TSTP Solution File: SEU110+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% 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 09:16:51 EDT 2022

% Result   : Theorem 0.23s 2.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (   6 unt;   0 def)
%            Number of atoms       :  116 (  12 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  132 (  52   ~;  60   |;  10   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   71 (   6 sgn  35   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t23_finsub_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => subset(finite_subsets(X1),finite_subsets(X2)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t23_finsub_1) ).

fof(t1_xboole_1,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_xboole_1) ).

fof(d5_finsub_1,axiom,
    ! [X1,X2] :
      ( preboolean(X2)
     => ( X2 = finite_subsets(X1)
      <=> ! [X3] :
            ( in(X3,X2)
          <=> ( subset(X3,X1)
              & finite(X3) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_finsub_1) ).

fof(dt_k5_finsub_1,axiom,
    ! [X1] : preboolean(finite_subsets(X1)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k5_finsub_1) ).

fof(cc3_finsub_1,axiom,
    ! [X1,X2] :
      ( element(X2,finite_subsets(X1))
     => finite(X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc3_finsub_1) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_subset) ).

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(c_0_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => subset(finite_subsets(X1),finite_subsets(X2)) ),
    inference(assume_negation,[status(cth)],[t23_finsub_1]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_9,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & ~ subset(finite_subsets(esk1_0),finite_subsets(esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X4,X5,X6,X6] :
      ( ( subset(X6,X4)
        | ~ in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( finite(X6)
        | ~ in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( ~ subset(X6,X4)
        | ~ finite(X6)
        | in(X6,X5)
        | X5 != finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | ~ subset(esk4_2(X4,X5),X4)
        | ~ finite(esk4_2(X4,X5))
        | X5 = finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( subset(esk4_2(X4,X5),X4)
        | in(esk4_2(X4,X5),X5)
        | X5 = finite_subsets(X4)
        | ~ preboolean(X5) )
      & ( finite(esk4_2(X4,X5))
        | in(esk4_2(X4,X5),X5)
        | X5 = finite_subsets(X4)
        | ~ preboolean(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_finsub_1])])])])])])]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( in(X3,X1)
    | ~ preboolean(X1)
    | X1 != finite_subsets(X2)
    | ~ finite(X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ( subset(X1,esk2_0)
    | ~ subset(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_15,plain,
    ! [X2] : preboolean(finite_subsets(X2)),
    inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).

fof(c_0_16,plain,
    ! [X3,X4] :
      ( ~ element(X4,finite_subsets(X3))
      | finite(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_finsub_1])]) ).

fof(c_0_17,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | element(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

cnf(c_0_18,negated_conjecture,
    ( in(X1,X2)
    | X2 != finite_subsets(esk2_0)
    | ~ subset(X1,esk1_0)
    | ~ preboolean(X2)
    | ~ finite(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,plain,
    preboolean(finite_subsets(X1)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    ( finite(X1)
    | ~ element(X1,finite_subsets(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_22,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk3_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk3_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_23,negated_conjecture,
    ( in(X1,finite_subsets(X2))
    | finite_subsets(X2) != finite_subsets(esk2_0)
    | ~ subset(X1,esk1_0)
    | ~ finite(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( finite(X1)
    | ~ in(X1,finite_subsets(X2)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( subset(X1,X2)
    | in(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,plain,
    ( subset(X3,X2)
    | ~ preboolean(X1)
    | X1 != finite_subsets(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_27,negated_conjecture,
    ( in(X1,finite_subsets(esk2_0))
    | ~ subset(X1,esk1_0)
    | ~ finite(X1) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_28,plain,
    ( subset(finite_subsets(X1),X2)
    | finite(esk3_2(finite_subsets(X1),X2)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,plain,
    ( subset(esk3_2(X1,X2),X3)
    | subset(X1,X2)
    | X1 != finite_subsets(X3)
    | ~ preboolean(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ( subset(finite_subsets(X1),X2)
    | in(esk3_2(finite_subsets(X1),X2),finite_subsets(esk2_0))
    | ~ subset(esk3_2(finite_subsets(X1),X2),esk1_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
    ( subset(esk3_2(finite_subsets(X1),X2),X1)
    | subset(finite_subsets(X1),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_19])]) ).

