TSTP Solution File: SET754+4 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET754+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n018.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 00:53:46 EDT 2022

% Result   : Theorem 0.23s 1.40s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   4 unt;   0 def)
%            Number of atoms       :  148 (   4 equ)
%            Maximal formula atoms :   55 (   5 avg)
%            Number of connectives :  181 (  62   ~;  78   |;  31   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-4 aty)
%            Number of variables   :   98 (  12 sgn  54   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(inverse_image2,axiom,
    ! [X6,X2,X3] :
      ( member(X3,inverse_image2(X6,X2))
    <=> ? [X5] :
          ( member(X5,X2)
          & apply(X6,X3,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).

fof(maps,axiom,
    ! [X6,X1,X2] :
      ( maps(X6,X1,X2)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => ? [X5] :
                ( member(X5,X2)
                & apply(X6,X3,X5) ) )
        & ! [X3,X7,X8] :
            ( ( member(X3,X1)
              & member(X7,X2)
              & member(X8,X2) )
           => ( ( apply(X6,X3,X7)
                & apply(X6,X3,X8) )
             => X7 = X8 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).

fof(image2,axiom,
    ! [X6,X1,X5] :
      ( member(X5,image2(X6,X1))
    <=> ? [X3] :
          ( member(X3,X1)
          & apply(X6,X3,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).

fof(thIIa04,conjecture,
    ! [X6,X1,X2,X11] :
      ( ( maps(X6,X1,X2)
        & subset(X11,X1) )
     => subset(X11,inverse_image2(X6,image2(X6,X11))) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIIa04) ).

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(c_0_5,plain,
    ! [X7,X8,X9,X7,X8,X9,X11] :
      ( ( member(esk6_3(X7,X8,X9),X8)
        | ~ member(X9,inverse_image2(X7,X8)) )
      & ( apply(X7,X9,esk6_3(X7,X8,X9))
        | ~ member(X9,inverse_image2(X7,X8)) )
      & ( ~ member(X11,X8)
        | ~ apply(X7,X9,X11)
        | member(X9,inverse_image2(X7,X8)) ) ),
    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)],[inverse_image2])])])])])])]) ).

fof(c_0_6,plain,
    ! [X9,X10,X11,X12,X14,X15,X16,X9,X10,X11,X18] :
      ( ( member(esk8_4(X9,X10,X11,X12),X11)
        | ~ member(X12,X10)
        | ~ maps(X9,X10,X11) )
      & ( apply(X9,X12,esk8_4(X9,X10,X11,X12))
        | ~ member(X12,X10)
        | ~ maps(X9,X10,X11) )
      & ( ~ member(X14,X10)
        | ~ member(X15,X11)
        | ~ member(X16,X11)
        | ~ apply(X9,X14,X15)
        | ~ apply(X9,X14,X16)
        | X15 = X16
        | ~ maps(X9,X10,X11) )
      & ( member(esk10_3(X9,X10,X11),X10)
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk11_3(X9,X10,X11),X11)
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk12_3(X9,X10,X11),X11)
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk10_3(X9,X10,X11),esk11_3(X9,X10,X11))
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk10_3(X9,X10,X11),esk12_3(X9,X10,X11))
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( esk11_3(X9,X10,X11) != esk12_3(X9,X10,X11)
        | member(esk9_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk10_3(X9,X10,X11),X10)
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( member(esk11_3(X9,X10,X11),X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( member(esk12_3(X9,X10,X11),X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk10_3(X9,X10,X11),esk11_3(X9,X10,X11))
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk10_3(X9,X10,X11),esk12_3(X9,X10,X11))
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( esk11_3(X9,X10,X11) != esk12_3(X9,X10,X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk9_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) ) ),
    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)],[maps])])])])])])]) ).

fof(c_0_7,plain,
    ! [X7,X8,X9,X7,X8,X9,X11] :
      ( ( member(esk7_3(X7,X8,X9),X8)
        | ~ member(X9,image2(X7,X8)) )
      & ( apply(X7,esk7_3(X7,X8,X9),X9)
        | ~ member(X9,image2(X7,X8)) )
      & ( ~ member(X11,X8)
        | ~ apply(X7,X11,X9)
        | member(X9,image2(X7,X8)) ) ),
    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)],[image2])])])])])])]) ).

cnf(c_0_8,plain,
    ( member(X1,inverse_image2(X2,X3))
    | ~ apply(X2,X1,X4)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( apply(X1,X4,esk8_4(X1,X2,X3,X4))
    | ~ maps(X1,X2,X3)
    | ~ member(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( member(X1,image2(X2,X3))
    | ~ apply(X2,X4,X1)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X6,X1,X2,X11] :
        ( ( maps(X6,X1,X2)
          & subset(X11,X1) )
       => subset(X11,inverse_image2(X6,image2(X6,X11))) ),
    inference(assume_negation,[status(cth)],[thIIa04]) ).

