%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 00:07:28 EDT 2022

% Result   : Unsatisfiable 1.14s 1.35s
% Output   : Refutation 1.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   6 unt;   0 nHn;  13 RR)
%            Number of literals    :   22 (   0 equ;  12 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(u,a),v)
    | ~ equal(compose(w,a),v)
    | equal(w,u) ),
    file('CAT004-3.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ equal(compose(u,b),v)
    | ~ equal(compose(w,b),v)
    | equal(w,u) ),
    file('CAT004-3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(compose(g,compose(a,b)),compose(h,compose(a,b))),
    file('CAT004-3.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(g,h),
    file('CAT004-3.p',unknown),
    [] ).

cnf(15,axiom,
    equal(compose(compose(u,v),w),compose(u,compose(v,w))),
    file('CAT004-3.p',unknown),
    [] ).

cnf(28,plain,
    ( ~ equal(compose(h,a),u)
    | ~ equal(compose(g,a),u) ),
    inference(res,[status(thm),theory(equality)],[2,6]),
    [iquote('0:Res:2.2,6.0')] ).

cnf(279,plain,
    ( ~ equal(compose(u,b),compose(v,b))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[3]),
    [iquote('0:EqR:3.0')] ).

cnf(1605,plain,
    ( ~ equal(compose(u,compose(v,b)),compose(w,b))
    | equal(compose(u,v),w) ),
    inference(spl,[status(thm),theory(equality)],[15,279]),
    [iquote('0:SpL:15.0,279.0')] ).

cnf(2168,plain,
    ~ equal(compose(g,a),compose(h,a)),
    inference(eqr,[status(thm),theory(equality)],[28]),
    [iquote('0:EqR:28.1')] ).

cnf(9610,plain,
    ( ~ equal(compose(h,compose(a,b)),compose(u,b))
    | equal(compose(g,a),u) ),
    inference(spl,[status(thm),theory(equality)],[5,1605]),
    [iquote('0:SpL:5.0,1605.0')] ).

cnf(9619,plain,
    ( ~ equal(compose(h,compose(a,b)),compose(u,compose(v,b)))
    | equal(compose(g,a),compose(u,v)) ),
    inference(spl,[status(thm),theory(equality)],[15,9610]),
    [iquote('0:SpL:15.0,9610.0')] ).

cnf(9699,plain,
    equal(compose(g,a),compose(h,a)),
    inference(eqr,[status(thm),theory(equality)],[9619]),
    [iquote('0:EqR:9619.0')] ).

cnf(9705,plain,
    $false,
    inference(mrr,[status(thm)],[9699,2168]),
    [iquote('0:MRR:9699.0,2168.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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 18:45:56 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.14/1.35  
% 1.14/1.35  SPASS V 3.9 
% 1.14/1.35  SPASS beiseite: Proof found.
% 1.14/1.35  % SZS status Theorem
% 1.14/1.35  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.14/1.35  SPASS derived 6540 clauses, backtracked 0 clauses, performed 6 splits and kept 1172 clauses.
% 1.14/1.35  SPASS allocated 81390 KBytes.
% 1.14/1.35  SPASS spent	0:00:00.81 on the problem.
% 1.14/1.35  		0:00:00.04 for the input.
% 1.14/1.35  		0:00:00.00 for the FLOTTER CNF translation.
% 1.14/1.35  		0:00:00.08 for inferences.
% 1.14/1.35  		0:00:00.02 for the backtracking.
% 1.14/1.35  		0:00:00.65 for the reduction.
% 1.14/1.35  
% 1.14/1.35  
% 1.14/1.35  Here is a proof with depth 5, length 13 :
% 1.14/1.35  % SZS output start Refutation
% See solution above
% 1.14/1.35  Formulae used in the proof : cancellation_for_product1 cancellation_for_product2 h_ab_equals_g_ab prove_h_equals_g associativity_of_compose
% 1.14/1.35  
%------------------------------------------------------------------------------