TSTP Solution File: SET664+3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:27:56 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   24 (  11 unt;   0 nHn;  24 RR)
%            Number of literals    :   46 (   0 equ;  27 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    ilf_type(u,set_type),
    file('SET664+3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(skc6,empty_set),
    file('SET664+3.p',unknown),
    [] ).

cnf(12,axiom,
    ilf_type(skc6,relation_type(skc5,skc4)),
    file('SET664+3.p',unknown),
    [] ).

cnf(13,axiom,
    ilf_type(skc6,relation_type(skc5,empty_set)),
    file('SET664+3.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ relation_like(u)
    | ~ ilf_type(u,set_type)
    | ilf_type(u,binary_relation_type) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(32,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ subset(u,empty_set)
    | equal(u,empty_set) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ ilf_type(u,binary_relation_type)
    | ~ equal(range_of(u),empty_set)
    | equal(u,empty_set) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,subset_type(cross_product(u,v)))
    | relation_like(w) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,relation_type(u,v))
    | subset(range_of(w),v) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ ilf_type(u,relation_type(v,w))
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ilf_type(u,subset_type(cross_product(v,w))) ),
    file('SET664+3.p',unknown),
    [] ).

cnf(72,plain,
    ( ~ relation_like(u)
    | ilf_type(u,binary_relation_type) ),
    inference(mrr,[status(thm)],[29,6]),
    [iquote('0:MRR:29.1,6.0')] ).

cnf(75,plain,
    ( ~ subset(u,empty_set)
    | equal(u,empty_set) ),
    inference(mrr,[status(thm)],[32,6]),
    [iquote('0:MRR:32.0,6.0')] ).

cnf(79,plain,
    ( ~ ilf_type(u,subset_type(cross_product(v,w)))
    | relation_like(u) ),
    inference(mrr,[status(thm)],[43,6]),
    [iquote('0:MRR:43.0,43.1,6.0,6.0')] ).

cnf(87,plain,
    ( ~ ilf_type(u,relation_type(v,w))
    | subset(range_of(u),w) ),
    inference(mrr,[status(thm)],[45,6]),
    [iquote('0:MRR:45.0,45.1,6.0,6.0')] ).

cnf(89,plain,
    ( ~ ilf_type(u,relation_type(v,w))
    | ilf_type(u,subset_type(cross_product(v,w))) ),
    inference(mrr,[status(thm)],[51,6]),
    [iquote('0:MRR:51.1,51.2,6.0,6.0')] ).

cnf(103,plain,
    ( ~ ilf_type(skc6,binary_relation_type)
    | ~ equal(range_of(skc6),empty_set) ),
    inference(res,[status(thm),theory(equality)],[35,7]),
    [iquote('0:Res:35.2,7.0')] ).

cnf(115,plain,
    subset(range_of(skc6),empty_set),
    inference(res,[status(thm),theory(equality)],[13,87]),
    [iquote('0:Res:13.0,87.0')] ).

cnf(120,plain,
    ilf_type(skc6,subset_type(cross_product(skc5,skc4))),
    inference(res,[status(thm),theory(equality)],[12,89]),
    [iquote('0:Res:12.0,89.0')] ).

cnf(132,plain,
    equal(range_of(skc6),empty_set),
    inference(res,[status(thm),theory(equality)],[115,75]),
    [iquote('0:Res:115.0,75.0')] ).

cnf(139,plain,
    ( ~ ilf_type(skc6,binary_relation_type)
    | ~ equal(empty_set,empty_set) ),
    inference(rew,[status(thm),theory(equality)],[132,103]),
    [iquote('0:Rew:132.0,103.1')] ).

cnf(140,plain,
    ~ ilf_type(skc6,binary_relation_type),
    inference(obv,[status(thm),theory(equality)],[139]),
    [iquote('0:Obv:139.1')] ).

cnf(142,plain,
    ~ relation_like(skc6),
    inference(res,[status(thm),theory(equality)],[72,140]),
    [iquote('0:Res:72.1,140.0')] ).

cnf(156,plain,
    relation_like(skc6),
    inference(res,[status(thm),theory(equality)],[120,79]),
    [iquote('0:Res:120.0,79.0')] ).

cnf(158,plain,
    $false,
    inference(mrr,[status(thm)],[156,142]),
    [iquote('0:MRR:156.0,142.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 11:06:58 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  
% 0.20/0.47  SPASS V 3.9 
% 0.20/0.47  SPASS beiseite: Proof found.
% 0.20/0.47  % SZS status Theorem
% 0.20/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.47  SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.20/0.47  SPASS allocated 97854 KBytes.
% 0.20/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.20/0.47  		0:00:00.04 for the input.
% 0.20/0.47  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.47  		0:00:00.00 for inferences.
% 0.20/0.47  		0:00:00.00 for the backtracking.
% 0.20/0.47  		0:00:00.01 for the reduction.
% 0.20/0.47  
% 0.20/0.47  
% 0.20/0.47  Here is a proof with depth 2, length 24 :
% 0.20/0.47  % SZS output start Refutation
% See solution above
% 0.20/0.47  Formulae used in the proof : p33 prove_relset_1_27 p13 p1 p2 p28 p3 p6
% 0.20/0.47  
%------------------------------------------------------------------------------