%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n006.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 08:38:15 EDT 2022

% Result   : Theorem 14.27s 3.42s
% Output   : CNFRefutation 14.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   52 (  11 unt;   6 nHn;  43 RR)
%            Number of literals    :  156 (  63 equ; 105 neg)
%            Maximal clause size   :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-4 aty)
%            Number of variables   :  128 (   9 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_22,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_22) ).

cnf(i_0_7,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_7) ).

cnf(i_0_13,plain,
    ( in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,X4,X1)),singleton(X1)),X2)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ in(X1,X4) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_13) ).

cnf(i_0_17,plain,
    ( X1 = X2
    | X3 != singleton(X2)
    | ~ in(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_17) ).

cnf(i_0_12,plain,
    ( in(esk1_4(X1,X2,X3,X4),X2)
    | X3 != relation_inverse_image(X1,X2)
    | ~ relation(X1)
    | ~ in(X4,X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_12) ).

cnf(i_0_18,plain,
    ( X1 = empty_set
    | in(esk5_1(X1),X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_18) ).

cnf(i_0_11,plain,
    ( in(X1,X2)
    | X2 != relation_inverse_image(X3,X4)
    | ~ relation(X3)
    | ~ in(X5,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_11) ).

cnf(i_0_23,plain,
    ( in(unordered_pair(unordered_pair(esk6_3(X1,X2,X3),X3),singleton(esk6_3(X1,X2,X3))),X1)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ in(X3,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_23) ).

cnf(i_0_16,plain,
    ( in(X1,X2)
    | X1 != X3
    | X2 != singleton(X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_16) ).

cnf(i_0_60,negated_conjecture,
    ( in(esk20_0,relation_rng(esk21_0))
    | relation_inverse_image(esk21_0,singleton(esk20_0)) != empty_set ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_60) ).

cnf(i_0_61,negated_conjecture,
    ( relation_inverse_image(esk21_0,singleton(esk20_0)) = empty_set
    | ~ in(esk20_0,relation_rng(esk21_0)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_61) ).

cnf(i_0_19,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_19) ).

cnf(i_0_62,negated_conjecture,
    relation(esk21_0),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kzhe1a9p/input.p',i_0_62) ).

cnf(c_0_76,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),X3) ),
    i_0_22 ).

cnf(c_0_77,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    i_0_7 ).

cnf(c_0_78,plain,
    ( in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,X4,X1)),singleton(X1)),X2)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ in(X1,X4) ),
    i_0_13 ).

cnf(c_0_79,plain,
    ( X1 = X2
    | X3 != singleton(X2)
    | ~ in(X1,X3) ),
    i_0_17 ).

cnf(c_0_80,plain,
    ( in(esk1_4(X1,X2,X3,X4),X2)
    | X3 != relation_inverse_image(X1,X2)
    | ~ relation(X1)
    | ~ in(X4,X3) ),
    i_0_12 ).

cnf(c_0_81,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),X3)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_82,plain,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_4(X2,X3,X4,X1))),X2)
    | X4 != relation_inverse_image(X2,X3)
    | ~ in(X1,X4)
    | ~ relation(X2) ),
    inference(rw,[status(thm)],[c_0_78,c_0_77]) ).

cnf(c_0_83,plain,
    ( esk1_4(X1,X2,X3,X4) = X5
    | X3 != relation_inverse_image(X1,X2)
    | X2 != singleton(X5)
    | ~ in(X4,X3)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_84,plain,
    ( in(esk1_4(X1,X2,X3,X4),X5)
    | X3 != relation_inverse_image(X1,X2)
    | X5 != relation_rng(X1)
    | ~ in(X4,X3)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_85,plain,
    ( esk1_4(X1,singleton(X2),X3,X4) = X2
    | X3 != relation_inverse_image(X1,singleton(X2))
    | ~ in(X4,X3)
    | ~ relation(X1) ),
    inference(er,[status(thm)],[c_0_83]) ).

cnf(c_0_86,plain,
    ( in(X1,X2)
    | X3 != relation_inverse_image(X4,singleton(X1))
    | X2 != relation_rng(X4)
    | ~ in(X5,X3)
    | ~ relation(X4) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_87,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ in(X4,relation_inverse_image(X3,singleton(X1)))
    | ~ relation(X3) ),
    inference(er,[status(thm)],[c_0_86]) ).

cnf(c_0_88,plain,
    ( X1 = empty_set
    | in(esk5_1(X1),X1) ),
    i_0_18 ).

cnf(c_0_89,plain,
    ( in(X1,X2)
    | X2 != relation_inverse_image(X3,X4)
    | ~ relation(X3)
    | ~ in(X5,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X3) ),
    i_0_11 ).

cnf(c_0_90,plain,
    ( in(unordered_pair(unordered_pair(esk6_3(X1,X2,X3),X3),singleton(esk6_3(X1,X2,X3))),X1)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ in(X3,X2) ),
    i_0_23 ).

cnf(c_0_91,plain,
    ( relation_inverse_image(X1,singleton(X2)) = empty_set
    | in(X2,X3)
    | X3 != relation_rng(X1)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_92,plain,
    ( in(X1,X2)
    | X1 != X3
    | X2 != singleton(X3) ),
    i_0_16 ).

