TSTP Solution File: SET980+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n008.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 00:55:51 EDT 2022

% Result   : Theorem 0.26s 1.44s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  129 (  57 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  135 (  54   ~;  62   |;  12   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   83 (  21 sgn  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t134_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
     => ( X1 = empty_set
        | X2 = empty_set
        | ( X1 = X3
          & X2 = X4 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t134_zfmisc_1) ).

fof(l55_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l55_zfmisc_1) ).

fof(t113_zfmisc_1,axiom,
    ! [X1,X2] :
      ( cartesian_product2(X1,X2) = empty_set
    <=> ( X1 = empty_set
        | X2 = empty_set ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t113_zfmisc_1) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_tarski) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
       => ( X1 = empty_set
          | X2 = empty_set
          | ( X1 = X3
            & X2 = X4 ) ) ),
    inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).

fof(c_0_6,plain,
    ! [X5,X6,X7,X8,X5,X6,X7,X8] :
      ( ( in(X5,X7)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( in(X6,X8)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0)
    & esk1_0 != empty_set
    & esk2_0 != empty_set
    & ( esk1_0 != esk3_0
      | esk2_0 != esk4_0 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X3,X4,X3,X4] :
      ( ( cartesian_product2(X3,X4) != empty_set
        | X3 = empty_set
        | X4 = empty_set )
      & ( X3 != empty_set
        | cartesian_product2(X3,X4) = empty_set )
      & ( X4 != empty_set
        | cartesian_product2(X3,X4) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])])])]) ).

cnf(c_0_9,plain,
    ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( in(X1,X3)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( X1 = empty_set
    | X2 = empty_set
    | cartesian_product2(X2,X1) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    esk2_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,negated_conjecture,
    esk1_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0))
    | ~ in(X2,esk2_0)
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_16,plain,
    ! [X3,X4,X3] :
      ( ( X3 != empty_set
        | ~ in(X4,X3) )
      & ( in(esk5_1(X3),X3)
        | X3 = empty_set ) ),
    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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( in(X1,esk1_0)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_18,negated_conjecture,
    cartesian_product2(esk3_0,esk4_0) != empty_set,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_13]),c_0_14]) ).

cnf(c_0_19,plain,
    ( cartesian_product2(X1,X2) = empty_set
    | X2 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X2,esk2_0)
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_21,plain,
    ( X1 = empty_set
    | in(esk5_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_22,plain,
    ! [X4,X5] :
      ( ( ~ in(esk6_2(X4,X5),X4)
        | ~ in(esk6_2(X4,X5),X5)
        | X4 = X5 )
      & ( in(esk6_2(X4,X5),X4)
        | in(esk6_2(X4,X5),X5)
        | X4 = X5 ) ),
    inference(distribute,[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)],[t2_tarski])])])])])]) ).

cnf(c_0_23,negated_conjecture,
    ( in(X1,esk1_0)
    | ~ in(X2,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_9]) ).

cnf(c_0_24,negated_conjecture,
    empty_set != esk4_0,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13]) ).

cnf(c_0_26,plain,
    ( X1 = X2
    | in(esk6_2(X1,X2),X2)
    | in(esk6_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( in(X2,X4)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | ~ in(esk6_2(X1,X2),X2)
    | ~ in(esk6_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( in(X1,esk1_0)
    | ~ in(X1,esk3_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( X1 = esk1_0
    | in(esk6_2(X1,esk1_0),esk3_0)
    | in(esk6_2(X1,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk2_0)
    | ~ in(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_15]) ).

cnf(c_0_32,negated_conjecture,
    ( X1 = esk1_0
    | ~ in(esk6_2(X1,esk1_0),esk3_0)
    | ~ in(esk6_2(X1,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ( esk1_0 = esk3_0
    | in(esk6_2(esk3_0,esk1_0),esk3_0) ),
    inference(ef,[status(thm)],[c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( esk2_0 = X1
    | in(esk6_2(esk2_0,X1),esk4_0)
    | in(esk6_2(esk2_0,X1),X1)
    | ~ in(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_31,c_0_26]) ).

cnf(c_0_35,negated_conjecture,
    esk1_0 = esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).

cnf(c_0_36,plain,
    ( cartesian_product2(X1,X2) = empty_set
    | X1 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_37,negated_conjecture,
    ( esk2_0 = X1
    | in(esk6_2(esk2_0,X1),esk4_0)
    | in(esk6_2(esk2_0,X1),X1)
    | ~ in(X2,esk3_0) ),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    empty_set != esk3_0,
    inference(spm,[status(thm)],[c_0_18,c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    ( esk2_0 != esk4_0
    | esk1_0 != esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_40,negated_conjecture,
    ( esk2_0 = X1
    | in(esk6_2(esk2_0,X1),esk4_0)
    | in(esk6_2(esk2_0,X1),X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    esk2_0 != esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35])]) ).

