TSTP Solution File: SYO556^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO556^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 : Tue May 21 08:48:03 EDT 2024

% Result   : Theorem 0.21s 0.49s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (  15 unt;   6 typ;   0 def)
%            Number of atoms       :   94 (  43 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  150 (  38   ~;  19   |;  18   &;  72   @)
%                                         (   0 <=>;   1  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-3 aty)
%            Number of variables   :   56 (  30   ^  10   !;  16   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    eps: ( $i > $o ) > $i ).

thf(decl_23,type,
    if: $o > $i > $i > $i ).

thf(decl_24,type,
    epred1_0: $i > $o ).

thf(decl_27,type,
    esk3_0: $i ).

thf(decl_29,type,
    esk5_0: $i ).

thf(decl_42,type,
    esk18_0: $i ).

thf(ifd,axiom,
    ( if
    = ( ^ [X3: $o,X2: $i,X4: $i] :
          ( eps
          @ ^ [X5: $i] :
              ( ( X3
                & ( X5 = X2 ) )
              | ( ~ X3
                & ( X5 = X4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifd) ).

thf(conj,conjecture,
    ! [X1: $i > $o] :
      ( ( eps @ X1 )
      = ( if
        @ ? [X2: $i] : ( X1 @ X2 )
        @ ( eps @ X1 )
        @ ( eps
          @ ^ [X2: $i] : ~ $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(choiceax,axiom,
    ! [X1: $i > $o] :
      ( ? [X2: $i] : ( X1 @ X2 )
     => ( X1 @ ( eps @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).

thf(c_0_3,plain,
    ( if
    = ( ^ [Z0: $o,Z1: $i,Z2: $i] :
          ( eps
          @ ^ [Z3: $i] :
              ( ( Z0
                & ( Z3 = Z1 ) )
              | ( ~ Z0
                & Z3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ifd]) ).

thf(c_0_4,negated_conjecture,
    ~ ! [X1: $i > $o] :
        ( ( eps @ X1 )
        = ( eps
          @ ^ [Z0: $i] :
              ( ( ? [X2: $i] : ( X1 @ X2 )
                & ( Z0
                  = ( eps @ X1 ) ) )
              | ( ~ ? [X2: $i] : ( X1 @ X2 )
                & ( Z0
                  = ( eps
                    @ ^ [Z1: $i] : ~ $true ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_3]) ).

thf(c_0_5,plain,
    ! [X10: $i > $o,X11: $i] :
      ( ~ ( X10 @ X11 )
      | ( X10 @ ( eps @ X10 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).

thf(c_0_6,negated_conjecture,
    ( ( eps @ epred1_0 )
   != ( eps
      @ ^ [Z0: $i] :
          ( ( ? [X2: $i] : ( epred1_0 @ X2 )
            & ( Z0
              = ( eps @ epred1_0 ) ) )
          | ( ~ ? [X2: $i] : ( epred1_0 @ X2 )
            & ( Z0
              = ( eps
                @ ^ [Z1: $i] : ~ $true ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

thf(c_0_7,plain,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ ( eps @ X1 ) )
      | ~ ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,negated_conjecture,
    ( ( eps @ epred1_0 )
   != ( eps
      @ ^ [Z0: $i] :
          ( ( ? [X59: $i] : ( epred1_0 @ X59 )
            & ( Z0
              = ( eps @ epred1_0 ) ) )
          | ( ~ ? [X60: $i] : ( epred1_0 @ X60 )
            & ( Z0
              = ( eps
                @ ^ [Z1: $i] : ~ $true ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,plain,
    ! [X2: $i] :
      ( ( eps
        @ ^ [Z0: $i] : ( Z0 = X2 ) )
      = X2 ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).

thf(c_0_10,plain,
    ( ( ^ [Z0: $i] :
          ( ( ? [X61: $i] : ( epred1_0 @ X61 )
            & ( Z0
              = ( eps @ epred1_0 ) ) )
          | ( ~ ? [X62: $i] : ( epred1_0 @ X62 )
            & ( Z0
              = ( eps
                @ ^ [Z1: $i] : ~ $true ) ) ) ) )
   != ( ^ [Z0: $i] :
          ( Z0
          = ( eps @ epred1_0 ) ) ) ),
    inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_8,c_0_9])]) ).

thf(c_0_11,negated_conjecture,
    ( ( ^ [Z0: $i] :
          ( ( ? [X63: $i] : ( epred1_0 @ X63 )
            & ( Z0
              = ( eps @ epred1_0 ) ) )
          | ( ~ ? [X64: $i] : ( epred1_0 @ X64 )
            & ( Z0
              = ( eps
                @ ^ [Z1: $i] : ~ $true ) ) ) ) )
   != epred1_0 ),
    inference(ext_eqres,[status(thm)],[c_0_8]) ).