cnf(c_0_93,plain,
    ( in(X1,X2)
    | X2 != relation_inverse_image(X3,X4)
    | ~ in(unordered_pair(unordered_pair(X5,X1),singleton(X1)),X3)
    | ~ in(X5,X4)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[c_0_89,c_0_77]) ).

cnf(c_0_94,plain,
    ( in(unordered_pair(unordered_pair(X1,esk6_3(X2,X3,X1)),singleton(esk6_3(X2,X3,X1))),X2)
    | X3 != relation_rng(X2)
    | ~ in(X1,X3)
    | ~ relation(X2) ),
    inference(rw,[status(thm)],[c_0_90,c_0_77]) ).

cnf(c_0_95,negated_conjecture,
    ( in(esk20_0,relation_rng(esk21_0))
    | relation_inverse_image(esk21_0,singleton(esk20_0)) != empty_set ),
    i_0_60 ).

cnf(c_0_96,plain,
    ( relation_inverse_image(X1,singleton(X2)) = empty_set
    | in(X2,relation_rng(X1))
    | ~ relation(X1) ),
    inference(er,[status(thm)],[c_0_91]) ).

cnf(c_0_97,plain,
    ( in(X1,X2)
    | X2 != singleton(X1) ),
    inference(er,[status(thm)],[c_0_92]) ).

cnf(c_0_98,plain,
    ( in(esk6_3(X1,X2,X3),X4)
    | X4 != relation_inverse_image(X1,X5)
    | X2 != relation_rng(X1)
    | ~ in(X3,X5)
    | ~ in(X3,X2)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_99,negated_conjecture,
    ( relation_inverse_image(esk21_0,singleton(esk20_0)) = empty_set
    | ~ in(esk20_0,relation_rng(esk21_0)) ),
    i_0_61 ).

cnf(c_0_100,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    i_0_19 ).

cnf(c_0_101,negated_conjecture,
    ( in(esk20_0,relation_rng(esk21_0))
    | ~ relation(esk21_0) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_102,negated_conjecture,
    relation(esk21_0),
    i_0_62 ).

cnf(c_0_103,plain,
    ( esk5_1(X1) = X2
    | X1 = empty_set
    | X1 != singleton(X2) ),
    inference(spm,[status(thm)],[c_0_79,c_0_88]) ).

cnf(c_0_104,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_97]) ).

cnf(c_0_105,negated_conjecture,
    ( X1 != relation_rng(esk21_0)
    | X2 != empty_set
    | ~ in(esk20_0,relation_rng(esk21_0))
    | ~ in(X3,singleton(esk20_0))
    | ~ in(X3,X1)
    | ~ relation(esk21_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).

cnf(c_0_106,negated_conjecture,
    in(esk20_0,relation_rng(esk21_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).

cnf(c_0_107,plain,
    ( esk5_1(singleton(X1)) = X1
    | singleton(X1) = empty_set ),
    inference(er,[status(thm)],[c_0_103]) ).

cnf(c_0_108,plain,
    singleton(X1) != empty_set,
    inference(spm,[status(thm)],[c_0_100,c_0_104]) ).

cnf(c_0_109,negated_conjecture,
    ( X1 != relation_rng(esk21_0)
    | X2 != empty_set
    | ~ in(X3,singleton(esk20_0))
    | ~ in(X3,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_102])]),c_0_106])]) ).

cnf(c_0_110,plain,
    esk5_1(singleton(X1)) = X1,
    inference(sr,[status(thm)],[c_0_107,c_0_108]) ).

cnf(c_0_111,plain,
    ( X1 != relation_rng(esk21_0)
    | X2 != empty_set
    | ~ in(esk20_0,X1) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_88]),c_0_110]),c_0_108]) ).

cnf(c_0_112,negated_conjecture,
    relation_inverse_image(esk21_0,singleton(esk20_0)) = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_106])]) ).

cnf(c_0_113,negated_conjecture,
    X1 != empty_set,
    inference(spm,[status(thm)],[c_0_111,c_0_106]) ).

cnf(c_0_114,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_112,c_0_113]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command  : enigmatic-eprover.py %s %d 1
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jun 19 19:49:12 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.48  # ENIGMATIC: Selected complete mode:
% 14.27/3.42  # ENIGMATIC: Solved by Enigma+tptp-cade20-model02-h2e15+lgb-t150-d30-l6400-e0.15+coop-mzr02:
% 14.27/3.42  # ENIGMA: LightGBM model '/export/starexec/sandbox2/solver/bin/data/Enigma/tptp-cade20-model02-h2e15/lgb-t150-d30-l6400-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 53; version: 991; iters: 150)
% 14.27/3.42  # Preprocessing time       : 0.853 s
% 14.27/3.42  
% 14.27/3.42  # Proof found!
% 14.27/3.42  # SZS status Theorem
% 14.27/3.42  # SZS output start CNFRefutation
% See solution above
% 14.27/3.42  # Training examples: 0 positive, 0 negative
% 14.27/3.42  
% 14.27/3.42  # -------------------------------------------------
% 14.27/3.42  # User time                : 0.775 s
% 14.27/3.42  # System time              : 0.112 s
% 14.27/3.42  # Total time               : 0.887 s
% 14.27/3.42  # ...preprocessing         : 0.853 s
% 14.27/3.42  # ...main loop             : 0.033 s
% 14.27/3.42  # Maximum resident set size: 168736 pages
% 14.27/3.42  
%------------------------------------------------------------------------------