TSTP Solution File: SET993+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SET993+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n015.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 00:15:44 EDT 2022

% Result   : Theorem 13.36s 3.03s
% Output   : CNFRefutation 13.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   53 (  17 unt;  15 nHn;  28 RR)
%            Number of literals    :  126 (  58 equ;  53 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :   91 (  14 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_9,plain,
    ( X1 = relation_rng(X2)
    | in(esk3_2(X2,X1),X1)
    | in(esk4_2(X2,X1),relation_dom(X2))
    | ~ function(X2)
    | ~ relation(X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_9) ).

cnf(i_0_47,plain,
    relation(esk14_2(X1,X2)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_47) ).

cnf(i_0_45,plain,
    relation_dom(esk14_2(X1,X2)) = X1,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_45) ).

cnf(i_0_46,plain,
    function(esk14_2(X1,X2)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_46) ).

cnf(i_0_8,plain,
    ( X1 = relation_rng(X2)
    | apply(X2,esk4_2(X2,X1)) = esk3_2(X2,X1)
    | in(esk3_2(X2,X1),X1)
    | ~ function(X2)
    | ~ relation(X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_8) ).

cnf(i_0_44,plain,
    ( apply(esk14_2(X1,X2),X3) = X2
    | ~ in(X3,X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_44) ).

cnf(i_0_2,plain,
    ( function(X1)
    | ~ empty(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_2) ).

cnf(i_0_17,plain,
    empty(empty_set),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_17) ).

cnf(i_0_16,plain,
    relation(empty_set),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_16) ).

cnf(i_0_26,plain,
    ( empty(relation_dom(X1))
    | ~ empty(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_26) ).

cnf(i_0_7,plain,
    ( X1 = X2
    | X3 != singleton(X2)
    | ~ in(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_7) ).

cnf(i_0_57,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_57) ).

cnf(i_0_6,plain,
    ( in(X1,X2)
    | X1 != X3
    | X2 != singleton(X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_6) ).

cnf(i_0_10,plain,
    ( X1 = relation_rng(X2)
    | esk3_2(X2,X1) != apply(X2,X3)
    | ~ function(X2)
    | ~ relation(X2)
    | ~ in(X3,relation_dom(X2))
    | ~ in(esk3_2(X2,X1),X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_10) ).

cnf(i_0_48,negated_conjecture,
    ( relation_dom(X1) != esk15_0
    | relation_rng(X1) != singleton(esk16_0)
    | ~ function(X1)
    | ~ relation(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_48) ).

cnf(i_0_49,negated_conjecture,
    esk15_0 != empty_set,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-fhn_qk85/input.p',i_0_49) ).

cnf(c_0_74,plain,
    ( X1 = relation_rng(X2)
    | in(esk3_2(X2,X1),X1)
    | in(esk4_2(X2,X1),relation_dom(X2))
    | ~ function(X2)
    | ~ relation(X2) ),
    i_0_9 ).

cnf(c_0_75,plain,
    relation(esk14_2(X1,X2)),
    i_0_47 ).

cnf(c_0_76,plain,
    relation_dom(esk14_2(X1,X2)) = X1,
    i_0_45 ).

cnf(c_0_77,plain,
    function(esk14_2(X1,X2)),
    i_0_46 ).

cnf(c_0_78,plain,
    ( X1 = relation_rng(X2)
    | apply(X2,esk4_2(X2,X1)) = esk3_2(X2,X1)
    | in(esk3_2(X2,X1),X1)
    | ~ function(X2)
    | ~ relation(X2) ),
    i_0_8 ).

cnf(c_0_79,plain,
    ( apply(esk14_2(X1,X2),X3) = X2
    | ~ in(X3,X1) ),
    i_0_44 ).

cnf(c_0_80,plain,
    ( X1 = relation_rng(esk14_2(X2,X3))
    | in(esk3_2(esk14_2(X2,X3),X1),X1)
    | in(esk4_2(esk14_2(X2,X3),X1),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77])]) ).

cnf(c_0_81,plain,
    ( function(X1)
    | ~ empty(X1) ),
    i_0_2 ).

cnf(c_0_82,plain,
    empty(empty_set),
    i_0_17 ).

cnf(c_0_83,plain,
    ( apply(esk14_2(X1,X2),esk4_2(esk14_2(X1,X2),X3)) = esk3_2(esk14_2(X1,X2),X3)
    | X3 = relation_rng(esk14_2(X1,X2))
    | in(esk3_2(esk14_2(X1,X2),X3),X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_75]),c_0_77])]) ).

cnf(c_0_84,plain,
    ( apply(esk14_2(X1,X2),esk4_2(esk14_2(X1,X3),X4)) = X2
    | X4 = relation_rng(esk14_2(X1,X3))
    | in(esk3_2(esk14_2(X1,X3),X4),X4) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_85,plain,
    relation(empty_set),
    i_0_16 ).

cnf(c_0_86,plain,
    function(empty_set),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_87,plain,
    ( empty(relation_dom(X1))
    | ~ empty(X1) ),
    i_0_26 ).

cnf(c_0_88,plain,
    ( X1 = X2
    | X3 != singleton(X2)
    | ~ in(X1,X3) ),
    i_0_7 ).

