thm)],[4468,9,10,11,12,13,14,15,16]),
    [iquote('0:SSi:4468.1,9.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0')] ).

cnf(6097,plain,
    ( ~ ssList(sk1)
    | ~ ssList(nil)
    | ~ equal(sk1,sk1) ),
    inference(spl,[status(thm),theory(equality)],[286,4469]),
    [iquote('0:SpL:286.0,4469.2')] ).

cnf(6506,plain,
    ( ~ ssList(sk1)
    | ~ ssList(nil) ),
    inference(obv,[status(thm),theory(equality)],[6097]),
    [iquote('0:Obv:6097.2')] ).

cnf(6507,plain,
    $false,
    inference(ssi,[status(thm)],[6506,9,10,11,12,13,14,15,16,1]),
    [iquote('0:SSi:6506.1,6506.0,9.0,10.0,11.0,12.0,13.0,14.0,15.0,16.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC094-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n016.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jun 12 20:30:28 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 2.80/2.98  
% 2.80/2.98  SPASS V 3.9 
% 2.80/2.98  SPASS beiseite: Proof found.
% 2.80/2.98  % SZS status Theorem
% 2.80/2.98  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.80/2.98  SPASS derived 3767 clauses, backtracked 801 clauses, performed 10 splits and kept 2647 clauses.
% 2.80/2.98  SPASS allocated 81925 KBytes.
% 2.80/2.98  SPASS spent	0:00:02.46 on the problem.
% 2.80/2.98  		0:00:00.04 for the input.
% 2.80/2.98  		0:00:00.00 for the FLOTTER CNF translation.
% 2.80/2.98  		0:00:00.05 for inferences.
% 2.80/2.98  		0:00:00.09 for the backtracking.
% 2.80/2.98  		0:00:02.17 for the reduction.
% 2.80/2.98  
% 2.80/2.98  
% 2.80/2.98  Here is a proof with depth 2, length 25 :
% 2.80/2.98  % SZS output start Refutation
% See solution above
% 2.80/2.98  Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause74 clause149
% 2.80/2.98  
%------------------------------------------------------------------------------