cnf(c_0_42,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(ordered_pair(X2,X1),cartesian_product2(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_10]) ).

cnf(c_0_43,negated_conjecture,
    in(esk6_2(esk2_0,esk4_0),esk4_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_40]),c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(X1,esk4_0)
    | ~ in(X2,esk3_0) ),
    inference(spm,[status(thm)],[c_0_42,c_0_9]) ).

cnf(c_0_45,negated_conjecture,
    ~ in(esk6_2(esk2_0,esk4_0),esk2_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(X1,esk4_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_38]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.14  % Command  : run_ET %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jul 10 20:08:38 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.26/1.44  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.44  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.44  # Preprocessing time       : 0.016 s
% 0.26/1.44  
% 0.26/1.44  # Proof found!
% 0.26/1.44  # SZS status Theorem
% 0.26/1.44  # SZS output start CNFRefutation
% See solution above
% 0.26/1.44  # Proof object total steps             : 48
% 0.26/1.44  # Proof object clause steps            : 37
% 0.26/1.44  # Proof object formula steps           : 11
% 0.26/1.44  # Proof object conjectures             : 31
% 0.26/1.44  # Proof object clause conjectures      : 28
% 0.26/1.44  # Proof object formula conjectures     : 3
% 0.26/1.44  # Proof object initial clauses used    : 13
% 0.26/1.44  # Proof object initial formulas used   : 5
% 0.26/1.44  # Proof object generating inferences   : 22
% 0.26/1.44  # Proof object simplifying inferences  : 14
% 0.26/1.44  # Training examples: 0 positive, 0 negative
% 0.26/1.44  # Parsed axioms                        : 12
% 0.26/1.44  # Removed by relevancy pruning/SinE    : 2
% 0.26/1.44  # Initial clauses                      : 19
% 0.26/1.44  # Removed in clause preprocessing      : 0
% 0.26/1.44  # Initial clauses in saturation        : 19
% 0.26/1.44  # Processed clauses                    : 205
% 0.26/1.44  # ...of these trivial                  : 3
% 0.26/1.44  # ...subsumed                          : 96
% 0.26/1.44  # ...remaining for further processing  : 106
% 0.26/1.44  # Other redundant clauses eliminated   : 0
% 0.26/1.44  # Clauses deleted for lack of memory   : 0
% 0.26/1.44  # Backward-subsumed                    : 9
% 0.26/1.44  # Backward-rewritten                   : 35
% 0.26/1.44  # Generated clauses                    : 294
% 0.26/1.44  # ...of the previous two non-trivial   : 300
% 0.26/1.44  # Contextual simplify-reflections      : 40
% 0.26/1.44  # Paramodulations                      : 284
% 0.26/1.44  # Factorizations                       : 8
% 0.26/1.44  # Equation resolutions                 : 2
% 0.26/1.44  # Current number of processed clauses  : 62
% 0.26/1.44  #    Positive orientable unit clauses  : 7
% 0.26/1.44  #    Positive unorientable unit clauses: 0
% 0.26/1.44  #    Negative unit clauses             : 13
% 0.26/1.44  #    Non-unit-clauses                  : 42
% 0.26/1.44  # Current number of unprocessed clauses: 12
% 0.26/1.44  # ...number of literals in the above   : 44
% 0.26/1.44  # Current number of archived formulas  : 0
% 0.26/1.44  # Current number of archived clauses   : 44
% 0.26/1.44  # Clause-clause subsumption calls (NU) : 2023
% 0.26/1.44  # Rec. Clause-clause subsumption calls : 1511
% 0.26/1.44  # Non-unit clause-clause subsumptions  : 98
% 0.26/1.44  # Unit Clause-clause subsumption calls : 184
% 0.26/1.44  # Rewrite failures with RHS unbound    : 0
% 0.26/1.44  # BW rewrite match attempts            : 2
% 0.26/1.44  # BW rewrite match successes           : 2
% 0.26/1.44  # Condensation attempts                : 0
% 0.26/1.44  # Condensation successes               : 0
% 0.26/1.44  # Termbank termtop insertions          : 4583
% 0.26/1.44  
% 0.26/1.44  # -------------------------------------------------
% 0.26/1.44  # User time                : 0.027 s
% 0.26/1.44  # System time              : 0.001 s
% 0.26/1.44  # Total time               : 0.028 s
% 0.26/1.44  # Maximum resident set size: 3040 pages
%------------------------------------------------------------------------------