thf(c_0_12,plain,
    ( ( ( ? [X65: $i] : ( epred1_0 @ X65 )
        & ( esk18_0
          = ( eps @ epred1_0 ) ) )
      | ( ~ ? [X66: $i] : ( epred1_0 @ X66 )
        & ( esk18_0
          = ( eps
            @ ^ [Z0: $i] : ~ $true ) ) ) )
  <~> ( esk18_0
      = ( eps @ epred1_0 ) ) ),
    inference(neg_ext,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ( ( ( ? [X67: $i] : ( epred1_0 @ X67 )
        & ( esk3_0
          = ( eps @ epred1_0 ) ) )
      | ( ~ ? [X68: $i] : ( epred1_0 @ X68 )
        & ( esk3_0
          = ( eps
            @ ^ [Z0: $i] : ~ $true ) ) ) )
  <~> ( epred1_0 @ esk3_0 ) ),
    inference(neg_ext,[status(thm)],[c_0_11]) ).

thf(c_0_14,plain,
    ! [X2: $i] :
      ( ( ( eps @ epred1_0 )
       != esk18_0 )
      | ~ ( epred1_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]) ).

thf(c_0_15,negated_conjecture,
    ( ( ( eps @ epred1_0 )
      = esk3_0 )
    | ( ( eps
        @ ^ [Z0: $i] : ~ $true )
      = esk3_0 )
    | ( epred1_0 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_13])]) ).

thf(c_0_16,plain,
    ! [X2: $i] :
      ~ ( epred1_0 @ X2 ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]),c_0_14]) ).

thf(c_0_17,negated_conjecture,
    ( ( ( eps
        @ ^ [Z0: $i] : ~ $true )
      = esk3_0 )
    | ( ( eps @ epred1_0 )
      = esk3_0 ) ),
    inference(sr,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_18,plain,
    ( ( ( eps @ epred1_0 )
      = esk3_0 )
    | ( ( ^ [Z0: $i] : ~ $true )
     != epred1_0 ) ),
    inference(ext_eqfact,[status(thm)],[c_0_17]) ).

thf(c_0_19,plain,
    ( ( eps @ epred1_0 )
    = esk3_0 ),
    inference(sr,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_18]),c_0_16]) ).

thf(c_0_20,negated_conjecture,
    ( ( ( eps
        @ ^ [Z0: $i] : ~ $true )
      = esk3_0 )
    | ( epred1_0 @ esk3_0 )
    | ( epred1_0 @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_13])]) ).

thf(c_0_21,plain,
    ( ( ( eps
        @ ^ [Z0: $i] : ~ $true )
     != esk18_0 )
    | ( esk3_0 != esk18_0 ) ),
    inference(cn,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12]),c_0_19]),c_0_16])]) ).

thf(c_0_22,negated_conjecture,
    ( ( eps
      @ ^ [Z0: $i] : ~ $true )
    = esk3_0 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_20,c_0_16]),c_0_16]) ).

thf(c_0_23,negated_conjecture,
    esk3_0 != esk18_0,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_24,plain,
    ( ( eps
      @ ^ [Z0: $i] : ~ $true )
    = esk18_0 ),
    inference(cn,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]),c_0_19]),c_0_23])]) ).

