TSTP Solution File: SYO535^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO535^1 : TPTP v8.2.0. Released v5.2.0.
% 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 : Tue May 21 08:47:59 EDT 2024

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   27 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :   22 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  123 (  10   ~;   5   |;   1   &; 103   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  74   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   63 (  27   ^  16   !;  20   ?;  63   :)

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

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

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

thf(decl_25,type,
    epsb: ( $i > ( $i > $i ) > $o ) > $i > $i ).

thf(decl_26,type,
    epred1_0: $i > ( $i > $i ) > $o ).

thf(decl_27,type,
    esk1_0: $i ).

thf(decl_28,type,
    esk2_0: $i > $i ).

thf(epsbd,axiom,
    ( epsb
    = ( ^ [X5: $i > ( $i > $i ) > $o] :
          ( epsii
          @ ^ [X6: $i > $i] : ( X5 @ ( epsa @ X5 ) @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsbd) ).

thf(epsad,axiom,
    ( epsa
    = ( ^ [X5: $i > ( $i > $i ) > $o] :
          ( eps
          @ ^ [X2: $i] :
            ? [X6: $i > $i] : ( X5 @ X2 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsad) ).

thf(conj,conjecture,
    ! [X5: $i > ( $i > $i ) > $o] :
      ( ? [X2: $i,X6: $i > $i] : ( X5 @ X2 @ X6 )
     => ( X5 @ ( epsa @ X5 ) @ ( epsb @ X5 ) ) ),
    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(choiceaxii,axiom,
    ! [X3: ( $i > $i ) > $o] :
      ( ? [X4: $i > $i] : ( X3 @ X4 )
     => ( X3 @ ( epsii @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxii) ).

thf(c_0_5,plain,
    ( epsb
    = ( ^ [Z0: $i > ( $i > $i ) > $o] :
          ( epsii
          @ ^ [Z1: $i > $i] :
              ( Z0
              @ ( eps
                @ ^ [Z2: $i] :
                  ? [X14: $i > $i] : ( Z0 @ Z2 @ X14 ) )
              @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[epsbd]) ).

thf(c_0_6,plain,
    ( epsa
    = ( ^ [Z0: $i > ( $i > $i ) > $o] :
          ( eps
          @ ^ [Z1: $i] :
            ? [X6: $i > $i] : ( Z0 @ Z1 @ X6 ) ) ) ),
    inference(fof_simplification,[status(thm)],[epsad]) ).

thf(c_0_7,plain,
    ( epsb
    = ( ^ [Z0: $i > ( $i > $i ) > $o] :
          ( epsii
          @ ^ [Z1: $i > $i] :
              ( Z0
              @ ( eps
                @ ^ [Z2: $i] :
                  ? [X14: $i > $i] : ( Z0 @ Z2 @ X14 ) )
              @ Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ~ ! [X5: $i > ( $i > $i ) > $o] :
        ( ? [X2: $i,X6: $i > $i] : ( X5 @ X2 @ X6 )
       => ( X5
          @ ( eps
            @ ^ [Z0: $i] :
              ? [X15: $i > $i] : ( X5 @ Z0 @ X15 ) )
          @ ( epsii
            @ ^ [Z0: $i > $i] :
                ( X5
                @ ( eps
                  @ ^ [Z1: $i] :
                    ? [X16: $i > $i] : ( X5 @ Z1 @ X16 ) )
                @ Z0 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[conj]),c_0_7]),c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ( ( epred1_0 @ esk1_0 @ esk2_0 )
    & ~ ( epred1_0
        @ ( eps
          @ ^ [Z0: $i] :
            ? [X15: $i > $i] : ( epred1_0 @ Z0 @ X15 ) )
        @ ( epsii
          @ ( epred1_0
            @ ( eps
              @ ^ [Z0: $i] :
                ? [X16: $i > $i] : ( epred1_0 @ Z0 @ X16 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

thf(c_0_10,plain,
    ! [X22: $i > $o,X23: $i] :
      ( ~ ( X22 @ X23 )
      | ( X22 @ ( eps @ X22 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).

