TSTP Solution File: SWC198+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWC198+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n005.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 20:27:17 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   40 (   9 unt;   0 def)
%            Number of atoms       :  168 (  63 equ)
%            Maximal formula atoms :   34 (   4 avg)
%            Number of connectives :  199 (  71   ~;  77   |;  32   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   47 (   1 sgn  26   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ? [X5] :
                        ( ssItem(X5)
                        & ! [X6] :
                            ( ssItem(X6)
                           => ( ~ memberP(X1,X6)
                              | X5 = X6 ) ) )
                    | ( ! [X7] :
                          ( ssItem(X7)
                         => ( cons(X7,nil) != X3
                            | ~ memberP(X4,X7)
                            | ? [X8] :
                                ( ssItem(X8)
                                & X7 != X8
                                & memberP(X4,X8)
                                & leq(X7,X8) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',co1) ).

fof(ax37,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).

fof(ax2,axiom,
    ? [X1] :
      ( ssItem(X1)
      & ? [X2] :
          ( ssItem(X2)
          & X1 != X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax2) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ! [X6] :
                              ( ssItem(X6)
                             => ( ~ memberP(X1,X6)
                                | X5 = X6 ) ) )
                      | ( ! [X7] :
                            ( ssItem(X7)
                           => ( cons(X7,nil) != X3
                              | ~ memberP(X4,X7)
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & X7 != X8
                                  & memberP(X4,X8)
                                  & leq(X7,X8) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_7,negated_conjecture,
    ! [X13,X16] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & ( ssItem(esk5_1(X13))
        | ~ ssItem(X13) )
      & ( memberP(esk1_0,esk5_1(X13))
        | ~ ssItem(X13) )
      & ( X13 != esk5_1(X13)
        | ~ ssItem(X13) )
      & ( nil = esk4_0
        | ssItem(esk6_0) )
      & ( nil = esk3_0
        | ssItem(esk6_0) )
      & ( nil = esk4_0
        | cons(esk6_0,nil) = esk3_0 )
      & ( nil = esk3_0
        | cons(esk6_0,nil) = esk3_0 )
      & ( nil = esk4_0
        | memberP(esk4_0,esk6_0) )
      & ( nil = esk3_0
        | memberP(esk4_0,esk6_0) )
      & ( nil = esk4_0
        | ~ ssItem(X16)
        | esk6_0 = X16
        | ~ memberP(esk4_0,X16)
        | ~ leq(esk6_0,X16) )
      & ( nil = esk3_0
        | ~ ssItem(X16)
        | esk6_0 = X16
        | ~ memberP(esk4_0,X16)
        | ~ leq(esk6_0,X16) ) ),
    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)],[inference(fof_simplification,[status(thm)],[c_0_6])])])])])])])]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] :
      ( ( ~ memberP(cons(X5,X6),X4)
        | X4 = X5
        | memberP(X6,X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) )
      & ( X4 != X5
        | memberP(cons(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) )
      & ( ~ memberP(X6,X4)
        | memberP(cons(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) ) ),
    inference(distribute,[status(thm)],[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)],[ax37])])])])])]) ).

cnf(c_0_9,negated_conjecture,
    ( cons(esk6_0,nil) = esk3_0
    | nil = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    ( ssItem(esk6_0)
    | nil = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])]) ).

cnf(c_0_13,plain,
    ( memberP(X3,X1)
    | X1 = X2
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ memberP(cons(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( cons(esk6_0,nil) = esk1_0
    | nil = esk1_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).

cnf(c_0_15,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_16,negated_conjecture,
    ( nil = esk1_0
    | ssItem(esk6_0) ),
    inference(rw,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_17,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    ( nil = esk1_0
    | X1 = esk6_0
    | ~ memberP(esk1_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]),c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    ( memberP(esk1_0,esk5_1(X1))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,negated_conjecture,
    ( ssItem(esk5_1(X1))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_21,plain,
    ! [X3,X4] :
      ( ~ ssList(X3)
      | ~ ssItem(X4)
      | nil != cons(X4,X3) ),
    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)],[ax21])])])])]) ).

cnf(c_0_22,negated_conjecture,
    ( cons(esk6_0,nil) = esk3_0
    | nil = esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_23,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_24,negated_conjecture,
    ( ssItem(esk6_0)
    | nil = esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ ssItem(X1)
    | X1 != esk5_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_26,negated_conjecture,
    ( esk5_1(X1) = esk6_0
    | nil = esk1_0
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_27,plain,
    ( nil != cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    ( cons(esk6_0,nil) = esk1_0
    | nil = esk2_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_10]) ).