thf(c_0_25,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO556^1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 10:43:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.21/0.47  Running higher-order theorem proving
% 0.21/0.47  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/benchmark/theBenchmark.p
% 0.21/0.49  # Version: 3.1.0-ho
% 0.21/0.49  # Preprocessing class: HSSSSMSSSSMCSSA.
% 0.21/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.49  # new_bool_3 with pid 9864 completed with status 0
% 0.21/0.49  # Result found by new_bool_3
% 0.21/0.49  # Preprocessing class: HSSSSMSSSSMCSSA.
% 0.21/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.49  # Search class: HHUSF-FFSF11-DSSFFMBC
% 0.21/0.49  # partial match(2): HHUSF-FFSF11-SSSFFMBN
% 0.21/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49  # Starting ehoh_best_nonlift with 163s (1) cores
% 0.21/0.49  # ehoh_best_nonlift with pid 9868 completed with status 0
% 0.21/0.49  # Result found by ehoh_best_nonlift
% 0.21/0.49  # Preprocessing class: HSSSSMSSSSMCSSA.
% 0.21/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.21/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.49  # Search class: HHUSF-FFSF11-DSSFFMBC
% 0.21/0.49  # partial match(2): HHUSF-FFSF11-SSSFFMBN
% 0.21/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49  # Starting ehoh_best_nonlift with 163s (1) cores
% 0.21/0.49  # Preprocessing time       : 0.001 s
% 0.21/0.49  # Presaturation interreduction done
% 0.21/0.49  
% 0.21/0.49  # Proof found!
% 0.21/0.49  # SZS status Theorem
% 0.21/0.49  # SZS output start CNFRefutation
% See solution above
% 0.21/0.49  # Parsed axioms                        : 5
% 0.21/0.49  # Removed by relevancy pruning/SinE    : 2
% 0.21/0.49  # Initial clauses                      : 2
% 0.21/0.49  # Removed in clause preprocessing      : 0
% 0.21/0.49  # Initial clauses in saturation        : 2
% 0.21/0.49  # Processed clauses                    : 81
% 0.21/0.49  # ...of these trivial                  : 3
% 0.21/0.49  # ...subsumed                          : 10
% 0.21/0.49  # ...remaining for further processing  : 68
% 0.21/0.49  # Other redundant clauses eliminated   : 12
% 0.21/0.49  # Clauses deleted for lack of memory   : 0
% 0.21/0.49  # Backward-subsumed                    : 33
% 0.21/0.49  # Backward-rewritten                   : 5
% 0.21/0.49  # Generated clauses                    : 156
% 0.21/0.49  # ...of the previous two non-redundant : 127
% 0.21/0.49  # ...aggressively subsumed             : 0
% 0.21/0.49  # Contextual simplify-reflections      : 12
% 0.21/0.49  # Paramodulations                      : 45
% 0.21/0.49  # Factorizations                       : 0
% 0.21/0.49  # NegExts                              : 15
% 0.21/0.49  # Equation resolutions                 : 13
% 0.21/0.49  # Disequality decompositions           : 0
% 0.21/0.49  # Total rewrite steps                  : 8
% 0.21/0.49  # ...of those cached                   : 6
% 0.21/0.49  # Propositional unsat checks           : 0
% 0.21/0.49  #    Propositional check models        : 0
% 0.21/0.49  #    Propositional check unsatisfiable : 0
% 0.21/0.49  #    Propositional clauses             : 0
% 0.21/0.49  #    Propositional clauses after purity: 0
% 0.21/0.49  #    Propositional unsat core size     : 0
% 0.21/0.49  #    Propositional preprocessing time  : 0.000
% 0.21/0.49  #    Propositional encoding time       : 0.000
% 0.21/0.49  #    Propositional solver time         : 0.000
% 0.21/0.49  #    Success case prop preproc time    : 0.000
% 0.21/0.49  #    Success case prop encoding time   : 0.000
% 0.21/0.49  #    Success case prop solver time     : 0.000
% 0.21/0.49  # Current number of processed clauses  : 16
% 0.21/0.49  #    Positive orientable unit clauses  : 3
% 0.21/0.49  #    Positive unorientable unit clauses: 2
% 0.21/0.49  #    Negative unit clauses             : 5
% 0.21/0.49  #    Non-unit-clauses                  : 6
% 0.21/0.49  # Current number of unprocessed clauses: 33
% 0.21/0.49  # ...number of literals in the above   : 106
% 0.21/0.49  # Current number of archived formulas  : 0
% 0.21/0.49  # Current number of archived clauses   : 52
% 0.21/0.49  # Clause-clause subsumption calls (NU) : 232
% 0.21/0.49  # Rec. Clause-clause subsumption calls : 144
% 0.21/0.49  # Non-unit clause-clause subsumptions  : 31
% 0.21/0.49  # Unit Clause-clause subsumption calls : 32
% 0.21/0.49  # Rewrite failures with RHS unbound    : 0
% 0.21/0.49  # BW rewrite match attempts            : 25
% 0.21/0.49  # BW rewrite match successes           : 10
% 0.21/0.49  # Condensation attempts                : 0
% 0.21/0.49  # Condensation successes               : 0
% 0.21/0.49  # Termbank termtop insertions          : 11829
% 0.21/0.49  # Search garbage collected termcells   : 85
% 0.21/0.49  
% 0.21/0.49  # -------------------------------------------------
% 0.21/0.49  # User time                : 0.013 s
% 0.21/0.49  # System time              : 0.002 s
% 0.21/0.49  # Total time               : 0.015 s
% 0.21/0.49  # Maximum resident set size: 1840 pages
% 0.21/0.49  
% 0.21/0.49  # -------------------------------------------------
% 0.21/0.49  # User time                : 0.014 s
% 0.21/0.49  # System time              : 0.004 s
% 0.21/0.49  # Total time               : 0.018 s
% 0.21/0.49  # Maximum resident set size: 1704 pages
% 0.21/0.49  % E---3.1 exiting
% 0.21/0.50  % E exiting
%------------------------------------------------------------------------------