TSTP Solution File: SEU780^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU780^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 03:30:11 EDT 2024

% Result   : Theorem 0.22s 0.50s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   40 (  11 unt;  16 typ;   0 def)
%            Number of atoms       :   94 (   8 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  376 (  20   ~;  16   |;  23   &; 299   @)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   8 con; 0-3 aty)
%            Number of variables   :   86 (  30   ^  49   !;   7   ?;  86   :)

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

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

thf(decl_24,type,
    kpair: $i > $i > $i ).

thf(decl_25,type,
    cartprod: $i > $i > $i ).

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

thf(decl_27,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

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

thf(decl_29,type,
    breln1: $i > $i > $o ).

thf(decl_30,type,
    breln1compset: $i > $i > $i > $i ).

thf(decl_31,type,
    esk1_0: $i ).

thf(decl_32,type,
    esk2_0: $i ).

thf(decl_33,type,
    esk3_0: $i ).

thf(decl_34,type,
    esk4_0: $i ).

thf(decl_35,type,
    esk5_0: $i ).

thf(decl_36,type,
    epred1_0: $i > $i > $o ).

thf(decl_37,type,
    esk6_2: $i > $i > $i ).

thf(breln1,axiom,
    ( breln1
    = ( ^ [X1: $i,X9: $i] : ( breln @ X1 @ X1 @ X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).

thf(breln,axiom,
    ( breln
    = ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).

thf(dpsetconstrER,axiom,
    ( dpsetconstrER
  <=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i,X6: $i] :
        ( ( in @ ( kpair @ X5 @ X6 )
          @ ( dpsetconstr @ X1 @ X2
            @ ^ [X7: $i,X8: $i] : ( X4 @ X7 @ X8 ) ) )
       => ( X4 @ X5 @ X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).

thf(breln1compset,axiom,
    ( breln1compset
    = ( ^ [X1: $i,X9: $i,X10: $i] :
          ( dpsetconstr @ X1 @ X1
          @ ^ [X5: $i,X6: $i] :
            ? [X7: $i] :
              ( ( in @ X7 @ X1 )
              & ( in @ ( kpair @ X5 @ X7 ) @ X9 )
              & ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compset) ).

thf(breln1compE,conjecture,
    ( dpsetconstrER
   => ! [X1: $i,X9: $i] :
        ( ( breln1 @ X1 @ X9 )
       => ! [X10: $i] :
            ( ( breln1 @ X1 @ X10 )
           => ! [X5: $i] :
                ( ( in @ X5 @ X1 )
               => ! [X6: $i] :
                    ( ( in @ X6 @ X1 )
                   => ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) )
                     => ? [X7: $i] :
                          ( ( in @ X7 @ X1 )
                          & ( in @ ( kpair @ X5 @ X7 ) @ X9 )
                          & ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).

thf(c_0_5,plain,
    ( breln1
    = ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln1]) ).

thf(c_0_6,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_7,plain,
    ( dpsetconstrER
  <=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i,X6: $i] :
        ( ( in @ ( kpair @ X5 @ X6 )
          @ ( dpsetconstr @ X1 @ X2
            @ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) ) )
       => ( X4 @ X5 @ X6 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).

thf(c_0_8,plain,
    ( breln1
    = ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).

thf(c_0_9,plain,
    ( breln1compset
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] :
          ( dpsetconstr @ Z0 @ Z0
          @ ^ [Z3: $i,Z4: $i] :
            ? [X7: $i] :
              ( ( in @ X7 @ Z0 )
              & ( in @ ( kpair @ Z3 @ X7 ) @ Z1 )
              & ( in @ ( kpair @ X7 @ Z4 ) @ Z2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln1compset]) ).

thf(c_0_10,negated_conjecture,
    ~ ( ! [X22: $i,X23: $i,X24: $i > $i > $o,X25: $i,X26: $i] :
          ( ( in @ ( kpair @ X25 @ X26 ) @ ( dpsetconstr @ X22 @ X23 @ X24 ) )
         => ( X24 @ X25 @ X26 ) )
     => ! [X1: $i,X9: $i] :
          ( ( subset @ X9 @ ( cartprod @ X1 @ X1 ) )
         => ! [X10: $i] :
              ( ( subset @ X10 @ ( cartprod @ X1 @ X1 ) )
             => ! [X5: $i] :
                  ( ( in @ X5 @ X1 )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ X1 )
                     => ( ( in @ ( kpair @ X5 @ X6 )
                          @ ( dpsetconstr @ X1 @ X1
                            @ ^ [Z0: $i,Z1: $i] :
                              ? [X27: $i] :
                                ( ( in @ X27 @ X1 )
                                & ( in @ ( kpair @ Z0 @ X27 ) @ X9 )
                                & ( in @ ( kpair @ X27 @ Z1 ) @ X10 ) ) ) )
                       => ? [X7: $i] :
                            ( ( in @ X7 @ X1 )
                            & ( in @ ( kpair @ X5 @ X7 ) @ X9 )
                            & ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1compE]),c_0_7]),c_0_8]),c_0_9])]) ).

