TSTP Solution File: SET707+4 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET707+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n029.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 00:53:16 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   55 (  12 unt;   0 def)
%            Number of atoms       :  127 (  67 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  107 (  35   ~;  54   |;  11   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   67 (  13 sgn  37   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thI50,conjecture,
    ! [X1,X2,X6,X7] :
      ( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
     => ( X1 = X6
        & X2 = X7 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thI50) ).

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

fof(unordered_pair,axiom,
    ! [X3,X1,X2] :
      ( member(X3,unordered_pair(X1,X2))
    <=> ( X3 = X1
        | X3 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).

fof(singleton,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X6,X7] :
        ( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
       => ( X1 = X6
          & X2 = X7 ) ),
    inference(assume_negation,[status(cth)],[thI50]) ).

fof(c_0_6,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)))
    & ( 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,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk5_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk5_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)],[subset])])])])])])]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ member(X4,unordered_pair(X5,X6))
        | X4 = X5
        | X4 = X6 )
      & ( X4 != X5
        | member(X4,unordered_pair(X5,X6)) )
      & ( X4 != X6
        | member(X4,unordered_pair(X5,X6)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])])])]) ).

cnf(c_0_12,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    subset(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_14,plain,
    ! [X4,X5,X4,X5] :
      ( ( ~ member(X4,singleton(X5))
        | X4 = X5 )
      & ( X4 != X5
        | member(X4,singleton(X5)) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])])]) ).

cnf(c_0_15,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    ( member(X1,unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)))
    | ~ member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    ( member(X1,unordered_pair(X2,X3))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( member(X1,singleton(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    ( X1 = unordered_pair(esk3_0,esk4_0)
    | X1 = singleton(esk3_0)
    | ~ member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    member(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( singleton(esk1_0) = unordered_pair(esk3_0,esk4_0)
    | singleton(esk3_0) = singleton(esk1_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,plain,
    ( subset(X2,X1)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_25,negated_conjecture,
    ( singleton(esk1_0) = unordered_pair(esk3_0,esk4_0)
    | member(esk3_0,singleton(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    subset(unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_23,c_0_10]) ).

cnf(c_0_27,plain,
    ( member(X1,unordered_pair(X2,X3))
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_28,negated_conjecture,
    ( singleton(esk1_0) = unordered_pair(esk3_0,esk4_0)
    | esk3_0 = esk1_0 ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)))
    | ~ member(X1,unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_26]) ).

cnf(c_0_30,plain,
    member(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( esk3_0 = esk1_0
    | member(esk1_0,unordered_pair(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    member(unordered_pair(esk3_0,esk4_0),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | singleton(esk3_0) = unordered_pair(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( esk3_0 = esk1_0
    | esk1_0 = esk4_0 ),
    inference(spm,[status(thm)],[c_0_15,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | singleton(esk1_0) = unordered_pair(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_15,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | singleton(esk1_0) = unordered_pair(esk1_0,esk2_0)
    | esk1_0 = esk4_0 ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    ( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | esk1_0 = esk4_0 ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_38,negated_conjecture,
    ( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
    | esk1_0 = esk4_0 ),
    inference(spm,[status(thm)],[c_0_37,c_0_34]) ).

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,
    ( esk1_0 = esk4_0
    | member(esk4_0,unordered_pair(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    ( esk1_0 = esk4_0
    | esk4_0 != esk2_0 ),
    inference(spm,[status(thm)],[c_0_39,c_0_34]) ).

cnf(c_0_42,negated_conjecture,
    esk1_0 = esk4_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_40]),c_0_41]) ).

cnf(c_0_43,negated_conjecture,
    ( singleton(esk4_0) = unordered_pair(esk3_0,esk4_0)
    | esk3_0 = esk4_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_42]),c_0_42]) ).

cnf(c_0_44,negated_conjecture,
    ( esk3_0 = esk4_0
    | X1 = esk4_0
    | ~ member(X1,unordered_pair(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_43]) ).

cnf(c_0_45,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk4_0,esk2_0)
    | singleton(esk3_0) = unordered_pair(esk4_0,esk2_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_42]),c_0_42]) ).

cnf(c_0_46,negated_conjecture,
    esk3_0 = esk4_0,
    inference(spm,[status(thm)],[c_0_44,c_0_20]) ).

cnf(c_0_47,negated_conjecture,
    ( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk4_0,esk2_0)
    | singleton(esk4_0) = unordered_pair(esk3_0,esk4_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_42]),c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk2_0)
    | singleton(esk4_0) = unordered_pair(esk4_0,esk2_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]) ).

cnf(c_0_49,negated_conjecture,
    ( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk2_0)
    | singleton(esk4_0) = unordered_pair(esk4_0,esk4_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_46]),c_0_46]) ).

cnf(c_0_50,negated_conjecture,
    unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk2_0),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_51,negated_conjecture,
    ( esk3_0 != esk4_0
    | esk4_0 != esk2_0 ),
    inference(rw,[status(thm)],[c_0_39,c_0_42]) ).

cnf(c_0_52,negated_conjecture,
    ( X1 = esk4_0
    | ~ member(X1,unordered_pair(esk4_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    esk4_0 != esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_46])]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_53]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET707+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 01:32:16 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.015 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 55
% 0.23/1.41  # Proof object clause steps            : 44
% 0.23/1.41  # Proof object formula steps           : 11
% 0.23/1.41  # Proof object conjectures             : 36
% 0.23/1.41  # Proof object clause conjectures      : 33
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 10
% 0.23/1.41  # Proof object initial formulas used   : 5
% 0.23/1.41  # Proof object generating inferences   : 24
% 0.23/1.41  # Proof object simplifying inferences  : 18
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 12
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 7
% 0.23/1.41  # Initial clauses                      : 13
% 0.23/1.41  # Removed in clause preprocessing      : 0
% 0.23/1.41  # Initial clauses in saturation        : 13
% 0.23/1.41  # Processed clauses                    : 113
% 0.23/1.41  # ...of these trivial                  : 7
% 0.23/1.41  # ...subsumed                          : 12
% 0.23/1.41  # ...remaining for further processing  : 94
% 0.23/1.41  # Other redundant clauses eliminated   : 5
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 9
% 0.23/1.41  # Backward-rewritten                   : 51
% 0.23/1.41  # Generated clauses                    : 423
% 0.23/1.41  # ...of the previous two non-trivial   : 394
% 0.23/1.41  # Contextual simplify-reflections      : 6
% 0.23/1.41  # Paramodulations                      : 413
% 0.23/1.41  # Factorizations                       : 5
% 0.23/1.41  # Equation resolutions                 : 5
% 0.23/1.41  # Current number of processed clauses  : 31
% 0.23/1.41  #    Positive orientable unit clauses  : 8
% 0.23/1.41  #    Positive unorientable unit clauses: 0
% 0.23/1.41  #    Negative unit clauses             : 1
% 0.23/1.41  #    Non-unit-clauses                  : 22
% 0.23/1.41  # Current number of unprocessed clauses: 22
% 0.23/1.41  # ...number of literals in the above   : 56
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 60
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 262
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 230
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 25
% 0.23/1.41  # Unit Clause-clause subsumption calls : 25
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 20
% 0.23/1.41  # BW rewrite match successes           : 4
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 7470
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.023 s
% 0.23/1.41  # System time              : 0.004 s
% 0.23/1.41  # Total time               : 0.027 s
% 0.23/1.41  # Maximum resident set size: 2940 pages
%------------------------------------------------------------------------------