TSTP Solution File: SET890+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n015.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 00:55:14 EDT 2022

% Result   : Theorem 0.24s 1.41s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   35 (   6 unt;   0 def)
%            Number of atoms       :  123 (  52 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  142 (  54   ~;  70   |;  11   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-3 aty)
%            Number of variables   :   88 (   8 sgn  34   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
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(d4_tarski,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d4_tarski) ).

fof(l50_zfmisc_1,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => subset(X1,union(X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l50_zfmisc_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(t31_zfmisc_1,conjecture,
    ! [X1] : union(singleton(X1)) = X1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t31_zfmisc_1) ).

fof(c_0_5,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk1_2(X4,X5),X5)
        | esk1_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk1_2(X4,X5),X5)
        | esk1_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])])])])])])]) ).

fof(c_0_6,plain,
    ! [X5,X6,X7,X7,X9,X5,X6,X11] :
      ( ( in(X7,esk3_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( in(esk3_3(X5,X6,X7),X5)
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( ~ in(X7,X9)
        | ~ in(X9,X5)
        | in(X7,X6)
        | X6 != union(X5) )
      & ( ~ in(esk4_2(X5,X6),X6)
        | ~ in(esk4_2(X5,X6),X11)
        | ~ in(X11,X5)
        | X6 = union(X5) )
      & ( in(esk4_2(X5,X6),esk5_2(X5,X6))
        | in(esk4_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk5_2(X5,X6),X5)
        | in(esk4_2(X5,X6),X6)
        | X6 = union(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_tarski])])])])])])]) ).

cnf(c_0_7,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( X1 = union(X2)
    | in(esk4_2(X2,X1),X1)
    | in(esk5_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( X1 = esk5_2(X2,X3)
    | X3 = union(X2)
    | in(esk4_2(X2,X3),X3)
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

fof(c_0_10,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | subset(X3,union(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).

cnf(c_0_11,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,plain,
    ( X1 = union(X2)
    | ~ in(X3,X2)
    | ~ in(esk4_2(X2,X1),X3)
    | ~ in(esk4_2(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( in(X3,esk3_3(X2,X1,X3))
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,plain,
    ( X1 = union(X2)
    | in(esk4_2(X2,X1),X1)
    | in(esk4_2(X2,X1),esk5_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,plain,
    ( esk5_2(singleton(X1),X2) = X1
    | X2 = union(singleton(X1))
    | in(esk4_2(singleton(X1),X2),X2) ),
    inference(er,[status(thm)],[c_0_9]) ).

fof(c_0_16,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk2_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk2_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_17,plain,
    ( subset(X1,union(X2))
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( in(X1,X2)
    | X2 != singleton(X1) ),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    ( X1 = union(X2)
    | X3 != union(X4)
    | ~ in(esk3_3(X4,X3,esk4_2(X2,X1)),X2)
    | ~ in(esk4_2(X2,X1),X1)
    | ~ in(esk4_2(X2,X1),X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_20,plain,
    ( in(esk3_3(X2,X1,X3),X2)
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_21,plain,
    ( X1 = union(singleton(X2))
    | in(esk4_2(singleton(X2),X1),X1)
    | in(esk4_2(singleton(X2),X1),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( subset(X1,union(X2))
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,plain,
    ( X1 = union(X2)
    | X3 != union(X2)
    | ~ in(esk4_2(X2,X1),X1)
    | ~ in(esk4_2(X2,X1),X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
    ( union(singleton(X1)) = X1
    | in(esk4_2(singleton(X1),X1),X1) ),
    inference(ef,[status(thm)],[c_0_21]) ).

cnf(c_0_26,plain,
    ( in(X1,union(X2))
    | X2 != singleton(X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_27,negated_conjecture,
    ~ ! [X1] : union(singleton(X1)) = X1,
    inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).

cnf(c_0_28,plain,
    ( union(singleton(X1)) = X1
    | X2 != union(singleton(X1))
    | ~ in(esk4_2(singleton(X1),X1),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,plain,
    ( union(singleton(X1)) = X1
    | in(esk4_2(singleton(X1),X1),union(X2))
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

fof(c_0_30,negated_conjecture,
    union(singleton(esk8_0)) != esk8_0,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).

