%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 00:07:26 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   15 (   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(compose(a,b),u),v)
    | ~ equal(compose(compose(a,b),w),v)
    | equal(u,w) ),
    file('CAT001-4.p',unknown),
    [] ).

cnf(4,axiom,
    equal(compose(b,g),compose(b,h)),
    file('CAT001-4.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(g,h),
    file('CAT001-4.p',unknown),
    [] ).

cnf(14,axiom,
    equal(compose(compose(u,v),w),compose(u,compose(v,w))),
    file('CAT001-4.p',unknown),
    [] ).

cnf(17,plain,
    ( ~ equal(compose(a,compose(b,u)),v)
    | ~ equal(compose(a,compose(b,w)),v)
    | equal(w,u) ),
    inference(rew,[status(thm),theory(equality)],[14,2]),
    [iquote('0:Rew:14.0,2.1,14.0,2.0')] ).

cnf(19,plain,
    ( ~ equal(compose(a,compose(b,g)),u)
    | ~ equal(compose(a,compose(b,h)),u) ),
    inference(res,[status(thm),theory(equality)],[17,5]),
    [iquote('0:Res:17.2,5.0')] ).

cnf(22,plain,
    ( ~ equal(compose(a,compose(b,h)),u)
    | ~ equal(compose(a,compose(b,h)),u) ),
    inference(rew,[status(thm),theory(equality)],[4,19]),
    [iquote('0:Rew:4.0,19.0')] ).

cnf(23,plain,
    ~ equal(compose(a,compose(b,h)),u),
    inference(obv,[status(thm),theory(equality)],[22]),
    [iquote('0:Obv:22.0')] ).

cnf(24,plain,
    $false,
    inference(unc,[status(thm)],[23,14]),
    [iquote('0:UnC:23.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n021.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 May 29 17:33:43 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.20/0.41  SPASS allocated 75602 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.04 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 1, length 9 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : monomorphism bh_equals_bg prove_h_equals_g associativity_of_compose
% 0.20/0.41  
%------------------------------------------------------------------------------