thf(c_0_11,plain,
    ! [X20: ( $i > $i ) > $o,X21: $i > $i] :
      ( ~ ( X20 @ X21 )
      | ( X20 @ ( epsii @ X20 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxii])])])]) ).

thf(c_0_12,negated_conjecture,
    ~ ( epred1_0
      @ ( eps
        @ ^ [Z0: $i] :
          ? [X30: $i > $i] :
            ( epred1_0 @ Z0
            @ ^ [Z1: $i] : ( X30 @ Z1 ) ) )
      @ ( epsii
        @ ( epred1_0
          @ ( eps
            @ ^ [Z0: $i] :
              ? [X31: $i > $i] :
                ( epred1_0 @ Z0
                @ ^ [Z1: $i] : ( X31 @ Z1 ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_13,plain,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ ( eps @ X1 ) )
      | ~ ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_14,plain,
    ! [X3: ( $i > $i ) > $o,X4: $i > $i] :
      ( ( X3 @ ( epsii @ X3 ) )
      | ~ ( X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_15,negated_conjecture,
    ! [X2: $i] :
      ( ? [X32: $i > $i] :
          ( epred1_0
          @ ( eps
            @ ^ [Z0: $i] :
              ? [X33: $i > $i] :
                ( epred1_0 @ Z0
                @ ^ [Z1: $i] : ( X33 @ Z1 ) ) )
          @ ^ [Z0: $i] : ( X32 @ Z0 ) )
      | ~ ? [X34: $i > $i] :
            ( epred1_0 @ X2
            @ ^ [Z0: $i] : ( X34 @ Z0 ) ) ),
    inference(choice_inst,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ! [X4: $i > $i] :
      ~ ( epred1_0
        @ ( eps
          @ ^ [Z0: $i] :
            ? [X35: $i > $i] :
              ( epred1_0 @ Z0
              @ ^ [Z1: $i] : ( X35 @ Z1 ) ) )
        @ X4 ),
    inference(sr,[status(thm)],[inference(choice_inst,[status(thm)],[c_0_12,c_0_14]),c_0_12]) ).

thf(c_0_17,negated_conjecture,
    epred1_0 @ esk1_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_18,negated_conjecture,
    ! [X2: $i,X4: $i > $i] :
      ~ ( epred1_0 @ X2 @ X4 ),
    inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_15]),c_0_16]) ).