cnf(c_0_31,plain,
    ( union(singleton(X1)) = X1
    | union(X2) != union(singleton(X1))
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    union(singleton(esk8_0)) != esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_33,plain,
    union(singleton(X1)) = X1,
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul 11 09:43:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.24/1.41  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.41  # Preprocessing time       : 0.015 s
% 0.24/1.41  
% 0.24/1.41  # Proof found!
% 0.24/1.41  # SZS status Theorem
% 0.24/1.41  # SZS output start CNFRefutation
% See solution above
% 0.24/1.41  # Proof object total steps             : 35
% 0.24/1.41  # Proof object clause steps            : 24
% 0.24/1.41  # Proof object formula steps           : 11
% 0.24/1.41  # Proof object conjectures             : 5
% 0.24/1.41  # Proof object clause conjectures      : 2
% 0.24/1.41  # Proof object formula conjectures     : 3
% 0.24/1.41  # Proof object initial clauses used    : 10
% 0.24/1.41  # Proof object initial formulas used   : 5
% 0.24/1.41  # Proof object generating inferences   : 12
% 0.24/1.41  # Proof object simplifying inferences  : 3
% 0.24/1.41  # Training examples: 0 positive, 0 negative
% 0.24/1.41  # Parsed axioms                        : 10
% 0.24/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.41  # Initial clauses                      : 22
% 0.24/1.41  # Removed in clause preprocessing      : 0
% 0.24/1.41  # Initial clauses in saturation        : 22
% 0.24/1.41  # Processed clauses                    : 2018
% 0.24/1.41  # ...of these trivial                  : 18
% 0.24/1.41  # ...subsumed                          : 979
% 0.24/1.41  # ...remaining for further processing  : 1021
% 0.24/1.41  # Other redundant clauses eliminated   : 81
% 0.24/1.41  # Clauses deleted for lack of memory   : 0
% 0.24/1.41  # Backward-subsumed                    : 1
% 0.24/1.41  # Backward-rewritten                   : 648
% 0.24/1.41  # Generated clauses                    : 9853
% 0.24/1.41  # ...of the previous two non-trivial   : 9937
% 0.24/1.41  # Contextual simplify-reflections      : 669
% 0.24/1.41  # Paramodulations                      : 9314
% 0.24/1.41  # Factorizations                       : 10
% 0.24/1.41  # Equation resolutions                 : 529
% 0.24/1.41  # Current number of processed clauses  : 369
% 0.24/1.41  #    Positive orientable unit clauses  : 4
% 0.24/1.41  #    Positive unorientable unit clauses: 0
% 0.24/1.41  #    Negative unit clauses             : 3
% 0.24/1.41  #    Non-unit-clauses                  : 362
% 0.24/1.41  # Current number of unprocessed clauses: 2093
% 0.24/1.41  # ...number of literals in the above   : 12361
% 0.24/1.41  # Current number of archived formulas  : 0
% 0.24/1.41  # Current number of archived clauses   : 649
% 0.24/1.41  # Clause-clause subsumption calls (NU) : 106857
% 0.24/1.41  # Rec. Clause-clause subsumption calls : 55527
% 0.24/1.41  # Non-unit clause-clause subsumptions  : 1500
% 0.24/1.41  # Unit Clause-clause subsumption calls : 296
% 0.24/1.41  # Rewrite failures with RHS unbound    : 0
% 0.24/1.41  # BW rewrite match attempts            : 79
% 0.24/1.41  # BW rewrite match successes           : 79
% 0.24/1.41  # Condensation attempts                : 0
% 0.24/1.41  # Condensation successes               : 0
% 0.24/1.41  # Termbank termtop insertions          : 266976
% 0.24/1.41  
% 0.24/1.41  # -------------------------------------------------
% 0.24/1.41  # User time                : 0.423 s
% 0.24/1.41  # System time              : 0.007 s
% 0.24/1.41  # Total time               : 0.430 s
% 0.24/1.41  # Maximum resident set size: 12016 pages
% 0.24/23.41  eprover: CPU time limit exceeded, terminating
% 0.24/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42  eprover: No such file or directory
% 0.24/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42  eprover: No such file or directory
% 0.24/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43  eprover: No such file or directory
% 0.24/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43  eprover: No such file or directory
% 0.24/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43  eprover: No such file or directory
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46  eprover: No such file or directory
%------------------------------------------------------------------------------