TSTP Solution File: SET918+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.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 00:55:26 EDT 2022

% Result   : Theorem 0.23s 1.42s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   31 (  13 unt;   0 def)
%            Number of atoms       :  112 (  62 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  133 (  52   ~;  55   |;  20   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   81 (  15 sgn  47   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_xboole_0) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).

fof(t59_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
        & in(X2,X3)
        & X1 != X2 ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t59_zfmisc_1) ).

fof(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_tarski) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).

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

fof(c_0_6,plain,
    ! [X5,X6,X7,X8,X8,X5,X6,X7] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(esk4_3(X5,X6,X7),X7)
        | ~ in(esk4_3(X5,X6,X7),X5)
        | ~ in(esk4_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk4_3(X5,X6,X7),X5)
        | in(esk4_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk4_3(X5,X6,X7),X6)
        | in(esk4_3(X5,X6,X7),X7)
        | X7 = set_intersection2(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)],[d3_xboole_0])])])])])])]) ).

fof(c_0_7,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    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)],[d1_tarski])])])])])])]) ).

cnf(c_0_8,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
          & in(X2,X3)
          & X1 != X2 ),
    inference(assume_negation,[status(cth)],[t59_zfmisc_1]) ).

cnf(c_0_10,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_8]) ).

fof(c_0_12,negated_conjecture,
    ( set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0)
    & in(esk2_0,esk3_0)
    & esk1_0 != esk2_0 ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

fof(c_0_13,plain,
    ! [X5,X6,X7,X8,X8,X5,X6,X7] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk6_3(X5,X6,X7) != X5
        | ~ in(esk6_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk6_3(X5,X6,X7) != X6
        | ~ in(esk6_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X7)
        | esk6_3(X5,X6,X7) = X5
        | esk6_3(X5,X6,X7) = X6
        | X7 = unordered_pair(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_tarski])])])])])])]) ).

cnf(c_0_14,plain,
    ( X1 = X2
    | set_intersection2(X3,X4) != singleton(X1)
    | ~ in(X2,X4)
    | ~ in(X2,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    in(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(c_0_17,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_18,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( X1 = esk2_0
    | set_intersection2(X2,esk3_0) != singleton(X1)
    | ~ in(esk2_0,X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( in(X1,X2)
    | X2 != unordered_pair(X3,X1) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( X1 = esk2_0
    | set_intersection2(esk3_0,X2) != singleton(X1)
    | ~ in(esk2_0,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    singleton(esk1_0) = set_intersection2(esk3_0,unordered_pair(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    esk1_0 != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_27,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ( set_intersection2(esk3_0,X1) != set_intersection2(esk3_0,unordered_pair(esk2_0,esk1_0))
    | ~ in(esk2_0,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_29,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(spm,[status(thm)],[c_0_27,c_0_22]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 22:57:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.23/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42  # Preprocessing time       : 0.015 s
% 0.23/1.42  
% 0.23/1.42  # Proof found!
% 0.23/1.42  # SZS status Theorem
% 0.23/1.42  # SZS output start CNFRefutation
% See solution above
% 0.23/1.42  # Proof object total steps             : 31
% 0.23/1.42  # Proof object clause steps            : 18
% 0.23/1.42  # Proof object formula steps           : 13
% 0.23/1.42  # Proof object conjectures             : 11
% 0.23/1.42  # Proof object clause conjectures      : 8
% 0.23/1.42  # Proof object formula conjectures     : 3
% 0.23/1.42  # Proof object initial clauses used    : 8
% 0.23/1.42  # Proof object initial formulas used   : 6
% 0.23/1.42  # Proof object generating inferences   : 8
% 0.23/1.42  # Proof object simplifying inferences  : 6
% 0.23/1.42  # Training examples: 0 positive, 0 negative
% 0.23/1.42  # Parsed axioms                        : 10
% 0.23/1.42  # Removed by relevancy pruning/SinE    : 2
% 0.23/1.42  # Initial clauses                      : 23
% 0.23/1.42  # Removed in clause preprocessing      : 0
% 0.23/1.42  # Initial clauses in saturation        : 23
% 0.23/1.42  # Processed clauses                    : 121
% 0.23/1.42  # ...of these trivial                  : 1
% 0.23/1.42  # ...subsumed                          : 46
% 0.23/1.42  # ...remaining for further processing  : 74
% 0.23/1.42  # Other redundant clauses eliminated   : 6
% 0.23/1.42  # Clauses deleted for lack of memory   : 0
% 0.23/1.42  # Backward-subsumed                    : 0
% 0.23/1.42  # Backward-rewritten                   : 1
% 0.23/1.42  # Generated clauses                    : 219
% 0.23/1.42  # ...of the previous two non-trivial   : 191
% 0.23/1.42  # Contextual simplify-reflections      : 0
% 0.23/1.42  # Paramodulations                      : 196
% 0.23/1.42  # Factorizations                       : 4
% 0.23/1.42  # Equation resolutions                 : 19
% 0.23/1.42  # Current number of processed clauses  : 70
% 0.23/1.42  #    Positive orientable unit clauses  : 8
% 0.23/1.42  #    Positive unorientable unit clauses: 2
% 0.23/1.42  #    Negative unit clauses             : 8
% 0.23/1.42  #    Non-unit-clauses                  : 52
% 0.23/1.42  # Current number of unprocessed clauses: 93
% 0.23/1.42  # ...number of literals in the above   : 321
% 0.23/1.42  # Current number of archived formulas  : 0
% 0.23/1.42  # Current number of archived clauses   : 1
% 0.23/1.42  # Clause-clause subsumption calls (NU) : 1040
% 0.23/1.42  # Rec. Clause-clause subsumption calls : 945
% 0.23/1.42  # Non-unit clause-clause subsumptions  : 40
% 0.23/1.42  # Unit Clause-clause subsumption calls : 64
% 0.23/1.42  # Rewrite failures with RHS unbound    : 0
% 0.23/1.42  # BW rewrite match attempts            : 5
% 0.23/1.42  # BW rewrite match successes           : 4
% 0.23/1.42  # Condensation attempts                : 0
% 0.23/1.42  # Condensation successes               : 0
% 0.23/1.42  # Termbank termtop insertions          : 3326
% 0.23/1.42  
% 0.23/1.42  # -------------------------------------------------
% 0.23/1.42  # User time                : 0.016 s
% 0.23/1.42  # System time              : 0.006 s
% 0.23/1.42  # Total time               : 0.022 s
% 0.23/1.42  # Maximum resident set size: 3040 pages
%------------------------------------------------------------------------------