TSTP Solution File: SEU187+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n007.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 09:17:37 EDT 2022

% Result   : Theorem 0.25s 1.44s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   45 (  18 unt;   0 def)
%            Number of atoms       :  116 (  42 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  125 (  54   ~;  48   |;  12   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   2 con; 0-3 aty)
%            Number of variables   :   67 (  17 sgn  40   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_xboole_0) ).

fof(t4_boole,axiom,
    ! [X1] : set_difference(empty_set,X1) = empty_set,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_boole) ).

fof(t65_zfmisc_1,lemma,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t65_zfmisc_1) ).

fof(d5_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_relat_1) ).

fof(fc4_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc4_relat_1) ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d4_relat_1) ).

fof(t60_relat_1,conjecture,
    ( relation_dom(empty_set) = empty_set
    & relation_rng(empty_set) = empty_set ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t60_relat_1) ).

fof(t3_xboole_1,lemma,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_xboole_1) ).

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

fof(c_0_10,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_11,plain,
    empty(esk12_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_12,plain,
    ! [X2] : set_difference(empty_set,X2) = empty_set,
    inference(variable_rename,[status(thm)],[t4_boole]) ).

cnf(c_0_13,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    empty(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,lemma,
    ! [X3,X4,X3,X4] :
      ( ( set_difference(X3,singleton(X4)) != X3
        | ~ in(X4,X3) )
      & ( in(X4,X3)
        | set_difference(X3,singleton(X4)) = X3 ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t65_zfmisc_1])])])])]) ).

cnf(c_0_16,plain,
    set_difference(empty_set,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    empty_set = esk12_0,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,lemma,
    ( ~ in(X1,X2)
    | set_difference(X2,singleton(X1)) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    set_difference(esk12_0,X1) = esk12_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).

fof(c_0_20,plain,
    ! [X5,X6,X7,X7,X9,X6,X11] :
      ( ( ~ in(X7,X6)
        | in(ordered_pair(esk2_3(X5,X6,X7),X7),X5)
        | X6 != relation_rng(X5)
        | ~ relation(X5) )
      & ( ~ in(ordered_pair(X9,X7),X5)
        | in(X7,X6)
        | X6 != relation_rng(X5)
        | ~ relation(X5) )
      & ( ~ in(esk3_2(X5,X6),X6)
        | ~ in(ordered_pair(X11,esk3_2(X5,X6)),X5)
        | X6 = relation_rng(X5)
        | ~ relation(X5) )
      & ( in(esk3_2(X5,X6),X6)
        | in(ordered_pair(esk4_2(X5,X6),esk3_2(X5,X6)),X5)
        | X6 = relation_rng(X5)
        | ~ relation(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)],[d5_relat_1])])])])])])]) ).

cnf(c_0_21,plain,
    relation(empty_set),
    inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).

cnf(c_0_22,lemma,
    ~ in(X1,esk12_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    ( in(ordered_pair(esk2_3(X1,X2,X3),X3),X1)
    | ~ relation(X1)
    | X2 != relation_rng(X1)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    relation(esk12_0),
    inference(rw,[status(thm)],[c_0_21,c_0_17]) ).

fof(c_0_25,plain,
    ! [X5,X6,X7,X7,X9,X6,X11] :
      ( ( ~ in(X7,X6)
        | in(ordered_pair(X7,esk5_3(X5,X6,X7)),X5)
        | X6 != relation_dom(X5)
        | ~ relation(X5) )
      & ( ~ in(ordered_pair(X7,X9),X5)
        | in(X7,X6)
        | X6 != relation_dom(X5)
        | ~ relation(X5) )
      & ( ~ in(esk6_2(X5,X6),X6)
        | ~ in(ordered_pair(esk6_2(X5,X6),X11),X5)
        | X6 = relation_dom(X5)
        | ~ relation(X5) )
      & ( in(esk6_2(X5,X6),X6)
        | in(ordered_pair(esk6_2(X5,X6),esk7_2(X5,X6)),X5)
        | X6 = relation_dom(X5)
        | ~ relation(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)],[d4_relat_1])])])])])])]) ).

fof(c_0_26,negated_conjecture,
    ~ ( relation_dom(empty_set) = empty_set
      & relation_rng(empty_set) = empty_set ),
    inference(assume_negation,[status(cth)],[t60_relat_1]) ).

fof(c_0_27,lemma,
    ! [X2] :
      ( ~ subset(X2,empty_set)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).

cnf(c_0_28,lemma,
    ( X1 != relation_rng(esk12_0)
    | ~ in(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

fof(c_0_29,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk8_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk8_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])])])])])])]) ).

cnf(c_0_30,plain,
    ( in(ordered_pair(X3,esk5_3(X1,X2,X3)),X1)
    | ~ relation(X1)
    | X2 != relation_dom(X1)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_31,negated_conjecture,
    ( relation_dom(empty_set) != empty_set
    | relation_rng(empty_set) != empty_set ),
    inference(fof_nnf,[status(thm)],[c_0_26]) ).

