TSTP Solution File: ALG074+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n019.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 : Thu Jul 14 16:47:35 EDT 2022

% Result   : Theorem 0.22s 1.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (  20 unt;   0 def)
%            Number of atoms       :  129 (  47 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  130 (  46   ~;  37   |;  25   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   56 (   0 sgn  34   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ( ( ! [X1] :
          ( sorti1(X1)
         => sorti2(h(X1)) )
      & ! [X2] :
          ( sorti2(X2)
         => sorti1(j(X2)) ) )
   => ~ ( ! [X3] :
            ( sorti1(X3)
           => ! [X4] :
                ( sorti1(X4)
               => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
        & ! [X5] :
            ( sorti2(X5)
           => ! [X6] :
                ( sorti2(X6)
               => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
        & ! [X7] :
            ( sorti2(X7)
           => h(j(X7)) = X7 )
        & ! [X8] :
            ( sorti1(X8)
           => j(h(X8)) = X8 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',co1) ).

fof(ax3,axiom,
    ? [X1] :
      ( sorti1(X1)
      & ? [X2] :
          ( sorti1(X2)
          & op1(X2,X1) != op1(X1,X2)
          & op1(op1(X1,X2),X2) = X1
          & op1(op1(X1,X2),X1) != X2 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax3) ).

fof(ax1,axiom,
    ! [X1] :
      ( sorti1(X1)
     => ! [X2] :
          ( sorti1(X2)
         => sorti1(op1(X1,X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax1) ).

fof(ax2,axiom,
    ! [X1] :
      ( sorti2(X1)
     => ! [X2] :
          ( sorti2(X2)
         => sorti2(op2(X1,X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax2) ).

fof(ax4,axiom,
    ~ ? [X1] :
        ( sorti2(X1)
        & ? [X2] :
            ( sorti2(X2)
            & op2(X2,X1) != op2(X1,X2)
            & op2(op2(X1,X2),X2) = X1
            & op2(op2(X1,X2),X1) != X2 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax4) ).

fof(c_0_5,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) )
        & ! [X2] :
            ( sorti2(X2)
           => sorti1(j(X2)) ) )
     => ~ ( ! [X3] :
              ( sorti1(X3)
             => ! [X4] :
                  ( sorti1(X4)
                 => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => ! [X6] :
                  ( sorti2(X6)
                 => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
          & ! [X7] :
              ( sorti2(X7)
             => h(j(X7)) = X7 )
          & ! [X8] :
              ( sorti1(X8)
             => j(h(X8)) = X8 ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_6,negated_conjecture,
    ! [X9,X10,X11,X12,X13,X14,X15,X16] :
      ( ( ~ sorti1(X9)
        | sorti2(h(X9)) )
      & ( ~ sorti2(X10)
        | sorti1(j(X10)) )
      & ( ~ sorti1(X11)
        | ~ sorti1(X12)
        | h(op1(X11,X12)) = op2(h(X11),h(X12)) )
      & ( ~ sorti2(X13)
        | ~ sorti2(X14)
        | j(op2(X13,X14)) = op1(j(X13),j(X14)) )
      & ( ~ sorti2(X15)
        | h(j(X15)) = X15 )
      & ( ~ sorti1(X16)
        | j(h(X16)) = X16 ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).

fof(c_0_7,plain,
    ( sorti1(esk1_0)
    & sorti1(esk2_0)
    & op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0)
    & op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0
    & op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0 ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[ax3])])])]) ).

fof(c_0_8,plain,
    ! [X3,X4] :
      ( ~ sorti1(X3)
      | ~ sorti1(X4)
      | sorti1(op1(X3,X4)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])])]) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( ~ sorti2(X3)
      | ~ sorti2(X4)
      | sorti2(op2(X3,X4)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])])]) ).