thf(c_0_11,negated_conjecture,
    ! [X28: $i,X29: $i,X30: $i > $i > $o,X31: $i,X32: $i,X38: $i] :
      ( ( ~ ( in @ ( kpair @ X31 @ X32 ) @ ( dpsetconstr @ X28 @ X29 @ X30 ) )
        | ( X30 @ X31 @ X32 ) )
      & ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
      & ( subset @ esk3_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
      & ( in @ esk4_0 @ esk1_0 )
      & ( in @ esk5_0 @ esk1_0 )
      & ( in @ ( kpair @ esk4_0 @ esk5_0 )
        @ ( dpsetconstr @ esk1_0 @ esk1_0
          @ ^ [Z0: $i,Z1: $i] :
            ? [X27: $i] :
              ( ( in @ X27 @ esk1_0 )
              & ( in @ ( kpair @ Z0 @ X27 ) @ esk2_0 )
              & ( in @ ( kpair @ X27 @ Z1 ) @ esk3_0 ) ) ) )
      & ( ~ ( in @ X38 @ esk1_0 )
        | ~ ( in @ ( kpair @ esk4_0 @ X38 ) @ esk2_0 )
        | ~ ( in @ ( kpair @ X38 @ esk5_0 ) @ esk3_0 ) ) ),
    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,plain,
    ! [X41: $i,X40: $i] :
      ( ( epred1_0 @ X40 @ X41 )
    <=> ? [X39: $i] :
          ( ( in @ X39 @ esk1_0 )
          & ( in @ ( kpair @ X40 @ X39 ) @ esk2_0 )
          & ( in @ ( kpair @ X39 @ X41 ) @ esk3_0 ) ) ),
    introduced(definition) ).

thf(c_0_13,plain,
    ! [X42: $i,X43: $i,X45: $i] :
      ( ( ( in @ ( esk6_2 @ X42 @ X43 ) @ esk1_0 )
        | ~ ( epred1_0 @ X43 @ X42 ) )
      & ( ( in @ ( kpair @ X43 @ ( esk6_2 @ X42 @ X43 ) ) @ esk2_0 )
        | ~ ( epred1_0 @ X43 @ X42 ) )
      & ( ( in @ ( kpair @ ( esk6_2 @ X42 @ X43 ) @ X42 ) @ esk3_0 )
        | ~ ( epred1_0 @ X43 @ X42 ) )
      & ( ~ ( in @ X45 @ esk1_0 )
        | ~ ( in @ ( kpair @ X43 @ X45 ) @ esk2_0 )
        | ~ ( in @ ( kpair @ X45 @ X42 ) @ esk3_0 )
        | ( epred1_0 @ X43 @ X42 ) ) ),
    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)],[])])])])])]) ).

thf(c_0_14,negated_conjecture,
    ( ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( dpsetconstr @ esk1_0 @ esk1_0 @ epred1_0 ) )
    = $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11]),c_0_12]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( in @ X1 @ esk1_0 )
      | ~ ( in @ ( kpair @ esk4_0 @ X1 ) @ esk2_0 )
      | ~ ( in @ ( kpair @ X1 @ esk5_0 ) @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ! [X2: $i,X1: $i] :
      ( ( in @ ( kpair @ ( esk6_2 @ X1 @ X2 ) @ X1 ) @ esk3_0 )
      | ~ ( epred1_0 @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_17,plain,
    ! [X2: $i,X1: $i] :
      ( ( in @ ( esk6_2 @ X1 @ X2 ) @ esk1_0 )
      | ~ ( epred1_0 @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i > $i > $o] :
      ( ( X4 @ X1 @ X2 )
      | ~ ( in @ ( kpair @ X1 @ X2 ) @ ( dpsetconstr @ X3 @ X5 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_19,negated_conjecture,
    in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( dpsetconstr @ esk1_0 @ esk1_0 @ epred1_0 ),
    inference(cn,[status(thm)],[c_0_14]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( in @ ( kpair @ esk4_0 @ ( esk6_2 @ esk5_0 @ X1 ) ) @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

