TSTP Solution File: SET656+3 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n003.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 00:13:14 EDT 2022

% Result   : Theorem 9.02s 2.41s
% Output   : CNFRefutation 9.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   72 (  14 unt;  25 nHn;  53 RR)
%            Number of literals    :  214 (  22 equ; 121 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :  135 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_11,plain,
    ( member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_11) ).

cnf(i_0_65,plain,
    ilf_type(X1,set_type),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_65) ).

cnf(i_0_47,plain,
    ( X1 = X2
    | member(esk11_2(X1,X2),X2)
    | member(esk11_2(X1,X2),X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_47) ).

cnf(i_0_13,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_13) ).

cnf(i_0_61,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_61) ).

cnf(i_0_10,plain,
    ( member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(X1,intersection(X3,X2)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_10) ).

cnf(i_0_29,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,subset_type(X2)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_29) ).

cnf(i_0_67,negated_conjecture,
    ilf_type(esk18_0,relation_type(esk16_0,esk17_0)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_67) ).

cnf(i_0_44,plain,
    ( empty(X1)
    | ilf_type(X2,member_type(X1))
    | ~ member(X2,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_44) ).

cnf(i_0_41,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,power_set(X2)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_41) ).

cnf(i_0_39,plain,
    ( member(X1,power_set(X2))
    | member(esk9_2(X1,X2),X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_39) ).

cnf(i_0_45,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X2,member_type(X1)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_45) ).

cnf(i_0_43,plain,
    ( ~ empty(power_set(X1))
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_43) ).

cnf(i_0_22,plain,
    ( intersection(X1,X2) = intersection(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_22) ).

cnf(i_0_9,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_9) ).

cnf(i_0_38,plain,
    ( member(X1,power_set(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(esk9_2(X1,X2),X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_38) ).

cnf(i_0_48,plain,
    ( X1 = X2
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(esk11_2(X1,X2),X2)
    | ~ member(esk11_2(X1,X2),X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_48) ).

cnf(i_0_66,negated_conjecture,
    intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-9bwef34t/lgb.p',i_0_66) ).

cnf(c_0_86,plain,
    ( member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(X1,intersection(X2,X3)) ),
    i_0_11 ).

cnf(c_0_87,plain,
    ilf_type(X1,set_type),
    i_0_65 ).

cnf(c_0_88,plain,
    ( X1 = X2
    | member(esk11_2(X1,X2),X2)
    | member(esk11_2(X1,X2),X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    i_0_47 ).

cnf(c_0_89,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    i_0_13 ).

cnf(c_0_90,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    i_0_61 ).

cnf(c_0_91,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_87]),c_0_87])]) ).

cnf(c_0_92,plain,
    ( X1 = X2
    | member(esk11_2(X1,X2),X1)
    | member(esk11_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_87]),c_0_87])]) ).

cnf(c_0_93,plain,
    ( member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(X1,intersection(X3,X2)) ),
    i_0_10 ).

cnf(c_0_94,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,subset_type(X2)) ),
    i_0_29 ).

cnf(c_0_95,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_87]),c_0_87])]) ).

cnf(c_0_96,negated_conjecture,
    ilf_type(esk18_0,relation_type(esk16_0,esk17_0)),
    i_0_67 ).

cnf(c_0_97,plain,
    ( empty(X1)
    | ilf_type(X2,member_type(X1))
    | ~ member(X2,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    i_0_44 ).

cnf(c_0_98,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_87]),c_0_87])]) ).

cnf(c_0_99,plain,
    ( X1 = intersection(X2,X3)
    | member(esk11_2(X1,intersection(X2,X3)),X1)
    | member(esk11_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_100,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_87]),c_0_87]),c_0_87])]) ).

cnf(c_0_101,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,power_set(X2)) ),
    i_0_41 ).

cnf(c_0_102,plain,
    ( member(X1,power_set(X2))
    | member(esk9_2(X1,X2),X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    i_0_39 ).

cnf(c_0_103,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X2,member_type(X1)) ),
    i_0_45 ).

cnf(c_0_104,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,subset_type(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_87]),c_0_87])]) ).

cnf(c_0_105,negated_conjecture,
    ilf_type(esk18_0,subset_type(cross_product(esk16_0,esk17_0))),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_106,plain,
    ( ~ empty(power_set(X1))
    | ~ ilf_type(X1,set_type) ),
    i_0_43 ).

cnf(c_0_107,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_87]),c_0_87])]),c_0_98]) ).

cnf(c_0_108,plain,
    ( intersection(X1,X2) = X1
    | member(esk11_2(X1,intersection(X1,X2)),X1) ),
    inference(ef,[status(thm)],[c_0_99]) ).

cnf(c_0_109,plain,
    ( intersection(X1,X2) = intersection(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    i_0_22 ).

cnf(c_0_110,plain,
    ( intersection(X1,X2) = X3
    | member(esk11_2(intersection(X1,X2),X3),X3)
    | member(esk11_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_100,c_0_92]) ).

cnf(c_0_111,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    i_0_9 ).

cnf(c_0_112,plain,
    ( member(X1,X2)
    | ~ member(X3,power_set(X2))
    | ~ member(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_87]),c_0_87]),c_0_87])]) ).

cnf(c_0_113,plain,
    ( member(esk9_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_87]),c_0_87])]) ).

cnf(c_0_114,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X2,member_type(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_87]),c_0_87])]) ).