cnf(c_0_32,plain,
    ( subset(X1,X2)
    | ~ in(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_33,negated_conjecture,
    ( subset(finite_subsets(esk1_0),X1)
    | in(esk3_2(finite_subsets(esk1_0),X1),finite_subsets(esk2_0)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ~ subset(finite_subsets(esk1_0),finite_subsets(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n029.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 Jun 19 20:50:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.23/2.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/2.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/2.41  # Preprocessing time       : 0.013 s
% 0.23/2.41  
% 0.23/2.41  # Proof found!
% 0.23/2.41  # SZS status Theorem
% 0.23/2.41  # SZS output start CNFRefutation
% See solution above
% 0.23/2.41  # Proof object total steps             : 36
% 0.23/2.41  # Proof object clause steps            : 21
% 0.23/2.41  # Proof object formula steps           : 15
% 0.23/2.41  # Proof object conjectures             : 12
% 0.23/2.41  # Proof object clause conjectures      : 9
% 0.23/2.41  # Proof object formula conjectures     : 3
% 0.23/2.41  # Proof object initial clauses used    : 10
% 0.23/2.41  # Proof object initial formulas used   : 7
% 0.23/2.41  # Proof object generating inferences   : 11
% 0.23/2.41  # Proof object simplifying inferences  : 3
% 0.23/2.41  # Training examples: 0 positive, 0 negative
% 0.23/2.41  # Parsed axioms                        : 34
% 0.23/2.41  # Removed by relevancy pruning/SinE    : 4
% 0.23/2.41  # Initial clauses                      : 53
% 0.23/2.41  # Removed in clause preprocessing      : 0
% 0.23/2.41  # Initial clauses in saturation        : 53
% 0.23/2.41  # Processed clauses                    : 10717
% 0.23/2.41  # ...of these trivial                  : 82
% 0.23/2.41  # ...subsumed                          : 7584
% 0.23/2.41  # ...remaining for further processing  : 3051
% 0.23/2.41  # Other redundant clauses eliminated   : 0
% 0.23/2.41  # Clauses deleted for lack of memory   : 0
% 0.23/2.41  # Backward-subsumed                    : 106
% 0.23/2.41  # Backward-rewritten                   : 142
% 0.23/2.41  # Generated clauses                    : 78129
% 0.23/2.41  # ...of the previous two non-trivial   : 71133
% 0.23/2.41  # Contextual simplify-reflections      : 3797
% 0.23/2.41  # Paramodulations                      : 78070
% 0.23/2.41  # Factorizations                       : 4
% 0.23/2.41  # Equation resolutions                 : 55
% 0.23/2.41  # Current number of processed clauses  : 2803
% 0.23/2.41  #    Positive orientable unit clauses  : 425
% 0.23/2.41  #    Positive unorientable unit clauses: 0
% 0.23/2.41  #    Negative unit clauses             : 125
% 0.23/2.41  #    Non-unit-clauses                  : 2253
% 0.23/2.41  # Current number of unprocessed clauses: 56125
% 0.23/2.41  # ...number of literals in the above   : 202401
% 0.23/2.41  # Current number of archived formulas  : 0
% 0.23/2.41  # Current number of archived clauses   : 248
% 0.23/2.41  # Clause-clause subsumption calls (NU) : 470391
% 0.23/2.41  # Rec. Clause-clause subsumption calls : 294786
% 0.23/2.41  # Non-unit clause-clause subsumptions  : 8098
% 0.23/2.41  # Unit Clause-clause subsumption calls : 16178
% 0.23/2.41  # Rewrite failures with RHS unbound    : 0
% 0.23/2.41  # BW rewrite match attempts            : 6834
% 0.23/2.41  # BW rewrite match successes           : 69
% 0.23/2.41  # Condensation attempts                : 0
% 0.23/2.41  # Condensation successes               : 0
% 0.23/2.41  # Termbank termtop insertions          : 1262511
% 0.23/2.41  
% 0.23/2.41  # -------------------------------------------------
% 0.23/2.41  # User time                : 1.226 s
% 0.23/2.41  # System time              : 0.030 s
% 0.23/2.41  # Total time               : 1.256 s
% 0.23/2.41  # Maximum resident set size: 60596 pages
%------------------------------------------------------------------------------