cnf(c_0_12,plain,
    ( member(X1,inverse_image2(X2,X3))
    | ~ maps(X2,X4,X5)
    | ~ member(esk8_4(X2,X4,X5,X1),X3)
    | ~ member(X1,X4) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( member(esk8_4(X1,X2,X3,X4),image2(X1,X5))
    | ~ maps(X1,X2,X3)
    | ~ member(X4,X5)
    | ~ member(X4,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

fof(c_0_14,negated_conjecture,
    ( maps(esk1_0,esk2_0,esk3_0)
    & subset(esk4_0,esk2_0)
    & ~ subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,esk4_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_15,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_16,plain,
    ( member(X1,inverse_image2(X2,image2(X2,X3)))
    | ~ maps(X2,X4,X5)
    | ~ member(X1,X4)
    | ~ member(X1,X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    maps(esk1_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    subset(esk4_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( subset(X1,X2)
    | ~ member(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( member(X1,inverse_image2(esk1_0,image2(esk1_0,X2)))
    | ~ member(X1,esk2_0)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    ( subset(X1,X2)
    | member(esk5_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    ( subset(X1,inverse_image2(esk1_0,image2(esk1_0,X2)))
    | ~ member(esk5_2(X1,inverse_image2(esk1_0,image2(esk1_0,X2))),esk2_0)
    | ~ member(esk5_2(X1,inverse_image2(esk1_0,image2(esk1_0,X2))),X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( member(esk5_2(esk4_0,X1),esk2_0)
    | subset(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    ( subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,X1)))
    | ~ member(esk5_2(esk4_0,inverse_image2(esk1_0,image2(esk1_0,X1))),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,negated_conjecture,
    ~ subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,esk4_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET754+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.00/0.12  % Command  : run_ET %s %d
% 0.12/0.32  % Computer : n018.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 20:11:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.23/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40  # Preprocessing time       : 0.016 s
% 0.23/1.40  
% 0.23/1.40  # Proof found!
% 0.23/1.40  # SZS status Theorem
% 0.23/1.40  # SZS output start CNFRefutation
% See solution above
% 0.23/1.40  # Proof object total steps             : 29
% 0.23/1.40  # Proof object clause steps            : 18
% 0.23/1.40  # Proof object formula steps           : 11
% 0.23/1.40  # Proof object conjectures             : 12
% 0.23/1.40  # Proof object clause conjectures      : 9
% 0.23/1.40  # Proof object formula conjectures     : 3
% 0.23/1.40  # Proof object initial clauses used    : 9
% 0.23/1.40  # Proof object initial formulas used   : 5
% 0.23/1.40  # Proof object generating inferences   : 9
% 0.23/1.40  # Proof object simplifying inferences  : 1
% 0.23/1.40  # Training examples: 0 positive, 0 negative
% 0.23/1.40  # Parsed axioms                        : 29
% 0.23/1.40  # Removed by relevancy pruning/SinE    : 24
% 0.23/1.40  # Initial clauses                      : 27
% 0.23/1.40  # Removed in clause preprocessing      : 0
% 0.23/1.40  # Initial clauses in saturation        : 27
% 0.23/1.40  # Processed clauses                    : 103
% 0.23/1.40  # ...of these trivial                  : 0
% 0.23/1.40  # ...subsumed                          : 16
% 0.23/1.40  # ...remaining for further processing  : 87
% 0.23/1.40  # Other redundant clauses eliminated   : 0
% 0.23/1.40  # Clauses deleted for lack of memory   : 0
% 0.23/1.40  # Backward-subsumed                    : 0
% 0.23/1.40  # Backward-rewritten                   : 0
% 0.23/1.40  # Generated clauses                    : 257
% 0.23/1.40  # ...of the previous two non-trivial   : 249
% 0.23/1.40  # Contextual simplify-reflections      : 6
% 0.23/1.40  # Paramodulations                      : 257
% 0.23/1.40  # Factorizations                       : 0
% 0.23/1.40  # Equation resolutions                 : 0
% 0.23/1.40  # Current number of processed clauses  : 87
% 0.23/1.40  #    Positive orientable unit clauses  : 10
% 0.23/1.40  #    Positive unorientable unit clauses: 0
% 0.23/1.40  #    Negative unit clauses             : 1
% 0.23/1.40  #    Non-unit-clauses                  : 76
% 0.23/1.40  # Current number of unprocessed clauses: 173
% 0.23/1.40  # ...number of literals in the above   : 744
% 0.23/1.40  # Current number of archived formulas  : 0
% 0.23/1.40  # Current number of archived clauses   : 0
% 0.23/1.40  # Clause-clause subsumption calls (NU) : 646
% 0.23/1.40  # Rec. Clause-clause subsumption calls : 477
% 0.23/1.40  # Non-unit clause-clause subsumptions  : 22
% 0.23/1.40  # Unit Clause-clause subsumption calls : 13
% 0.23/1.40  # Rewrite failures with RHS unbound    : 0
% 0.23/1.40  # BW rewrite match attempts            : 5
% 0.23/1.40  # BW rewrite match successes           : 0
% 0.23/1.40  # Condensation attempts                : 0
% 0.23/1.40  # Condensation successes               : 0
% 0.23/1.40  # Termbank termtop insertions          : 7498
% 0.23/1.40  
% 0.23/1.40  # -------------------------------------------------
% 0.23/1.40  # User time                : 0.025 s
% 0.23/1.40  # System time              : 0.003 s
% 0.23/1.40  # Total time               : 0.028 s
% 0.23/1.40  # Maximum resident set size: 3316 pages
% 0.23/23.39  eprover: CPU time limit exceeded, terminating
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.41  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.41  eprover: No such file or directory
% 0.23/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42  eprover: No such file or directory
% 0.23/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42  eprover: No such file or directory
% 0.23/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.42  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
%------------------------------------------------------------------------------