cnf(c_0_115,plain,
    ilf_type(esk18_0,member_type(power_set(cross_product(esk16_0,esk17_0)))),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_116,plain,
    ~ empty(power_set(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_87])]) ).

cnf(c_0_117,plain,
    ( intersection(X1,X2) = X1
    | ilf_type(esk11_2(X1,intersection(X1,X2)),member_type(X1)) ),
    inference(spm,[status(thm)],[c_0_107,c_0_108]) ).

cnf(c_0_118,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_87]),c_0_87])]) ).

cnf(c_0_119,plain,
    ( intersection(X1,X2) = X2
    | member(esk11_2(intersection(X1,X2),X2),X2) ),
    inference(ef,[status(thm)],[c_0_110]) ).

cnf(c_0_120,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_87]),c_0_87]),c_0_87])]) ).

cnf(c_0_121,plain,
    ( member(esk9_2(X1,X2),X3)
    | member(X1,power_set(X2))
    | ~ member(X1,power_set(X3)) ),
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

cnf(c_0_122,plain,
    member(esk18_0,power_set(cross_product(esk16_0,esk17_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).

cnf(c_0_123,plain,
    ( intersection(X1,X2) = X2
    | ilf_type(esk11_2(X2,intersection(X1,X2)),member_type(X2)) ),
    inference(spm,[status(thm)],[c_0_117,c_0_118]) ).

cnf(c_0_124,plain,
    ( intersection(X1,X2) = X2
    | ~ empty(X2) ),
    inference(spm,[status(thm)],[c_0_98,c_0_119]) ).

cnf(c_0_125,plain,
    ( member(X1,power_set(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(esk9_2(X1,X2),X2) ),
    i_0_38 ).

cnf(c_0_126,plain,
    ( member(esk9_2(X1,X2),intersection(X3,X1))
    | member(X1,power_set(X2))
    | ~ member(esk9_2(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_120,c_0_113]) ).

cnf(c_0_127,plain,
    ( member(esk9_2(esk18_0,X1),cross_product(esk16_0,esk17_0))
    | member(esk18_0,power_set(X1)) ),
    inference(spm,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_128,plain,
    ( intersection(X1,X2) = X2
    | member(esk11_2(X2,intersection(X1,X2)),X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_123]),c_0_124]) ).

cnf(c_0_129,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk9_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_87]),c_0_87])]) ).

cnf(c_0_130,plain,
    ( member(esk9_2(esk18_0,X1),intersection(esk18_0,cross_product(esk16_0,esk17_0)))
    | member(esk18_0,power_set(X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_118]) ).

cnf(c_0_131,plain,
    ( intersection(X1,X2) = X2
    | member(esk11_2(X2,intersection(X1,X2)),X3)
    | ~ member(X2,power_set(X3)) ),
    inference(spm,[status(thm)],[c_0_112,c_0_128]) ).

cnf(c_0_132,plain,
    member(esk18_0,power_set(intersection(esk18_0,cross_product(esk16_0,esk17_0)))),
    inference(spm,[status(thm)],[c_0_129,c_0_130]) ).

cnf(c_0_133,plain,
    ( X1 = X2
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(esk11_2(X1,X2),X2)
    | ~ member(esk11_2(X1,X2),X1) ),
    i_0_48 ).

cnf(c_0_134,plain,
    ( intersection(X1,esk18_0) = esk18_0
    | member(esk11_2(esk18_0,intersection(X1,esk18_0)),intersection(esk18_0,cross_product(esk16_0,esk17_0))) ),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_135,plain,
    ( X1 = X2
    | ~ member(esk11_2(X1,X2),X2)
    | ~ member(esk11_2(X1,X2),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_87]),c_0_87])]) ).

cnf(c_0_136,plain,
    ( intersection(esk18_0,X1) = esk18_0
    | member(esk11_2(esk18_0,intersection(esk18_0,X1)),intersection(esk18_0,cross_product(esk16_0,esk17_0))) ),
    inference(spm,[status(thm)],[c_0_134,c_0_118]) ).

cnf(c_0_137,negated_conjecture,
    intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0,
    i_0_66 ).

cnf(c_0_138,plain,
    ~ member(esk11_2(esk18_0,intersection(esk18_0,cross_product(esk16_0,esk17_0))),esk18_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).

cnf(c_0_139,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_108]),c_0_137]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n003.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 20:31:01 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  # ENIGMATIC: Selected complete mode:
% 9.02/2.41  # ENIGMATIC: Solved by autoschedule-lgb:
% 9.02/2.41  # No SInE strategy applied
% 9.02/2.41  # Trying AutoSched0 for 150 seconds
% 9.02/2.41  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 9.02/2.41  # and selection function SelectCQArNTNpEqFirst.
% 9.02/2.41  #
% 9.02/2.41  # Preprocessing time       : 0.013 s
% 9.02/2.41  # Presaturation interreduction done
% 9.02/2.41  
% 9.02/2.41  # Proof found!
% 9.02/2.41  # SZS status Theorem
% 9.02/2.41  # SZS output start CNFRefutation
% See solution above
% 9.02/2.41  # Training examples: 0 positive, 0 negative
% 9.02/2.41  
% 9.02/2.41  # -------------------------------------------------
% 9.02/2.41  # User time                : 0.161 s
% 9.02/2.41  # System time              : 0.012 s
% 9.02/2.41  # Total time               : 0.174 s
% 9.02/2.41  # Maximum resident set size: 7124 pages
% 9.02/2.41  
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