thf(c_0_21,plain,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( kpair @ X1 @ ( esk6_2 @ X2 @ X1 ) ) @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_22,negated_conjecture,
    epred1_0 @ esk4_0 @ esk5_0,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_23,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU780^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.13/0.37  % Computer : n013.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit   : 300
% 0.13/0.37  % WCLimit    : 300
% 0.13/0.37  % DateTime   : Sun May 19 17:05:53 EDT 2024
% 0.13/0.38  % CPUTime    : 
% 0.22/0.49  Running higher-order theorem proving
% 0.22/0.49  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
% 0.22/0.50  # Version: 3.1.0-ho
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.22/0.50  # Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.50  # Starting sh4l with 300s (1) cores
% 0.22/0.50  # Starting lpo8_s with 300s (1) cores
% 0.22/0.50  # lpo8_s with pid 7897 completed with status 0
% 0.22/0.50  # Result found by lpo8_s
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.22/0.50  # Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.50  # Starting sh4l with 300s (1) cores
% 0.22/0.50  # Starting lpo8_s with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.22/0.50  # Search class: HHHNF-FFSS32-SSFFMFBN
% 0.22/0.50  # partial match(3): HGHNF-FFSS32-SFFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # new_ho_10 with pid 7900 completed with status 0
% 0.22/0.50  # Result found by new_ho_10
% 0.22/0.50  # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.22/0.50  # Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.50  # Starting sh4l with 300s (1) cores
% 0.22/0.50  # Starting lpo8_s with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.22/0.50  # Search class: HHHNF-FFSS32-SSFFMFBN
% 0.22/0.50  # partial match(3): HGHNF-FFSS32-SFFFMFNN
% 0.22/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50  # Preprocessing time       : 0.001 s
% 0.22/0.50  # Presaturation interreduction done
% 0.22/0.50  
% 0.22/0.50  # Proof found!
% 0.22/0.50  # SZS status Theorem
% 0.22/0.50  # SZS output start CNFRefutation
% See solution above
% 0.22/0.50  # Parsed axioms                        : 14
% 0.22/0.50  # Removed by relevancy pruning/SinE    : 9
% 0.22/0.50  # Initial clauses                      : 11
% 0.22/0.50  # Removed in clause preprocessing      : 0
% 0.22/0.50  # Initial clauses in saturation        : 11
% 0.22/0.50  # Processed clauses                    : 23
% 0.22/0.50  # ...of these trivial                  : 0
% 0.22/0.50  # ...subsumed                          : 0
% 0.22/0.50  # ...remaining for further processing  : 23
% 0.22/0.50  # Other redundant clauses eliminated   : 0
% 0.22/0.50  # Clauses deleted for lack of memory   : 0
% 0.22/0.50  # Backward-subsumed                    : 0
% 0.22/0.50  # Backward-rewritten                   : 0
% 0.22/0.50  # Generated clauses                    : 3
% 0.22/0.50  # ...of the previous two non-redundant : 2
% 0.22/0.50  # ...aggressively subsumed             : 0
% 0.22/0.50  # Contextual simplify-reflections      : 1
% 0.22/0.50  # Paramodulations                      : 3
% 0.22/0.50  # Factorizations                       : 0
% 0.22/0.50  # NegExts                              : 0
% 0.22/0.50  # Equation resolutions                 : 0
% 0.22/0.50  # Disequality decompositions           : 0
% 0.22/0.50  # Total rewrite steps                  : 1
% 0.22/0.50  # ...of those cached                   : 0
% 0.22/0.50  # Propositional unsat checks           : 0
% 0.22/0.50  #    Propositional check models        : 0
% 0.22/0.50  #    Propositional check unsatisfiable : 0
% 0.22/0.50  #    Propositional clauses             : 0
% 0.22/0.50  #    Propositional clauses after purity: 0
% 0.22/0.50  #    Propositional unsat core size     : 0
% 0.22/0.50  #    Propositional preprocessing time  : 0.000
% 0.22/0.50  #    Propositional encoding time       : 0.000
% 0.22/0.50  #    Propositional solver time         : 0.000
% 0.22/0.50  #    Success case prop preproc time    : 0.000
% 0.22/0.50  #    Success case prop encoding time   : 0.000
% 0.22/0.50  #    Success case prop solver time     : 0.000
% 0.22/0.50  # Current number of processed clauses  : 12
% 0.22/0.50  #    Positive orientable unit clauses  : 6
% 0.22/0.50  #    Positive unorientable unit clauses: 0
% 0.22/0.50  #    Negative unit clauses             : 0
% 0.22/0.50  #    Non-unit-clauses                  : 6
% 0.22/0.50  # Current number of unprocessed clauses: 1
% 0.22/0.50  # ...number of literals in the above   : 4
% 0.22/0.50  # Current number of archived formulas  : 0
% 0.22/0.50  # Current number of archived clauses   : 11
% 0.22/0.50  # Clause-clause subsumption calls (NU) : 9
% 0.22/0.50  # Rec. Clause-clause subsumption calls : 7
% 0.22/0.50  # Non-unit clause-clause subsumptions  : 1
% 0.22/0.50  # Unit Clause-clause subsumption calls : 0
% 0.22/0.50  # Rewrite failures with RHS unbound    : 0
% 0.22/0.50  # BW rewrite match attempts            : 0
% 0.22/0.50  # BW rewrite match successes           : 0
% 0.22/0.50  # Condensation attempts                : 23
% 0.22/0.50  # Condensation successes               : 0
% 0.22/0.50  # Termbank termtop insertions          : 1419
% 0.22/0.50  # Search garbage collected termcells   : 449
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.005 s
% 0.22/0.50  # System time              : 0.001 s
% 0.22/0.50  # Total time               : 0.006 s
% 0.22/0.50  # Maximum resident set size: 1912 pages
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.007 s
% 0.22/0.50  # System time              : 0.003 s
% 0.22/0.50  # Total time               : 0.009 s
% 0.22/0.50  # Maximum resident set size: 1736 pages
% 0.22/0.50  % E---3.1 exiting
% 0.22/0.51  % E exiting
%------------------------------------------------------------------------------