cnf(c_0_89,plain,
    ( esk3_2(esk14_2(X1,X2),X3) = X2
    | X3 = relation_rng(esk14_2(X1,X2))
    | in(esk3_2(esk14_2(X1,X2),X3),X3) ),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_90,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    i_0_57 ).

cnf(c_0_91,plain,
    ( X1 = relation_rng(empty_set)
    | in(esk4_2(empty_set,X1),relation_dom(empty_set))
    | in(esk3_2(empty_set,X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_85]),c_0_86])]) ).

cnf(c_0_92,plain,
    empty(relation_dom(empty_set)),
    inference(spm,[status(thm)],[c_0_87,c_0_82]) ).

cnf(c_0_93,plain,
    ( esk3_2(esk14_2(X1,X2),X3) = X2
    | esk3_2(esk14_2(X1,X2),X3) = X4
    | X3 = relation_rng(esk14_2(X1,X2))
    | X3 != singleton(X4) ),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_94,plain,
    ( in(X1,X2)
    | X1 != X3
    | X2 != singleton(X3) ),
    i_0_6 ).

cnf(c_0_95,plain,
    ( X1 = relation_rng(empty_set)
    | in(esk3_2(empty_set,X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).

cnf(c_0_96,plain,
    ( esk3_2(esk14_2(X1,X2),singleton(X3)) = X3
    | esk3_2(esk14_2(X1,X2),singleton(X3)) = X2
    | singleton(X3) = relation_rng(esk14_2(X1,X2)) ),
    inference(er,[status(thm)],[c_0_93]) ).

cnf(c_0_97,plain,
    ( in(X1,X2)
    | X2 != singleton(X1) ),
    inference(er,[status(thm)],[c_0_94]) ).

cnf(c_0_98,plain,
    ( X1 = relation_rng(empty_set)
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_90,c_0_95]) ).

cnf(c_0_99,plain,
    ( X1 = relation_rng(X2)
    | esk3_2(X2,X1) != apply(X2,X3)
    | ~ function(X2)
    | ~ relation(X2)
    | ~ in(X3,relation_dom(X2))
    | ~ in(esk3_2(X2,X1),X1) ),
    i_0_10 ).

cnf(c_0_100,plain,
    ( esk3_2(esk14_2(X1,X2),singleton(X2)) = X2
    | relation_rng(esk14_2(X1,X2)) = singleton(X2) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_96])]) ).

cnf(c_0_101,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_97]) ).

cnf(c_0_102,plain,
    relation_rng(empty_set) = empty_set,
    inference(spm,[status(thm)],[c_0_98,c_0_82]) ).

cnf(c_0_103,plain,
    ( relation_rng(esk14_2(X1,X2)) = singleton(X2)
    | ~ in(X3,X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_76]),c_0_75]),c_0_77])]),c_0_79]) ).

cnf(c_0_104,plain,
    ( X1 = empty_set
    | in(esk3_2(empty_set,X1),X1) ),
    inference(rw,[status(thm)],[c_0_95,c_0_102]) ).

cnf(c_0_105,negated_conjecture,
    ( relation_dom(X1) != esk15_0
    | relation_rng(X1) != singleton(esk16_0)
    | ~ function(X1)
    | ~ relation(X1) ),
    i_0_48 ).

cnf(c_0_106,plain,
    ( relation_rng(esk14_2(X1,X2)) = singleton(X2)
    | X1 = empty_set ),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_107,negated_conjecture,
    ( X1 = empty_set
    | singleton(X2) != singleton(esk16_0)
    | X1 != esk15_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_76]),c_0_75]),c_0_77])]) ).

cnf(c_0_108,negated_conjecture,
    ( X1 = empty_set
    | X1 != esk15_0 ),
    inference(er,[status(thm)],[c_0_107]) ).

cnf(c_0_109,negated_conjecture,
    esk15_0 != empty_set,
    i_0_49 ).

cnf(c_0_110,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_108]),c_0_109]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET993+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n015.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 03:28:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  # ENIGMATIC: Selected complete mode:
% 13.36/3.03  # ENIGMATIC: Solved by Enigma+tptp-cade20-model02-h2e15+lgb-t150-d30-l4800-e0.15+coop-paramils157:
% 13.36/3.03  # SinE strategy is GSinE(CountFormulas,hypos,5.0,,3,500,1.0)
% 13.36/3.03  # ENIGMA: LightGBM model '/export/starexec/sandbox2/solver/bin/data/Enigma/tptp-cade20-model02-h2e15/lgb-t150-d30-l4800-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 37; version: 991; iters: 150)
% 13.36/3.03  # Preprocessing time       : 0.758 s
% 13.36/3.03  
% 13.36/3.03  # Proof found!
% 13.36/3.03  # SZS status Theorem
% 13.36/3.03  # SZS output start CNFRefutation
% See solution above
% 13.36/3.03  # Training examples: 0 positive, 0 negative
% 13.36/3.03  
% 13.36/3.03  # -------------------------------------------------
% 13.36/3.03  # User time                : 0.703 s
% 13.36/3.03  # System time              : 0.098 s
% 13.36/3.03  # Total time               : 0.801 s
% 13.36/3.03  # ...preprocessing         : 0.758 s
% 13.36/3.03  # ...main loop             : 0.044 s
% 13.36/3.03  # Maximum resident set size: 151512 pages
% 13.36/3.03  
%------------------------------------------------------------------------------