TSTP Solution File: SWC122+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWC122+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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 20:26:49 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  11 unt;   0 def)
%            Number of atoms       :  133 (  26 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  173 (  69   ~;  65   |;  24   &)
%                                         (   2 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn  21   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ neq(X2,nil)
                    | ( nil != X3
                      & nil = X4 )
                    | ( neq(X1,nil)
                      & segmentP(X2,X1) )
                    | ( neq(X4,nil)
                      & ( ~ neq(X3,nil)
                        | ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',co1) ).

fof(ax7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

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

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ( nil != X3
                        & nil = X4 )
                      | ( neq(X1,nil)
                        & segmentP(X2,X1) )
                      | ( neq(X4,nil)
                        & ( ~ neq(X3,nil)
                          | ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_6,plain,
    ! [X5,X6,X9,X10] :
      ( ( ssList(esk8_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk9_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( app(app(esk8_2(X5,X6),X6),esk9_2(X5,X6)) = X5
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ~ ssList(X9)
        | ~ ssList(X10)
        | app(app(X9,X6),X10) != X5
        | segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(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)],[ax7])])])])])])]) ).

fof(c_0_7,plain,
    ! [X4,X5,X7] :
      ( ( ssList(esk5_2(X4,X5))
        | ~ rearsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( app(esk5_2(X4,X5),X5) = X4
        | ~ rearsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( ~ ssList(X7)
        | app(X7,X5) != X4
        | rearsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(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)],[ax6])])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ( ssList(esk1_0)
    & ssList(esk2_0)
    & ssList(esk3_0)
    & ssList(esk4_0)
    & esk2_0 = esk4_0
    & esk1_0 = esk3_0
    & neq(esk2_0,nil)
    & ( nil = esk3_0
      | nil != esk4_0 )
    & ( ~ neq(esk1_0,nil)
      | ~ segmentP(esk2_0,esk1_0) )
    & ( neq(esk3_0,nil)
      | ~ neq(esk4_0,nil) )
    & ( rearsegP(esk4_0,esk3_0)
      | ~ neq(esk4_0,nil) ) ),
    inference(distribute,[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_5])])])])])])]) ).

cnf(c_0_9,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( app(esk5_2(X1,X2),X2) = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( ssList(esk5_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_13,negated_conjecture,
    ( neq(esk3_0,nil)
    | ~ neq(esk4_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    neq(esk2_0,nil),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,plain,
    ( segmentP(X1,X2)
    | app(X3,X4) != X1
    | ~ rearsegP(X3,X2)
    | ~ ssList(X4)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_18,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_20,negated_conjecture,
    ( rearsegP(esk4_0,esk3_0)
    | ~ neq(esk4_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ( ~ segmentP(esk2_0,esk1_0)
    | ~ neq(esk1_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_22,negated_conjecture,
    neq(esk1_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).

cnf(c_0_23,plain,
    ( segmentP(X1,X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])])]) ).

cnf(c_0_24,negated_conjecture,
    rearsegP(esk2_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15]),c_0_14]),c_0_15]),c_0_16])]) ).

cnf(c_0_25,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_26,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_27,negated_conjecture,
    ~ segmentP(esk2_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC122+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13  % Command  : run_ET %s %d
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jun 12 23:57:51 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.020 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 29
% 0.24/1.42  # Proof object clause steps            : 19
% 0.24/1.42  # Proof object formula steps           : 10
% 0.24/1.42  # Proof object conjectures             : 15
% 0.24/1.42  # Proof object clause conjectures      : 12
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 13
% 0.24/1.42  # Proof object initial formulas used   : 5
% 0.24/1.42  # Proof object generating inferences   : 3
% 0.24/1.42  # Proof object simplifying inferences  : 19
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 96
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 63
% 0.24/1.42  # Initial clauses                      : 59
% 0.24/1.42  # Removed in clause preprocessing      : 0
% 0.24/1.42  # Initial clauses in saturation        : 59
% 0.24/1.42  # Processed clauses                    : 804
% 0.24/1.42  # ...of these trivial                  : 24
% 0.24/1.42  # ...subsumed                          : 555
% 0.24/1.42  # ...remaining for further processing  : 225
% 0.24/1.42  # Other redundant clauses eliminated   : 54
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 14
% 0.24/1.42  # Backward-rewritten                   : 2
% 0.24/1.42  # Generated clauses                    : 4102
% 0.24/1.42  # ...of the previous two non-trivial   : 3575
% 0.24/1.42  # Contextual simplify-reflections      : 297
% 0.24/1.42  # Paramodulations                      : 4027
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 75
% 0.24/1.42  # Current number of processed clauses  : 207
% 0.24/1.42  #    Positive orientable unit clauses  : 14
% 0.24/1.42  #    Positive unorientable unit clauses: 0
% 0.24/1.42  #    Negative unit clauses             : 6
% 0.24/1.42  #    Non-unit-clauses                  : 187
% 0.24/1.42  # Current number of unprocessed clauses: 2766
% 0.24/1.42  # ...number of literals in the above   : 17945
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 16
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 14946
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 9015
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 693
% 0.24/1.42  # Unit Clause-clause subsumption calls : 63
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 5
% 0.24/1.42  # BW rewrite match successes           : 5
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 69106
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.139 s
% 0.24/1.42  # System time              : 0.003 s
% 0.24/1.42  # Total time               : 0.142 s
% 0.24/1.42  # Maximum resident set size: 5816 pages
%------------------------------------------------------------------------------