cnf(c_0_32,lemma,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,lemma,
    ~ in(X1,relation_rng(esk12_0)),
    inference(er,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    ( subset(X1,X2)
    | in(esk8_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,lemma,
    ( X1 != relation_dom(esk12_0)
    | ~ in(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_24])]) ).

cnf(c_0_36,negated_conjecture,
    ( relation_rng(empty_set) != empty_set
    | relation_dom(empty_set) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,lemma,
    ( X1 = esk12_0
    | ~ subset(X1,esk12_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_17]),c_0_17]) ).

cnf(c_0_38,lemma,
    subset(relation_rng(esk12_0),X1),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,lemma,
    ~ in(X1,relation_dom(esk12_0)),
    inference(er,[status(thm)],[c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    ( relation_dom(esk12_0) != esk12_0
    | relation_rng(esk12_0) != esk12_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).

cnf(c_0_41,lemma,
    relation_rng(esk12_0) = esk12_0,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,lemma,
    subset(relation_dom(esk12_0),X1),
    inference(spm,[status(thm)],[c_0_39,c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    relation_dom(esk12_0) != esk12_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).

cnf(c_0_44,lemma,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 01:45:58 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.25/1.44  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.44  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.44  # Preprocessing time       : 0.023 s
% 0.25/1.44  
% 0.25/1.44  # Proof found!
% 0.25/1.44  # SZS status Theorem
% 0.25/1.44  # SZS output start CNFRefutation
% See solution above
% 0.25/1.44  # Proof object total steps             : 45
% 0.25/1.44  # Proof object clause steps            : 25
% 0.25/1.44  # Proof object formula steps           : 20
% 0.25/1.44  # Proof object conjectures             : 6
% 0.25/1.44  # Proof object clause conjectures      : 3
% 0.25/1.44  # Proof object formula conjectures     : 3
% 0.25/1.44  # Proof object initial clauses used    : 10
% 0.25/1.44  # Proof object initial formulas used   : 10
% 0.25/1.44  # Proof object generating inferences   : 10
% 0.25/1.44  # Proof object simplifying inferences  : 16
% 0.25/1.44  # Training examples: 0 positive, 0 negative
% 0.25/1.44  # Parsed axioms                        : 167
% 0.25/1.44  # Removed by relevancy pruning/SinE    : 91
% 0.25/1.44  # Initial clauses                      : 128
% 0.25/1.44  # Removed in clause preprocessing      : 0
% 0.25/1.44  # Initial clauses in saturation        : 128
% 0.25/1.44  # Processed clauses                    : 218
% 0.25/1.44  # ...of these trivial                  : 5
% 0.25/1.44  # ...subsumed                          : 45
% 0.25/1.44  # ...remaining for further processing  : 168
% 0.25/1.44  # Other redundant clauses eliminated   : 33
% 0.25/1.44  # Clauses deleted for lack of memory   : 0
% 0.25/1.44  # Backward-subsumed                    : 0
% 0.25/1.44  # Backward-rewritten                   : 29
% 0.25/1.44  # Generated clauses                    : 722
% 0.25/1.44  # ...of the previous two non-trivial   : 553
% 0.25/1.44  # Contextual simplify-reflections      : 1
% 0.25/1.44  # Paramodulations                      : 665
% 0.25/1.44  # Factorizations                       : 10
% 0.25/1.44  # Equation resolutions                 : 47
% 0.25/1.44  # Current number of processed clauses  : 136
% 0.25/1.44  #    Positive orientable unit clauses  : 32
% 0.25/1.44  #    Positive unorientable unit clauses: 1
% 0.25/1.44  #    Negative unit clauses             : 10
% 0.25/1.44  #    Non-unit-clauses                  : 93
% 0.25/1.44  # Current number of unprocessed clauses: 355
% 0.25/1.44  # ...number of literals in the above   : 1078
% 0.25/1.44  # Current number of archived formulas  : 0
% 0.25/1.44  # Current number of archived clauses   : 29
% 0.25/1.44  # Clause-clause subsumption calls (NU) : 1450
% 0.25/1.44  # Rec. Clause-clause subsumption calls : 1138
% 0.25/1.44  # Non-unit clause-clause subsumptions  : 31
% 0.25/1.44  # Unit Clause-clause subsumption calls : 433
% 0.25/1.44  # Rewrite failures with RHS unbound    : 0
% 0.25/1.44  # BW rewrite match attempts            : 27
% 0.25/1.44  # BW rewrite match successes           : 11
% 0.25/1.44  # Condensation attempts                : 0
% 0.25/1.44  # Condensation successes               : 0
% 0.25/1.44  # Termbank termtop insertions          : 13390
% 0.25/1.44  
% 0.25/1.44  # -------------------------------------------------
% 0.25/1.44  # User time                : 0.036 s
% 0.25/1.44  # System time              : 0.004 s
% 0.25/1.44  # Total time               : 0.040 s
% 0.25/1.44  # Maximum resident set size: 3816 pages
%------------------------------------------------------------------------------