TSTP Solution File: SEU494^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 03:27:34 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   37 (  14 unt;  10 typ;   0 def)
%            Number of atoms       :   67 (   9 equ;   0 cnn)
%            Maximal formula atoms :   17 (   2 avg)
%            Number of connectives :  230 (  22   ~;  21   |;  18   &; 155   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   57 (  13   ^  44   !;   0   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    inv: ( $i > $i > $o ) > $i > $i > $o ).

thf(decl_32,type,
    asymm: ( $i > $i > $o ) > $o ).

thf(decl_34,type,
    trans: ( $i > $i > $o ) > $o ).

thf(decl_39,type,
    so: ( $i > $i > $o ) > $o ).

thf(decl_51,type,
    epred1_0: $i > $i > $o ).

thf(decl_52,type,
    esk1_0: $i ).

thf(decl_53,type,
    esk2_0: $i ).

thf(decl_54,type,
    esk3_0: $i ).

thf(decl_55,type,
    esk4_0: $i ).

thf(decl_56,type,
    esk5_0: $i ).

thf(strict_order,axiom,
    ( so
    = ( ^ [X1: $i > $i > $o] :
          ( ( asymm @ X1 )
          & ( trans @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',strict_order) ).

thf(asymmetric,axiom,
    ( asymm
    = ( ^ [X1: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( X1 @ X3 @ X4 )
         => ~ ( X1 @ X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',asymmetric) ).

thf(transitive,axiom,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( X1 @ X3 @ X4 )
            & ( X1 @ X4 @ X6 ) )
         => ( X1 @ X3 @ X6 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).

thf(inverse,axiom,
    ( inv
    = ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] : ( X1 @ X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',inverse) ).

thf(inverse_of_strict_order_is_strict_order,conjecture,
    ! [X1: $i > $i > $o] :
      ( ( so @ X1 )
     => ( so @ ( inv @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_strict_order_is_strict_order) ).

thf(c_0_5,plain,
    ( so
    = ( ^ [Z0: $i > $i > $o] :
          ( ! [X39: $i,X40: $i] :
              ( ( Z0 @ X39 @ X40 )
             => ~ ( Z0 @ X40 @ X39 ) )
          & ! [X41: $i,X42: $i,X43: $i] :
              ( ( ( Z0 @ X41 @ X42 )
                & ( Z0 @ X42 @ X43 ) )
             => ( Z0 @ X41 @ X43 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[strict_order]) ).

thf(c_0_6,plain,
    ( asymm
    = ( ^ [Z0: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( Z0 @ X3 @ X4 )
         => ~ ( Z0 @ X4 @ X3 ) ) ) ),
    inference(fof_simplification,[status(thm)],[asymmetric]) ).

thf(c_0_7,plain,
    ( trans
    = ( ^ [Z0: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( Z0 @ X3 @ X4 )
            & ( Z0 @ X4 @ X6 ) )
         => ( Z0 @ X3 @ X6 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive]) ).

thf(c_0_8,plain,
    ( inv
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] : ( Z0 @ Z2 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[inverse]) ).

thf(c_0_9,plain,
    ( so
    = ( ^ [Z0: $i > $i > $o] :
          ( ! [X39: $i,X40: $i] :
              ( ( Z0 @ X39 @ X40 )
             => ~ ( Z0 @ X40 @ X39 ) )
          & ! [X41: $i,X42: $i,X43: $i] :
              ( ( ( Z0 @ X41 @ X42 )
                & ( Z0 @ X42 @ X43 ) )
             => ( Z0 @ X41 @ X43 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

