TSTP Solution File: SEU681^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 03:29:05 EDT 2024

% Result   : Theorem 0.16s 0.41s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   34 (   6 unt;  14 typ;   0 def)
%            Number of atoms       :   80 (   6 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  309 (  28   ~;  25   |;  11   &; 221   @)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :   65 (   6   ^  55   !;   4   ?;  65   :)

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

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

thf(decl_24,type,
    subsetE: $o ).

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

thf(decl_26,type,
    cartprod: $i > $i > $i ).

thf(decl_27,type,
    cartprodmempair1: $o ).

thf(decl_28,type,
    breln: $i > $i > $i > $o ).

thf(decl_29,type,
    esk1_3: $i > $i > $i > $i ).

thf(decl_30,type,
    esk2_3: $i > $i > $i > $i ).

thf(decl_31,type,
    esk3_0: $i ).

thf(decl_32,type,
    esk4_0: $i ).

thf(decl_33,type,
    esk5_0: $i ).

thf(decl_34,type,
    epred1_0: $i > $o ).

thf(decl_35,type,
    esk6_0: $i ).

thf(breln,axiom,
    ( breln
    = ( ^ [X1: $i,X2: $i,X6: $i] : ( subset @ X6 @ ( cartprod @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).

thf(brelnall1,conjecture,
    ( subsetE
   => ( cartprodmempair1
     => ! [X1: $i,X2: $i,X7: $i] :
          ( ( breln @ X1 @ X2 @ X7 )
         => ! [X8: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ X2 )
                     => ( ( in @ ( kpair @ X3 @ X5 ) @ X7 )
                       => ( X8 @ ( kpair @ X3 @ X5 ) ) ) ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X7 )
                 => ( X8 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).

thf(subsetE,axiom,
    ( subsetE
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( subset @ X1 @ X2 )
       => ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).

thf(cartprodmempair1,axiom,
    ( cartprodmempair1
  <=> ! [X1: $i,X2: $i,X4: $i] :
        ( ( in @ X4 @ ( cartprod @ X1 @ X2 ) )
       => ? [X3: $i] :
            ( ( in @ X3 @ X1 )
            & ? [X5: $i] :
                ( ( in @ X5 @ X2 )
                & ( X4
                  = ( kpair @ X3 @ X5 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(c_0_4,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_5,negated_conjecture,
    ~ ( ! [X24: $i,X25: $i,X26: $i] :
          ( ( subset @ X24 @ X25 )
         => ( ( in @ X26 @ X24 )
           => ( in @ X26 @ X25 ) ) )
     => ( ! [X27: $i,X28: $i,X29: $i] :
            ( ( in @ X29 @ ( cartprod @ X27 @ X28 ) )
           => ? [X30: $i] :
                ( ( in @ X30 @ X27 )
                & ? [X31: $i] :
                    ( ( in @ X31 @ X28 )
                    & ( X29
                      = ( kpair @ X30 @ X31 ) ) ) ) )
       => ! [X1: $i,X2: $i,X7: $i] :
            ( ( subset @ X7 @ ( cartprod @ X1 @ X2 ) )
           => ! [X8: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ X2 )
                       => ( ( in @ ( kpair @ X3 @ X5 ) @ X7 )
                         => ( X8 @ ( kpair @ X3 @ X5 ) ) ) ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X7 )
                   => ( X8 @ X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[brelnall1]),subsetE]),c_0_4]),cartprodmempair1]) ).

