TSTP Solution File: SEU180+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% 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 09:17:32 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   46 (  21 unt;   0 def)
%            Number of atoms       :  117 (  21 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  118 (  47   ~;  47   |;  13   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :   89 (  14 sgn  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_tarski) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t69_enumset1) ).

fof(t30_relat_1,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_field(X3))
          & in(X2,relation_field(X3)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t30_relat_1) ).

fof(t20_relat_1,lemma,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t20_relat_1) ).

fof(d6_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d6_relat_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).

fof(t7_xboole_1,lemma,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_xboole_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_xboole_0) ).

fof(c_0_9,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_10,lemma,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(ordered_pair(X1,X2),X3)
         => ( in(X1,relation_field(X3))
            & in(X2,relation_field(X3)) ) ) ),
    inference(assume_negation,[status(cth)],[t30_relat_1]) ).

fof(c_0_12,lemma,
    ! [X4,X5,X6] :
      ( ( in(X4,relation_dom(X6))
        | ~ in(ordered_pair(X4,X5),X6)
        | ~ relation(X6) )
      & ( in(X5,relation_rng(X6))
        | ~ in(ordered_pair(X4,X5),X6)
        | ~ relation(X6) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).

cnf(c_0_13,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,negated_conjecture,
    ( relation(esk3_0)
    & in(ordered_pair(esk1_0,esk2_0),esk3_0)
    & ( ~ in(esk1_0,relation_field(esk3_0))
      | ~ in(esk2_0,relation_field(esk3_0)) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_16,plain,
    ! [X2] :
      ( ~ relation(X2)
      | relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).

fof(c_0_17,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk4_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).

fof(c_0_18,lemma,
    ! [X3,X4] : subset(X3,set_union2(X3,X4)),
    inference(variable_rename,[status(thm)],[t7_xboole_1]) ).

cnf(c_0_19,lemma,
    ( in(X2,relation_dom(X1))
    | ~ relation(X1)
    | ~ in(ordered_pair(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_21,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_22,negated_conjecture,
    in(ordered_pair(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ in(esk2_0,relation_field(esk3_0))
    | ~ in(esk1_0,relation_field(esk3_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_26,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,lemma,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,lemma,
    ( in(X2,relation_dom(X1))
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,negated_conjecture,
    in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),esk3_0),
    inference(rw,[status(thm)],[c_0_22,c_0_20]) ).

cnf(c_0_31,lemma,
    ( in(X3,relation_rng(X1))
    | ~ relation(X1)
    | ~ in(ordered_pair(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ in(esk1_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0)))
    | ~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_33,lemma,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,lemma,
    ( in(X1,relation_dom(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X1,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),esk3_0),
    inference(rw,[status(thm)],[c_0_30,c_0_29]) ).

fof(c_0_36,plain,
    ! [X5,X6,X7,X8,X8,X5,X6,X7] :
      ( ( ~ in(X8,X7)
        | in(X8,X5)
        | in(X8,X6)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(esk11_3(X5,X6,X7),X5)
        | ~ in(esk11_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( ~ in(esk11_3(X5,X6,X7),X6)
        | ~ in(esk11_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( in(esk11_3(X5,X6,X7),X7)
        | in(esk11_3(X5,X6,X7),X5)
        | in(esk11_3(X5,X6,X7),X6)
        | X7 = set_union2(X5,X6) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])])]) ).

cnf(c_0_37,lemma,
    ( in(X3,relation_rng(X1))
    | ~ relation(X1)
    | ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
    inference(rw,[status(thm)],[c_0_31,c_0_20]) ).

cnf(c_0_38,negated_conjecture,
    ( ~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0)))
    | ~ in(esk1_0,relation_dom(esk3_0)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    in(esk1_0,relation_dom(esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25])]) ).

cnf(c_0_40,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,lemma,
    ( in(X1,relation_rng(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X3,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_29]) ).

cnf(c_0_42,negated_conjecture,
    ~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).

cnf(c_0_43,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    in(esk2_0,relation_rng(esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_25])]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n020.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 Jun 19 14:07:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.025 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 46
% 0.22/1.40  # Proof object clause steps            : 27
% 0.22/1.40  # Proof object formula steps           : 19
% 0.22/1.40  # Proof object conjectures             : 14
% 0.22/1.40  # Proof object clause conjectures      : 11
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 12
% 0.22/1.40  # Proof object initial formulas used   : 9
% 0.22/1.40  # Proof object generating inferences   : 9
% 0.22/1.40  # Proof object simplifying inferences  : 15
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 150
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 63
% 0.22/1.40  # Initial clauses                      : 158
% 0.22/1.40  # Removed in clause preprocessing      : 2
% 0.22/1.40  # Initial clauses in saturation        : 156
% 0.22/1.40  # Processed clauses                    : 1115
% 0.22/1.40  # ...of these trivial                  : 43
% 0.22/1.40  # ...subsumed                          : 636
% 0.22/1.40  # ...remaining for further processing  : 436
% 0.22/1.40  # Other redundant clauses eliminated   : 60
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 8
% 0.22/1.40  # Backward-rewritten                   : 47
% 0.22/1.40  # Generated clauses                    : 4285
% 0.22/1.40  # ...of the previous two non-trivial   : 3329
% 0.22/1.40  # Contextual simplify-reflections      : 29
% 0.22/1.40  # Paramodulations                      : 4177
% 0.22/1.40  # Factorizations                       : 10
% 0.22/1.40  # Equation resolutions                 : 96
% 0.22/1.40  # Current number of processed clauses  : 374
% 0.22/1.40  #    Positive orientable unit clauses  : 69
% 0.22/1.40  #    Positive unorientable unit clauses: 2
% 0.22/1.40  #    Negative unit clauses             : 36
% 0.22/1.40  #    Non-unit-clauses                  : 267
% 0.22/1.40  # Current number of unprocessed clauses: 2169
% 0.22/1.40  # ...number of literals in the above   : 6726
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 59
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 31296
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 27308
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 419
% 0.22/1.40  # Unit Clause-clause subsumption calls : 4530
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 70
% 0.22/1.40  # BW rewrite match successes           : 40
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 48445
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.111 s
% 0.22/1.40  # System time              : 0.008 s
% 0.22/1.40  # Total time               : 0.119 s
% 0.22/1.40  # Maximum resident set size: 5996 pages
%------------------------------------------------------------------------------