TSTP Solution File: NUM830^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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  : 300s
% DateTime : Sat May  4 08:58:06 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   27 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :   34 (  25 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  185 (   4   ~;   0   |;  10   &; 165   @)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   30 (   0   ^  30   !;   0   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    n: $tType ).

thf(decl_22,type,
    c0: n ).

thf(decl_23,type,
    cS: n > n ).

thf(decl_24,type,
    c_plus: n > n > n ).

thf(decl_25,type,
    c_star: n > n > n ).

thf(decl_26,type,
    cPA_1: $o ).

thf(decl_27,type,
    cPA_2: $o ).

thf(decl_28,type,
    cPA_3: $o ).

thf(decl_29,type,
    cPA_4: $o ).

thf(cPA_THM1,conjecture,
    ( ( cPA_1
      & cPA_2
      & cPA_3
      & cPA_4 )
   => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
      = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p',cPA_THM1) ).

thf(cPA_4_def,axiom,
    ( cPA_4
  <=> ! [X1: n,X2: n] :
        ( ( c_star @ X1 @ ( cS @ X2 ) )
        = ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p',cPA_4_def) ).

thf(cPA_1_def,axiom,
    ( cPA_1
  <=> ! [X1: n] :
        ( ( c_plus @ X1 @ c0 )
        = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p',cPA_1_def) ).

thf(cPA_2_def,axiom,
    ( cPA_2
  <=> ! [X1: n,X2: n] :
        ( ( c_plus @ X1 @ ( cS @ X2 ) )
        = ( cS @ ( c_plus @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p',cPA_2_def) ).

thf(cPA_3_def,axiom,
    ( cPA_3
  <=> ! [X1: n] :
        ( ( c_star @ X1 @ c0 )
        = c0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p',cPA_3_def) ).

thf(c_0_5,negated_conjecture,
    ~ ( ( ! [X9: n] :
            ( ( c_plus @ X9 @ c0 )
            = X9 )
        & ! [X10: n,X11: n] :
            ( ( c_plus @ X10 @ ( cS @ X11 ) )
            = ( cS @ ( c_plus @ X10 @ X11 ) ) )
        & ! [X12: n] :
            ( ( c_star @ X12 @ c0 )
            = c0 )
        & ! [X13: n,X14: n] :
            ( ( c_star @ X13 @ ( cS @ X14 ) )
            = ( c_plus @ ( c_star @ X13 @ X14 ) @ X13 ) ) )
     => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
        = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cPA_THM1]),cPA_4_def]),cPA_1_def]),cPA_2_def]),cPA_3_def]) ).

thf(c_0_6,negated_conjecture,
    ! [X15: n,X16: n,X17: n,X18: n,X19: n,X20: n] :
      ( ( ( c_plus @ X15 @ c0 )
        = X15 )
      & ( ( c_plus @ X16 @ ( cS @ X17 ) )
        = ( cS @ ( c_plus @ X16 @ X17 ) ) )
      & ( ( c_star @ X18 @ c0 )
        = c0 )
      & ( ( c_star @ X19 @ ( cS @ X20 ) )
        = ( c_plus @ ( c_star @ X19 @ X20 ) @ X19 ) )
      & ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
       != ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: n,X2: n] :
      ( ( c_plus @ X1 @ ( cS @ X2 ) )
      = ( cS @ ( c_plus @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X2: n,X1: n] :
      ( ( c_star @ X1 @ ( cS @ X2 ) )
      = ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: n,X2: n] :
      ( ( cS @ ( c_plus @ ( c_star @ ( cS @ X1 ) @ X2 ) @ X1 ) )
      = ( c_star @ ( cS @ X1 ) @ ( cS @ X2 ) ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: n,X2: n] :
      ( ( cS @ ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ X1 ) ) @ X2 ) @ X1 ) ) )
      = ( c_star @ ( cS @ ( cS @ X1 ) ) @ ( cS @ X2 ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_7]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: n] :
      ( ( c_plus @ X1 @ c0 )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: n] :
      ( ( c_star @ X1 @ c0 )
      = c0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_13,negated_conjecture,
    ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
   != ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: n] :
      ( ( cS @ ( cS @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ X1 ) ) )
      = ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: n] :
      ( ( c_star @ X1 @ ( cS @ c0 ) )
      = ( c_plus @ c0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
   != ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_7]),c_0_7]),c_0_11]) ).

thf(c_0_17,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_7]),c_0_7]),c_0_11]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.11/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 09:37:28 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  Running higher-order theorem proving
% 0.21/0.50  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.8z7jc12lbT/E---3.1_11972.p
% 0.21/0.51  # Version: 3.1.0-ho
% 0.21/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho2 with 300s (1) cores
% 0.21/0.51  # post_as_ho8 with pid 12109 completed with status 0
% 0.21/0.51  # Result found by post_as_ho8
% 0.21/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.51  # Search class: HUUPM-FFSF21-MFFFMFNN
% 0.21/0.51  # partial match(2): FUUPM-FFSF21-MFFFFFNN
% 0.21/0.51  # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 0.21/0.51  # H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 12112 completed with status 0
% 0.21/0.51  # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 0.21/0.51  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.51  # Search class: HUUPM-FFSF21-MFFFMFNN
% 0.21/0.51  # partial match(2): FUUPM-FFSF21-MFFFFFNN
% 0.21/0.51  # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.001 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 14
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 9
% 0.21/0.51  # Initial clauses                      : 5
% 0.21/0.51  # Removed in clause preprocessing      : 0
% 0.21/0.51  # Initial clauses in saturation        : 5
% 0.21/0.51  # Processed clauses                    : 23
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 3
% 0.21/0.51  # ...remaining for further processing  : 20
% 0.21/0.51  # Other redundant clauses eliminated   : 0
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 0
% 0.21/0.51  # Backward-rewritten                   : 1
% 0.21/0.51  # Generated clauses                    : 94
% 0.21/0.51  # ...of the previous two non-redundant : 74
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 0
% 0.21/0.51  # Paramodulations                      : 94
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 0
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 100
% 0.21/0.51  # ...of those cached                   : 47
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 14
% 0.21/0.51  #    Positive orientable unit clauses  : 10
% 0.21/0.51  #    Positive unorientable unit clauses: 3
% 0.21/0.51  #    Negative unit clauses             : 1
% 0.21/0.51  #    Non-unit-clauses                  : 0
% 0.21/0.51  # Current number of unprocessed clauses: 51
% 0.21/0.51  # ...number of literals in the above   : 51
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 6
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 0
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 0
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 0
% 0.21/0.51  # Unit Clause-clause subsumption calls : 0
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 6
% 0.21/0.51  # BW rewrite match successes           : 6
% 0.21/0.51  # Condensation attempts                : 0
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 2233
% 0.21/0.51  # Search garbage collected termcells   : 118
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.006 s
% 0.21/0.51  # System time              : 0.002 s
% 0.21/0.51  # Total time               : 0.007 s
% 0.21/0.51  # Maximum resident set size: 1804 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.006 s
% 0.21/0.51  # System time              : 0.005 s
% 0.21/0.51  # Total time               : 0.011 s
% 0.21/0.51  # Maximum resident set size: 1728 pages
% 0.21/0.51  % E---3.1 exiting
% 0.21/0.51  % E exiting
%------------------------------------------------------------------------------