cnf(c_0_29,negated_conjecture,
    ( nil = esk2_0
    | ssItem(esk6_0) ),
    inference(rw,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_30,negated_conjecture,
    ( nil = esk1_0
    | esk6_0 != X1
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ( nil = esk2_0
    | nil != esk1_0 ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_15])]),c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    nil = esk1_0,
    inference(spm,[status(thm)],[c_0_30,c_0_16]) ).

cnf(c_0_33,negated_conjecture,
    esk1_0 = esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32])]) ).

fof(c_0_34,plain,
    ( ssItem(esk11_0)
    & ssItem(esk12_0)
    & esk11_0 != esk12_0 ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[ax2])])])]) ).

cnf(c_0_35,plain,
    ( ~ memberP(esk2_0,X1)
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_32]),c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ( memberP(esk2_0,esk5_1(X1))
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[c_0_19,c_0_33]) ).

cnf(c_0_37,plain,
    ssItem(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    ~ ssItem(X1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_20]) ).

cnf(c_0_39,plain,
    $false,
    inference(sr,[status(thm)],[c_0_37,c_0_38]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC198+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n005.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 : Sun Jun 12 23:52:09 EDT 2022
% 0.12/0.34  % 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       : 0.021 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             : 40
% 0.23/1.41  # Proof object clause steps            : 28
% 0.23/1.41  # Proof object formula steps           : 12
% 0.23/1.41  # Proof object conjectures             : 24
% 0.23/1.41  # Proof object clause conjectures      : 21
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 14
% 0.23/1.41  # Proof object initial formulas used   : 6
% 0.23/1.41  # Proof object generating inferences   : 6
% 0.23/1.41  # Proof object simplifying inferences  : 22
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 96
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 66
% 0.23/1.41  # Initial clauses                      : 62
% 0.23/1.41  # Removed in clause preprocessing      : 0
% 0.23/1.41  # Initial clauses in saturation        : 62
% 0.23/1.41  # Processed clauses                    : 223
% 0.23/1.41  # ...of these trivial                  : 15
% 0.23/1.41  # ...subsumed                          : 78
% 0.23/1.41  # ...remaining for further processing  : 130
% 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                    : 5
% 0.23/1.41  # Backward-rewritten                   : 72
% 0.23/1.41  # Generated clauses                    : 731
% 0.23/1.41  # ...of the previous two non-trivial   : 622
% 0.23/1.41  # Contextual simplify-reflections      : 105
% 0.23/1.41  # Paramodulations                      : 714
% 0.23/1.41  # Factorizations                       : 0
% 0.23/1.41  # Equation resolutions                 : 15
% 0.23/1.41  # Current number of processed clauses  : 49
% 0.23/1.41  #    Positive orientable unit clauses  : 5
% 0.23/1.41  #    Positive unorientable unit clauses: 0
% 0.23/1.41  #    Negative unit clauses             : 2
% 0.23/1.41  #    Non-unit-clauses                  : 42
% 0.23/1.41  # Current number of unprocessed clauses: 83
% 0.23/1.41  # ...number of literals in the above   : 449
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.42  # Current number of archived clauses   : 79
% 0.23/1.42  # Clause-clause subsumption calls (NU) : 3849
% 0.23/1.42  # Rec. Clause-clause subsumption calls : 952
% 0.23/1.42  # Non-unit clause-clause subsumptions  : 188
% 0.23/1.42  # Unit Clause-clause subsumption calls : 35
% 0.23/1.42  # Rewrite failures with RHS unbound    : 0
% 0.23/1.42  # BW rewrite match attempts            : 2
% 0.23/1.42  # BW rewrite match successes           : 2
% 0.23/1.42  # Condensation attempts                : 0
% 0.23/1.42  # Condensation successes               : 0
% 0.23/1.42  # Termbank termtop insertions          : 15794
% 0.23/1.42  
% 0.23/1.42  # -------------------------------------------------
% 0.23/1.42  # User time                : 0.057 s
% 0.23/1.42  # System time              : 0.002 s
% 0.23/1.42  # Total time               : 0.059 s
% 0.23/1.42  # Maximum resident set size: 3448 pages
%------------------------------------------------------------------------------