thf(c_0_10,negated_conjecture,
    ~ ! [X1: $i > $i > $o] :
        ( ( ! [X158: $i,X159: $i] :
              ( ( X1 @ X158 @ X159 )
             => ~ ( X1 @ X159 @ X158 ) )
          & ! [X160: $i,X161: $i,X162: $i] :
              ( ( ( X1 @ X160 @ X161 )
                & ( X1 @ X161 @ X162 ) )
             => ( X1 @ X160 @ X162 ) ) )
       => ( ! [X163: $i,X164: $i] :
              ( ( X1 @ X164 @ X163 )
             => ~ ( X1 @ X163 @ X164 ) )
          & ! [X165: $i,X166: $i,X167: $i] :
              ( ( ( X1 @ X166 @ X165 )
                & ( X1 @ X167 @ X166 ) )
             => ( X1 @ X167 @ X165 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[inverse_of_strict_order_is_strict_order]),c_0_8]),c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ! [X169: $i,X170: $i,X171: $i,X172: $i,X173: $i] :
      ( ( ~ ( epred1_0 @ X169 @ X170 )
        | ~ ( epred1_0 @ X170 @ X169 ) )
      & ( ~ ( epred1_0 @ X171 @ X172 )
        | ~ ( epred1_0 @ X172 @ X173 )
        | ( epred1_0 @ X171 @ X173 ) )
      & ( ( epred1_0 @ esk4_0 @ esk3_0 )
        | ( epred1_0 @ esk2_0 @ esk1_0 ) )
      & ( ( epred1_0 @ esk5_0 @ esk4_0 )
        | ( epred1_0 @ esk2_0 @ esk1_0 ) )
      & ( ~ ( epred1_0 @ esk5_0 @ esk3_0 )
        | ( epred1_0 @ esk2_0 @ esk1_0 ) )
      & ( ( epred1_0 @ esk4_0 @ esk3_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) )
      & ( ( epred1_0 @ esk5_0 @ esk4_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( epred1_0 @ esk5_0 @ esk3_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: $i,X4: $i,X6: $i] :
      ( ( epred1_0 @ X3 @ X6 )
      | ~ ( epred1_0 @ X3 @ X4 )
      | ~ ( epred1_0 @ X4 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_13,negated_conjecture,
    ( ( epred1_0 @ esk4_0 @ esk3_0 )
    | ( epred1_0 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ! [X3: $i] :
      ( ( epred1_0 @ esk1_0 @ esk2_0 )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ~ ( epred1_0 @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_15,negated_conjecture,
    ( ( epred1_0 @ esk5_0 @ esk4_0 )
    | ( epred1_0 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,negated_conjecture,
    ( ( epred1_0 @ esk1_0 @ esk2_0 )
    | ~ ( epred1_0 @ esk5_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_17,negated_conjecture,
    ! [X4: $i,X3: $i] :
      ( ~ ( epred1_0 @ X3 @ X4 )
      | ~ ( epred1_0 @ X4 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_18,negated_conjecture,
    epred1_0 @ esk1_0 @ esk2_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

thf(c_0_19,negated_conjecture,
    ( ( epred1_0 @ esk4_0 @ esk3_0 )
    | ( epred1_0 @ esk2_0 @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_20,negated_conjecture,
    ~ ( epred1_0 @ esk2_0 @ esk1_0 ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_21,negated_conjecture,
    epred1_0 @ esk4_0 @ esk3_0,
    inference(sr,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_22,negated_conjecture,
    ( ( epred1_0 @ esk5_0 @ esk4_0 )
    | ( epred1_0 @ esk2_0 @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_23,negated_conjecture,
    ( ( epred1_0 @ esk2_0 @ esk1_0 )
    | ~ ( epred1_0 @ esk5_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_24,negated_conjecture,
    ! [X3: $i] :
      ( ( epred1_0 @ X3 @ esk3_0 )
      | ~ ( epred1_0 @ X3 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_21]) ).

thf(c_0_25,negated_conjecture,
    epred1_0 @ esk5_0 @ esk4_0,
    inference(sr,[status(thm)],[c_0_22,c_0_20]) ).