cnf(c_0_10,negated_conjecture,
    ( sorti2(h(X1))
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    sorti1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( sorti1(op1(X1,X2))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( h(op1(X1,X2)) = op2(h(X1),h(X2))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,plain,
    sorti1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    ( j(h(X1)) = X1
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,plain,
    ( sorti2(op2(X1,X2))
    | ~ sorti2(X2)
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,negated_conjecture,
    sorti2(h(esk2_0)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_18,plain,
    ( sorti1(op1(X1,esk2_0))
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    ( h(op1(X1,esk2_0)) = op2(h(X1),h(esk2_0))
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    ( j(op2(X1,X2)) = op1(j(X1),j(X2))
    | ~ sorti2(X2)
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_21,negated_conjecture,
    sorti2(h(esk1_0)),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    j(h(esk1_0)) = esk1_0,
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    ( sorti2(op2(X1,h(esk2_0)))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_24,plain,
    sorti1(op1(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_25,negated_conjecture,
    h(op1(esk1_0,esk2_0)) = op2(h(esk1_0),h(esk2_0)),
    inference(spm,[status(thm)],[c_0_19,c_0_14]) ).

fof(c_0_26,plain,
    ! [X3,X4] :
      ( ~ sorti2(X3)
      | ~ sorti2(X4)
      | op2(X4,X3) = op2(X3,X4)
      | op2(op2(X3,X4),X4) != X3
      | op2(op2(X3,X4),X3) = X4 ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

cnf(c_0_27,plain,
    op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_28,negated_conjecture,
    ( j(op2(X1,h(esk1_0))) = op1(j(X1),esk1_0)
    | ~ sorti2(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    sorti2(op2(h(esk1_0),h(esk2_0))),
    inference(spm,[status(thm)],[c_0_23,c_0_21]) ).

cnf(c_0_30,negated_conjecture,
    j(op2(h(esk1_0),h(esk2_0))) = op1(esk1_0,esk2_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_25]) ).

cnf(c_0_31,plain,
    ( op2(op2(X1,X2),X1) = X2
    | op2(X2,X1) = op2(X1,X2)
    | op2(op2(X1,X2),X2) != X1
    | ~ sorti2(X2)
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    op2(op2(h(esk1_0),h(esk2_0)),h(esk2_0)) = h(esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_27]),c_0_25]) ).

cnf(c_0_33,plain,
    ( sorti1(op1(X1,esk1_0))
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

cnf(c_0_34,negated_conjecture,
    ( h(op1(X1,esk1_0)) = op2(h(X1),h(esk1_0))
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_35,negated_conjecture,
    j(op2(op2(h(esk1_0),h(esk2_0)),h(esk1_0))) = op1(op1(esk1_0,esk2_0),esk1_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_36,negated_conjecture,
    ( op2(h(esk1_0),h(esk2_0)) = op2(h(esk2_0),h(esk1_0))
    | op2(op2(h(esk1_0),h(esk2_0)),h(esk1_0)) = h(esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_21])]) ).

cnf(c_0_37,negated_conjecture,
    j(h(esk2_0)) = esk2_0,
    inference(spm,[status(thm)],[c_0_15,c_0_11]) ).

cnf(c_0_38,plain,
    op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_39,plain,
    sorti1(op1(esk2_0,esk1_0)),
    inference(spm,[status(thm)],[c_0_33,c_0_11]) ).

cnf(c_0_40,negated_conjecture,
    h(op1(esk2_0,esk1_0)) = op2(h(esk2_0),h(esk1_0)),
    inference(spm,[status(thm)],[c_0_34,c_0_11]) ).

cnf(c_0_41,negated_conjecture,
    op2(h(esk1_0),h(esk2_0)) = op2(h(esk2_0),h(esk1_0)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    j(op2(h(esk2_0),h(esk1_0))) = op1(esk2_0,esk1_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_39]),c_0_40]) ).

