%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 05:26:57 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    operation(xf1),
    file('SET558-6.p',unknown),
    [] ).

cnf(2,axiom,
    compatible(xh,xf1,xf2),
    file('SET558-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(cross_product(domain_of(xh),domain_of(xh)),domain_of(xf1)),
    file('SET558-6.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ operation(u)
    | equal(cross_product(domain_of(domain_of(u)),domain_of(domain_of(u))),domain_of(u)) ),
    file('SET558-6.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ compatible(u,v,w)
    | equal(domain_of(domain_of(v)),domain_of(u)) ),
    file('SET558-6.p',unknown),
    [] ).

cnf(120,plain,
    equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),domain_of(xf1)),
    inference(res,[status(thm),theory(equality)],[1,82]),
    [iquote('0:Res:1.0,82.0')] ).

cnf(125,plain,
    equal(domain_of(domain_of(xf1)),domain_of(xh)),
    inference(res,[status(thm),theory(equality)],[2,86]),
    [iquote('0:Res:2.0,86.0')] ).

cnf(139,plain,
    equal(cross_product(domain_of(xh),domain_of(xh)),domain_of(xf1)),
    inference(rew,[status(thm),theory(equality)],[125,120]),
    [iquote('0:Rew:125.0,120.0')] ).

cnf(140,plain,
    $false,
    inference(mrr,[status(thm)],[139,3]),
    [iquote('0:MRR:139.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 19:37:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.20/0.44  SPASS allocated 75808 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.01 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 1, length 9 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : prove_compatible_functions_alternate_defn1_1 prove_compatible_functions_alternate_defn1_2 prove_compatible_functions_alternate_defn1_3 operation2 compatible2
% 0.20/0.44  
%------------------------------------------------------------------------------