thf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 17:12:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.20/0.50  # Version: 3.1.0-ho
% 0.20/0.50  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.50  # Starting sh1l with 300s (1) cores
% 0.20/0.50  # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.50  # post_as_ho1 with pid 21516 completed with status 0
% 0.20/0.50  # Result found by post_as_ho1
% 0.20/0.50  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.50  # No SInE strategy applied
% 0.20/0.50  # Search class: HGHNF-FFSS00-SHSSMFNN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # new_ho_10 with pid 21522 completed with status 0
% 0.20/0.50  # Result found by new_ho_10
% 0.20/0.50  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.50  # No SInE strategy applied
% 0.20/0.50  # Search class: HGHNF-FFSS00-SHSSMFNN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # Preprocessing time       : 0.001 s
% 0.20/0.50  # Presaturation interreduction done
% 0.20/0.50  
% 0.20/0.50  # Proof found!
% 0.20/0.50  # SZS status Theorem
% 0.20/0.50  # SZS output start CNFRefutation
% See solution above
% 0.20/0.50  # Parsed axioms                        : 59
% 0.20/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.50  # Initial clauses                      : 37
% 0.20/0.50  # Removed in clause preprocessing      : 29
% 0.20/0.50  # Initial clauses in saturation        : 8
% 0.20/0.50  # Processed clauses                    : 31
% 0.20/0.50  # ...of these trivial                  : 0
% 0.20/0.50  # ...subsumed                          : 0
% 0.20/0.50  # ...remaining for further processing  : 31
% 0.20/0.50  # Other redundant clauses eliminated   : 0
% 0.20/0.50  # Clauses deleted for lack of memory   : 0
% 0.20/0.50  # Backward-subsumed                    : 3
% 0.20/0.50  # Backward-rewritten                   : 7
% 0.20/0.50  # Generated clauses                    : 21
% 0.20/0.50  # ...of the previous two non-redundant : 18
% 0.20/0.50  # ...aggressively subsumed             : 0
% 0.20/0.50  # Contextual simplify-reflections      : 1
% 0.20/0.50  # Paramodulations                      : 19
% 0.20/0.50  # Factorizations                       : 0
% 0.20/0.50  # NegExts                              : 0
% 0.20/0.50  # Equation resolutions                 : 0
% 0.20/0.50  # Disequality decompositions           : 0
% 0.20/0.50  # Total rewrite steps                  : 8
% 0.20/0.50  # ...of those cached                   : 6
% 0.20/0.50  # Propositional unsat checks           : 0
% 0.20/0.50  #    Propositional check models        : 0
% 0.20/0.50  #    Propositional check unsatisfiable : 0
% 0.20/0.50  #    Propositional clauses             : 0
% 0.20/0.50  #    Propositional clauses after purity: 0
% 0.20/0.50  #    Propositional unsat core size     : 0
% 0.20/0.50  #    Propositional preprocessing time  : 0.000
% 0.20/0.50  #    Propositional encoding time       : 0.000
% 0.20/0.50  #    Propositional solver time         : 0.000
% 0.20/0.50  #    Success case prop preproc time    : 0.000
% 0.20/0.50  #    Success case prop encoding time   : 0.000
% 0.20/0.50  #    Success case prop solver time     : 0.000
% 0.20/0.50  # Current number of processed clauses  : 11
% 0.20/0.50  #    Positive orientable unit clauses  : 3
% 0.20/0.50  #    Positive unorientable unit clauses: 0
% 0.20/0.50  #    Negative unit clauses             : 3
% 0.20/0.50  #    Non-unit-clauses                  : 5
% 0.20/0.50  # Current number of unprocessed clauses: 3
% 0.20/0.50  # ...number of literals in the above   : 8
% 0.20/0.50  # Current number of archived formulas  : 0
% 0.20/0.50  # Current number of archived clauses   : 20
% 0.20/0.50  # Clause-clause subsumption calls (NU) : 83
% 0.20/0.50  # Rec. Clause-clause subsumption calls : 77
% 0.20/0.50  # Non-unit clause-clause subsumptions  : 2
% 0.20/0.50  # Unit Clause-clause subsumption calls : 15
% 0.20/0.50  # Rewrite failures with RHS unbound    : 0
% 0.20/0.50  # BW rewrite match attempts            : 1
% 0.20/0.50  # BW rewrite match successes           : 1
% 0.20/0.50  # Condensation attempts                : 31
% 0.20/0.50  # Condensation successes               : 0
% 0.20/0.50  # Termbank termtop insertions          : 3563
% 0.20/0.50  # Search garbage collected termcells   : 913
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.006 s
% 0.20/0.50  # System time              : 0.003 s
% 0.20/0.50  # Total time               : 0.009 s
% 0.20/0.50  # Maximum resident set size: 2148 pages
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.010 s
% 0.20/0.50  # System time              : 0.004 s
% 0.20/0.50  # Total time               : 0.014 s
% 0.20/0.50  # Maximum resident set size: 1788 pages
% 0.20/0.50  % E---3.1 exiting
% 0.20/0.50  % E exiting
%------------------------------------------------------------------------------