thf(c_0_6,negated_conjecture,
    ! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X44: $i,X45: $i] :
      ( ( ~ ( subset @ X32 @ X33 )
        | ~ ( in @ X34 @ X32 )
        | ( in @ X34 @ X33 ) )
      & ( ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
      & ( ( X37
          = ( kpair @ ( esk1_3 @ X35 @ X36 @ X37 ) @ ( esk2_3 @ X35 @ X36 @ X37 ) ) )
        | ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
      & ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
      & ( ~ ( in @ X44 @ esk3_0 )
        | ~ ( in @ X45 @ esk4_0 )
        | ~ ( in @ ( kpair @ X44 @ X45 ) @ esk5_0 )
        | ( epred1_0 @ ( kpair @ X44 @ X45 ) ) )
      & ( in @ esk6_0 @ esk5_0 )
      & ~ ( epred1_0 @ esk6_0 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( epred1_0 @ ( kpair @ X1 @ X2 ) )
      | ~ ( in @ X1 @ esk3_0 )
      | ~ ( in @ X2 @ esk4_0 )
      | ~ ( in @ ( kpair @ X1 @ X2 ) @ esk5_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( X1
        = ( kpair @ ( esk1_3 @ X2 @ X3 @ X1 ) @ ( esk2_3 @ X2 @ X3 @ X1 ) ) )
      | ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( in @ ( esk2_3 @ X2 @ X3 @ X1 ) @ esk4_0 )
      | ~ ( in @ ( esk1_3 @ X2 @ X3 @ X1 ) @ esk3_0 )
      | ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) )
      | ~ ( in @ X1 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_11,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ X3 @ X2 )
      | ~ ( subset @ X1 @ X2 )
      | ~ ( in @ X3 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_12,negated_conjecture,
    subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_13,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( in @ ( esk1_3 @ X2 @ esk4_0 @ X1 ) @ esk3_0 )
      | ~ ( in @ X1 @ ( cartprod @ X2 @ esk4_0 ) )
      | ~ ( in @ X1 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] :
      ( ( in @ X1 @ ( cartprod @ esk3_0 @ esk4_0 ) )
      | ~ ( in @ X1 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( in @ X1 @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

