%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET479-6 : 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 05:26:31 EDT 2022

% Result   : Unsatisfiable 0.59s 0.77s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   8 unt;   0 nHn;  14 RR)
%            Number of literals    :   21 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(x__dfg,universal_class),
    file('SET479-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(domain_of(x__dfg),universal_class),
    file('SET479-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET479-6.p',unknown),
    [] ).

cnf(6,axiom,
    subclass(u,universal_class),
    file('SET479-6.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(v,x) ),
    file('SET479-6.p',unknown),
    [] ).

cnf(100,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('SET479-6.p',unknown),
    [] ).

cnf(102,axiom,
    ( ~ member(u,universal_class)
    | member(ordered_pair(u,domain_of(u)),domain_relation) ),
    file('SET479-6.p',unknown),
    [] ).

cnf(120,plain,
    member(ordered_pair(x__dfg,domain_of(x__dfg)),domain_relation),
    inference(res,[status(thm),theory(equality)],[1,102]),
    [iquote('0:Res:1.0,102.0')] ).

cnf(138,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(domain_of(x__dfg),u) ),
    inference(res,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Res:3.2,2.0')] ).

cnf(140,plain,
    ~ member(domain_of(x__dfg),u),
    inference(mrr,[status(thm)],[138,6]),
    [iquote('0:MRR:138.0,6.0')] ).

cnf(542,plain,
    ( ~ subclass(domain_relation,u)
    | member(ordered_pair(x__dfg,domain_of(x__dfg)),u) ),
    inference(res,[status(thm),theory(equality)],[120,3]),
    [iquote('0:Res:120.0,3.0')] ).

cnf(2537,plain,
    ( ~ subclass(domain_relation,cross_product(u,v))
    | member(domain_of(x__dfg),v) ),
    inference(res,[status(thm),theory(equality)],[542,17]),
    [iquote('0:Res:542.1,17.0')] ).

cnf(2557,plain,
    ~ subclass(domain_relation,cross_product(u,v)),
    inference(mrr,[status(thm)],[2537,140]),
    [iquote('0:MRR:2537.1,140.0')] ).

cnf(2558,plain,
    $false,
    inference(unc,[status(thm)],[2557,100]),
    [iquote('0:UnC:2557.0,100.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET479-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  9 18:06:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.59/0.77  
% 0.59/0.77  SPASS V 3.9 
% 0.59/0.77  SPASS beiseite: Proof found.
% 0.59/0.77  % SZS status Theorem
% 0.59/0.77  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.59/0.77  SPASS derived 2287 clauses, backtracked 32 clauses, performed 3 splits and kept 1218 clauses.
% 0.59/0.77  SPASS allocated 77960 KBytes.
% 0.59/0.77  SPASS spent	0:00:00.40 on the problem.
% 0.59/0.77  		0:00:00.04 for the input.
% 0.59/0.77  		0:00:00.00 for the FLOTTER CNF translation.
% 0.59/0.77  		0:00:00.03 for inferences.
% 0.59/0.77  		0:00:00.01 for the backtracking.
% 0.59/0.77  		0:00:00.28 for the reduction.
% 0.59/0.77  
% 0.59/0.77  
% 0.59/0.77  Here is a proof with depth 3, length 14 :
% 0.59/0.77  % SZS output start Refutation
% See solution above
% 0.59/0.77  Formulae used in the proof : prove_replacement_property1_1 prove_replacement_property1_2 subclass_members class_elements_are_sets cartesian_product2 definition_of_domain_relation1 definition_of_domain_relation3
% 0.59/0.77  
%------------------------------------------------------------------------------