TSTP Solution File: SET641+3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 05:27:47 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   25 (   6 unt;   5 nHn;  25 RR)
%            Number of literals    :   64 (   0 equ;  39 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ilf_type(u,set_type),
    file('SET641+3.p',unknown),
    [] ).

cnf(9,axiom,
    subset(skc3,cross_product(skc4,skc5)),
    file('SET641+3.p',unknown),
    [] ).

cnf(12,axiom,
    ~ ilf_type(skc3,relation_type(skc4,skc5)),
    file('SET641+3.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ empty(u)
    | ~ ilf_type(v,set_type)
    | ~ member(v,u)
    | ~ ilf_type(u,set_type) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | member(skf16(v,u),u)
    | member(u,power_set(v)) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(32,axiom,
    ( ~ ilf_type(u,member_type(power_set(v)))
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(u,set_type)
    | ilf_type(u,subset_type(v)) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ member(skf16(u,v),u)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(u,set_type)
    | member(v,power_set(u)) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ member(u,v)
    | ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ilf_type(u,member_type(v))
    | empty(v) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ ilf_type(u,subset_type(cross_product(v,w)))
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ilf_type(u,relation_type(v,w)) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ subset(u,v)
    | ~ ilf_type(w,set_type)
    | ~ member(w,u)
    | ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | member(w,v) ),
    file('SET641+3.p',unknown),
    [] ).

cnf(53,plain,
    ( ~ empty(u)
    | ~ member(v,u) ),
    inference(mrr,[status(thm)],[26,4]),
    [iquote('0:MRR:26.1,26.3,4.0,4.0')] ).

cnf(57,plain,
    ( member(u,power_set(v))
    | member(skf16(v,u),u) ),
    inference(mrr,[status(thm)],[29,4]),
    [iquote('0:MRR:29.0,29.1,4.0,4.0')] ).

cnf(59,plain,
    ( ~ member(u,v)
    | ilf_type(u,member_type(v)) ),
    inference(mrr,[status(thm)],[35,4,53]),
    [iquote('0:MRR:35.1,35.2,35.4,4.0,4.0,53.0')] ).

cnf(61,plain,
    ( ~ member(skf16(u,v),u)
    | member(v,power_set(u)) ),
    inference(mrr,[status(thm)],[33,4]),
    [iquote('0:MRR:33.1,33.2,4.0,4.0')] ).

cnf(62,plain,
    ( ~ ilf_type(u,member_type(power_set(v)))
    | ilf_type(u,subset_type(v)) ),
    inference(mrr,[status(thm)],[32,4]),
    [iquote('0:MRR:32.1,32.2,4.0,4.0')] ).

cnf(65,plain,
    ( ~ ilf_type(u,subset_type(cross_product(v,w)))
    | ilf_type(u,relation_type(v,w)) ),
    inference(mrr,[status(thm)],[37,4]),
    [iquote('0:MRR:37.1,37.2,4.0,4.0')] ).

cnf(68,plain,
    ( ~ member(u,v)
    | ~ subset(v,w)
    | member(u,w) ),
    inference(mrr,[status(thm)],[40,4]),
    [iquote('0:MRR:40.1,40.3,40.4,4.0,4.0,4.0')] ).

cnf(75,plain,
    ~ ilf_type(skc3,subset_type(cross_product(skc4,skc5))),
    inference(res,[status(thm),theory(equality)],[65,12]),
    [iquote('0:Res:65.1,12.0')] ).

cnf(89,plain,
    ( ~ member(u,power_set(v))
    | ilf_type(u,subset_type(v)) ),
    inference(res,[status(thm),theory(equality)],[59,62]),
    [iquote('0:Res:59.1,62.0')] ).

cnf(119,plain,
    ( ~ subset(u,v)
    | member(u,power_set(w))
    | member(skf16(w,u),v) ),
    inference(res,[status(thm),theory(equality)],[57,68]),
    [iquote('0:Res:57.1,68.0')] ).

cnf(392,plain,
    ( ~ subset(u,v)
    | member(u,power_set(v))
    | member(u,power_set(v)) ),
    inference(res,[status(thm),theory(equality)],[119,61]),
    [iquote('0:Res:119.2,61.0')] ).

cnf(402,plain,
    ( ~ subset(u,v)
    | member(u,power_set(v)) ),
    inference(obv,[status(thm),theory(equality)],[392]),
    [iquote('0:Obv:392.1')] ).

cnf(408,plain,
    ( ~ subset(u,v)
    | ilf_type(u,subset_type(v)) ),
    inference(res,[status(thm),theory(equality)],[402,89]),
    [iquote('0:Res:402.1,89.0')] ).

cnf(412,plain,
    ~ subset(skc3,cross_product(skc4,skc5)),
    inference(res,[status(thm),theory(equality)],[408,75]),
    [iquote('0:Res:408.1,75.0')] ).

cnf(413,plain,
    $false,
    inference(mrr,[status(thm)],[412,9]),
    [iquote('0:MRR:412.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.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 Jul 10 08:18:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.48  
% 0.18/0.48  SPASS V 3.9 
% 0.18/0.48  SPASS beiseite: Proof found.
% 0.18/0.48  % SZS status Theorem
% 0.18/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.48  SPASS derived 317 clauses, backtracked 0 clauses, performed 0 splits and kept 274 clauses.
% 0.18/0.48  SPASS allocated 98040 KBytes.
% 0.18/0.48  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.48  		0:00:00.03 for the input.
% 0.18/0.48  		0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.48  		0:00:00.01 for inferences.
% 0.18/0.48  		0:00:00.00 for the backtracking.
% 0.18/0.48  		0:00:00.04 for the reduction.
% 0.18/0.48  
% 0.18/0.48  
% 0.18/0.48  Here is a proof with depth 4, length 25 :
% 0.18/0.48  % SZS output start Refutation
% See solution above
% 0.18/0.48  Formulae used in the proof : p18 prove_relset_1_3 p14 p10 p7 p12 p1 p5
% 0.18/0.48  
%------------------------------------------------------------------------------