thf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_17,c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYO535^1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n021.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 10:53:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 0.19/0.48  # Version: 3.1.0-ho
% 0.19/0.48  # Preprocessing class: HSSSSMSSSSMCHHA.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # new_bool_3 with pid 7584 completed with status 0
% 0.19/0.48  # Result found by new_bool_3
% 0.19/0.48  # Preprocessing class: HSSSSMSSSSMCHHA.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.48  # Search class: HHUNF-FFSF21-DHHFFMBC
% 0.19/0.48  # partial match(3): HHUSS-FFSF21-MHHFFMBC
% 0.19/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.48  # new_ho_10 with pid 7587 completed with status 0
% 0.19/0.48  # Result found by new_ho_10
% 0.19/0.48  # Preprocessing class: HSSSSMSSSSMCHHA.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.48  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.48  # Search class: HHUNF-FFSF21-DHHFFMBC
% 0.19/0.48  # partial match(3): HHUSS-FFSF21-MHHFFMBC
% 0.19/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.48  # Preprocessing time       : 0.001 s
% 0.19/0.48  # Presaturation interreduction done
% 0.19/0.48  
% 0.19/0.48  # Proof found!
% 0.19/0.48  # SZS status Theorem
% 0.19/0.48  # SZS output start CNFRefutation
% See solution above
% 0.19/0.48  # Parsed axioms                        : 9
% 0.19/0.48  # Removed by relevancy pruning/SinE    : 4
% 0.19/0.48  # Initial clauses                      : 4
% 0.19/0.48  # Removed in clause preprocessing      : 0
% 0.19/0.48  # Initial clauses in saturation        : 4
% 0.19/0.48  # Processed clauses                    : 12
% 0.19/0.48  # ...of these trivial                  : 0
% 0.19/0.48  # ...subsumed                          : 0
% 0.19/0.48  # ...remaining for further processing  : 12
% 0.19/0.48  # Other redundant clauses eliminated   : 0
% 0.19/0.48  # Clauses deleted for lack of memory   : 0
% 0.19/0.48  # Backward-subsumed                    : 2
% 0.19/0.48  # Backward-rewritten                   : 0
% 0.19/0.48  # Generated clauses                    : 9
% 0.19/0.48  # ...of the previous two non-redundant : 6
% 0.19/0.48  # ...aggressively subsumed             : 0
% 0.19/0.48  # Contextual simplify-reflections      : 0
% 0.19/0.48  # Paramodulations                      : 2
% 0.19/0.48  # Factorizations                       : 0
% 0.19/0.48  # NegExts                              : 0
% 0.19/0.48  # Equation resolutions                 : 0
% 0.19/0.48  # Disequality decompositions           : 0
% 0.19/0.48  # Total rewrite steps                  : 1
% 0.19/0.48  # ...of those cached                   : 0
% 0.19/0.48  # Propositional unsat checks           : 0
% 0.19/0.48  #    Propositional check models        : 0
% 0.19/0.48  #    Propositional check unsatisfiable : 0
% 0.19/0.48  #    Propositional clauses             : 0
% 0.19/0.48  #    Propositional clauses after purity: 0
% 0.19/0.48  #    Propositional unsat core size     : 0
% 0.19/0.48  #    Propositional preprocessing time  : 0.000
% 0.19/0.48  #    Propositional encoding time       : 0.000
% 0.19/0.48  #    Propositional solver time         : 0.000
% 0.19/0.48  #    Success case prop preproc time    : 0.000
% 0.19/0.48  #    Success case prop encoding time   : 0.000
% 0.19/0.48  #    Success case prop solver time     : 0.000
% 0.19/0.48  # Current number of processed clauses  : 3
% 0.19/0.48  #    Positive orientable unit clauses  : 0
% 0.19/0.48  #    Positive unorientable unit clauses: 0
% 0.19/0.48  #    Negative unit clauses             : 1
% 0.19/0.48  #    Non-unit-clauses                  : 2
% 0.19/0.48  # Current number of unprocessed clauses: 2
% 0.19/0.48  # ...number of literals in the above   : 4
% 0.19/0.48  # Current number of archived formulas  : 0
% 0.19/0.48  # Current number of archived clauses   : 9
% 0.19/0.48  # Clause-clause subsumption calls (NU) : 1
% 0.19/0.48  # Rec. Clause-clause subsumption calls : 1
% 0.19/0.48  # Non-unit clause-clause subsumptions  : 0
% 0.19/0.48  # Unit Clause-clause subsumption calls : 2
% 0.19/0.48  # Rewrite failures with RHS unbound    : 0
% 0.19/0.48  # BW rewrite match attempts            : 0
% 0.19/0.48  # BW rewrite match successes           : 0
% 0.19/0.48  # Condensation attempts                : 12
% 0.19/0.48  # Condensation successes               : 0
% 0.19/0.48  # Termbank termtop insertions          : 1362
% 0.19/0.48  # Search garbage collected termcells   : 202
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.005 s
% 0.19/0.48  # System time              : 0.001 s
% 0.19/0.48  # Total time               : 0.006 s
% 0.19/0.48  # Maximum resident set size: 1896 pages
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.008 s
% 0.19/0.48  # System time              : 0.001 s
% 0.19/0.48  # Total time               : 0.010 s
% 0.19/0.48  # Maximum resident set size: 1732 pages
% 0.19/0.48  % E---3.1 exiting
% 0.19/0.48  % E exiting
%------------------------------------------------------------------------------