cnf(c_0_43,plain,
    op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_41]),c_0_42]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.12  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n019.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 : Thu Jun  9 04:18:25 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.22/1.41  # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.22/1.41  # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.22/1.41  # Preprocessing time       : 0.014 s
% 0.22/1.41  
% 0.22/1.41  # Proof found!
% 0.22/1.41  # SZS status Theorem
% 0.22/1.41  # SZS output start CNFRefutation
% See solution above
% 0.22/1.41  # Proof object total steps             : 45
% 0.22/1.41  # Proof object clause steps            : 34
% 0.22/1.41  # Proof object formula steps           : 11
% 0.22/1.41  # Proof object conjectures             : 25
% 0.22/1.41  # Proof object clause conjectures      : 22
% 0.22/1.41  # Proof object formula conjectures     : 3
% 0.22/1.41  # Proof object initial clauses used    : 12
% 0.22/1.41  # Proof object initial formulas used   : 5
% 0.22/1.41  # Proof object generating inferences   : 21
% 0.22/1.41  # Proof object simplifying inferences  : 14
% 0.22/1.41  # Training examples: 0 positive, 0 negative
% 0.22/1.41  # Parsed axioms                        : 5
% 0.22/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.22/1.41  # Initial clauses                      : 14
% 0.22/1.41  # Removed in clause preprocessing      : 0
% 0.22/1.41  # Initial clauses in saturation        : 14
% 0.22/1.41  # Processed clauses                    : 339
% 0.22/1.41  # ...of these trivial                  : 24
% 0.22/1.41  # ...subsumed                          : 22
% 0.22/1.41  # ...remaining for further processing  : 293
% 0.22/1.41  # Other redundant clauses eliminated   : 0
% 0.22/1.41  # Clauses deleted for lack of memory   : 0
% 0.22/1.41  # Backward-subsumed                    : 0
% 0.22/1.41  # Backward-rewritten                   : 77
% 0.22/1.41  # Generated clauses                    : 6689
% 0.22/1.41  # ...of the previous two non-trivial   : 6727
% 0.22/1.41  # Contextual simplify-reflections      : 0
% 0.22/1.41  # Paramodulations                      : 6689
% 0.22/1.41  # Factorizations                       : 0
% 0.22/1.41  # Equation resolutions                 : 0
% 0.22/1.41  # Current number of processed clauses  : 216
% 0.22/1.41  #    Positive orientable unit clauses  : 110
% 0.22/1.41  #    Positive unorientable unit clauses: 0
% 0.22/1.41  #    Negative unit clauses             : 2
% 0.22/1.41  #    Non-unit-clauses                  : 104
% 0.22/1.41  # Current number of unprocessed clauses: 4915
% 0.22/1.41  # ...number of literals in the above   : 5001
% 0.22/1.41  # Current number of archived formulas  : 0
% 0.22/1.41  # Current number of archived clauses   : 77
% 0.22/1.41  # Clause-clause subsumption calls (NU) : 1468
% 0.22/1.41  # Rec. Clause-clause subsumption calls : 1468
% 0.22/1.41  # Non-unit clause-clause subsumptions  : 22
% 0.22/1.41  # Unit Clause-clause subsumption calls : 121
% 0.22/1.41  # Rewrite failures with RHS unbound    : 0
% 0.22/1.41  # BW rewrite match attempts            : 692
% 0.22/1.41  # BW rewrite match successes           : 15
% 0.22/1.41  # Condensation attempts                : 0
% 0.22/1.41  # Condensation successes               : 0
% 0.22/1.41  # Termbank termtop insertions          : 132673
% 0.22/1.41  
% 0.22/1.41  # -------------------------------------------------
% 0.22/1.41  # User time                : 0.072 s
% 0.22/1.41  # System time              : 0.004 s
% 0.22/1.41  # Total time               : 0.076 s
% 0.22/1.41  # Maximum resident set size: 8064 pages
% 0.22/23.41  eprover: CPU time limit exceeded, terminating
% 0.22/23.41  eprover: CPU time limit exceeded, terminating
% 0.22/23.42  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.42  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------