thf(c_0_17,negated_conjecture,
    in @ esk6_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_18,negated_conjecture,
    ~ ( epred1_0 @ esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.10  % Command    : run_E %s %d THM
% 0.11/0.30  % Computer : n029.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Sun May 19 15:32:23 EDT 2024
% 0.16/0.30  % CPUTime    : 
% 0.16/0.40  Running higher-order theorem proving
% 0.16/0.40  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
% 0.16/0.41  # Version: 3.1.0-ho
% 0.16/0.41  # partial match(1): HSSSSLSSSLMNSSA
% 0.16/0.41  # Preprocessing class: HSSSSLSSSLSNSSA.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.41  # Starting new_bool_2 with 300s (1) cores
% 0.16/0.41  # Starting new_bool_9 with 300s (1) cores
% 0.16/0.41  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.16/0.41  # new_bool_2 with pid 16632 completed with status 0
% 0.16/0.41  # Result found by new_bool_2
% 0.16/0.41  # partial match(1): HSSSSLSSSLMNSSA
% 0.16/0.41  # Preprocessing class: HSSSSLSSSLSNSSA.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.41  # Starting new_bool_2 with 300s (1) cores
% 0.16/0.41  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.41  # Search class: HHUSF-FFSF32-SSSFMFNN
% 0.16/0.41  # partial match(2): HHUSF-FFSF32-SFFFMFNN
% 0.16/0.41  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.41  # Starting new_ho_10 with 181s (1) cores
% 0.16/0.41  # new_ho_10 with pid 16635 completed with status 0
% 0.16/0.41  # Result found by new_ho_10
% 0.16/0.41  # partial match(1): HSSSSLSSSLMNSSA
% 0.16/0.41  # Preprocessing class: HSSSSLSSSLSNSSA.
% 0.16/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.41  # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.41  # Starting new_bool_2 with 300s (1) cores
% 0.16/0.41  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.41  # Search class: HHUSF-FFSF32-SSSFMFNN
% 0.16/0.41  # partial match(2): HHUSF-FFSF32-SFFFMFNN
% 0.16/0.41  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.41  # Starting new_ho_10 with 181s (1) cores
% 0.16/0.41  # Preprocessing time       : 0.001 s
% 0.16/0.41  # Presaturation interreduction done
% 0.16/0.41  
% 0.16/0.41  # Proof found!
% 0.16/0.41  # SZS status Theorem
% 0.16/0.41  # SZS output start CNFRefutation
% See solution above
% 0.16/0.41  # Parsed axioms                        : 11
% 0.16/0.41  # Removed by relevancy pruning/SinE    : 7
% 0.16/0.41  # Initial clauses                      : 8
% 0.16/0.41  # Removed in clause preprocessing      : 0
% 0.16/0.41  # Initial clauses in saturation        : 8
% 0.16/0.41  # Processed clauses                    : 20
% 0.16/0.41  # ...of these trivial                  : 0
% 0.16/0.41  # ...subsumed                          : 0
% 0.16/0.41  # ...remaining for further processing  : 20
% 0.16/0.41  # Other redundant clauses eliminated   : 0
% 0.16/0.41  # Clauses deleted for lack of memory   : 0
% 0.16/0.41  # Backward-subsumed                    : 3
% 0.16/0.41  # Backward-rewritten                   : 0
% 0.16/0.41  # Generated clauses                    : 7
% 0.16/0.41  # ...of the previous two non-redundant : 4
% 0.16/0.41  # ...aggressively subsumed             : 0
% 0.16/0.41  # Contextual simplify-reflections      : 1
% 0.16/0.41  # Paramodulations                      : 7
% 0.16/0.41  # Factorizations                       : 0
% 0.16/0.41  # NegExts                              : 0
% 0.16/0.41  # Equation resolutions                 : 0
% 0.16/0.41  # Disequality decompositions           : 0
% 0.16/0.41  # Total rewrite steps                  : 0
% 0.16/0.41  # ...of those cached                   : 0
% 0.16/0.41  # Propositional unsat checks           : 0
% 0.16/0.41  #    Propositional check models        : 0
% 0.16/0.41  #    Propositional check unsatisfiable : 0
% 0.16/0.41  #    Propositional clauses             : 0
% 0.16/0.41  #    Propositional clauses after purity: 0
% 0.16/0.41  #    Propositional unsat core size     : 0
% 0.16/0.41  #    Propositional preprocessing time  : 0.000
% 0.16/0.41  #    Propositional encoding time       : 0.000
% 0.16/0.41  #    Propositional solver time         : 0.000
% 0.16/0.41  #    Success case prop preproc time    : 0.000
% 0.16/0.41  #    Success case prop encoding time   : 0.000
% 0.16/0.41  #    Success case prop solver time     : 0.000
% 0.16/0.41  # Current number of processed clauses  : 9
% 0.16/0.41  #    Positive orientable unit clauses  : 2
% 0.16/0.41  #    Positive unorientable unit clauses: 0
% 0.16/0.41  #    Negative unit clauses             : 1
% 0.16/0.41  #    Non-unit-clauses                  : 6
% 0.16/0.41  # Current number of unprocessed clauses: 0
% 0.16/0.41  # ...number of literals in the above   : 0
% 0.16/0.41  # Current number of archived formulas  : 0
% 0.16/0.41  # Current number of archived clauses   : 11
% 0.16/0.41  # Clause-clause subsumption calls (NU) : 18
% 0.16/0.41  # Rec. Clause-clause subsumption calls : 11
% 0.16/0.41  # Non-unit clause-clause subsumptions  : 4
% 0.16/0.41  # Unit Clause-clause subsumption calls : 0
% 0.16/0.41  # Rewrite failures with RHS unbound    : 0
% 0.16/0.41  # BW rewrite match attempts            : 0
% 0.16/0.41  # BW rewrite match successes           : 0
% 0.16/0.41  # Condensation attempts                : 20
% 0.16/0.41  # Condensation successes               : 0
% 0.16/0.41  # Termbank termtop insertions          : 1164
% 0.16/0.41  # Search garbage collected termcells   : 353
% 0.16/0.41  
% 0.16/0.41  # -------------------------------------------------
% 0.16/0.41  # User time                : 0.003 s
% 0.16/0.41  # System time              : 0.002 s
% 0.16/0.41  # Total time               : 0.005 s
% 0.16/0.41  # Maximum resident set size: 1944 pages
% 0.16/0.41  
% 0.16/0.41  # -------------------------------------------------
% 0.16/0.41  # User time                : 0.005 s
% 0.16/0.41  # System time              : 0.002 s
% 0.16/0.41  # Total time               : 0.008 s
% 0.16/0.41  # Maximum resident set size: 1716 pages
% 0.16/0.41  % E---3.1 exiting
% 0.16/0.42  % E exiting
%------------------------------------------------------------------------------