%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 : Fri Jul 15 00:07:27 EDT 2022

% Result   : Unsatisfiable 0.75s 0.94s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   19 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 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(2,axiom,
    ( ~ equal(compose(a,u),v)
    | ~ equal(compose(a,w),v)
    | equal(w,u) ),
    file('CAT002-4.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ equal(compose(b,u),v)
    | ~ equal(compose(b,w),v)
    | equal(w,u) ),
    file('CAT002-4.p',unknown),
    [] ).

cnf(5,axiom,
    equal(compose(compose(a,b),g),compose(compose(a,b),h)),
    file('CAT002-4.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(g,h),
    file('CAT002-4.p',unknown),
    [] ).

cnf(15,axiom,
    equal(compose(compose(u,v),w),compose(u,compose(v,w))),
    file('CAT002-4.p',unknown),
    [] ).

cnf(18,plain,
    equal(compose(a,compose(b,g)),compose(a,compose(b,h))),
    inference(rew,[status(thm),theory(equality)],[15,5]),
    [iquote('0:Rew:15.0,5.0,15.0,5.0')] ).

cnf(21,plain,
    ( ~ equal(compose(b,h),u)
    | ~ equal(compose(b,g),u) ),
    inference(res,[status(thm),theory(equality)],[3,6]),
    [iquote('0:Res:3.2,6.0')] ).

cnf(315,plain,
    ( ~ equal(compose(a,u),compose(a,v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[2]),
    [iquote('0:EqR:2.0')] ).

cnf(602,plain,
    ( ~ equal(compose(a,compose(b,h)),compose(a,u))
    | equal(compose(b,g),u) ),
    inference(spl,[status(thm),theory(equality)],[18,315]),
    [iquote('0:SpL:18.0,315.0')] ).

cnf(717,plain,
    ~ equal(compose(b,g),compose(b,h)),
    inference(eqr,[status(thm),theory(equality)],[21]),
    [iquote('0:EqR:21.1')] ).

cnf(7999,plain,
    equal(compose(b,g),compose(b,h)),
    inference(eqr,[status(thm),theory(equality)],[602]),
    [iquote('0:EqR:602.0')] ).

cnf(8014,plain,
    $false,
    inference(mrr,[status(thm)],[7999,717]),
    [iquote('0:MRR:7999.0,717.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n027.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 May 29 17:33:45 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.75/0.94  
% 0.75/0.94  SPASS V 3.9 
% 0.75/0.94  SPASS beiseite: Proof found.
% 0.75/0.94  % SZS status Theorem
% 0.75/0.94  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.75/0.94  SPASS derived 5432 clauses, backtracked 0 clauses, performed 0 splits and kept 998 clauses.
% 0.75/0.94  SPASS allocated 80416 KBytes.
% 0.75/0.94  SPASS spent	0:00:00.56 on the problem.
% 0.75/0.94  		0:00:00.03 for the input.
% 0.75/0.94  		0:00:00.00 for the FLOTTER CNF translation.
% 0.75/0.94  		0:00:00.05 for inferences.
% 0.75/0.94  		0:00:00.00 for the backtracking.
% 0.75/0.94  		0:00:00.45 for the reduction.
% 0.75/0.94  
% 0.75/0.94  
% 0.75/0.94  Here is a proof with depth 3, length 12 :
% 0.75/0.94  % SZS output start Refutation
% See solution above
% 0.75/0.94  Formulae used in the proof : cancellation_for_compose1 cancellation_for_compose2 ab_h_equals_ab_g prove_g_equals_h associativity_of_compose
% 0.75/0.94  
%------------------------------------------------------------------------------