TSTP Solution File: SEU667^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU667^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 03:28:59 EDT 2024

% Result   : Theorem 0.18s 0.45s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (   4 unt;   8 typ;   0 def)
%            Number of atoms       :   21 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   84 (   3   ~;   0   |;   1   &;  76   @)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   33 (  12   ^  21   !;   0   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_24,type,
    subset: $i > $i > $o ).

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

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

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

thf(decl_29,type,
    dpsetconstrSub: $o ).

thf(decl_30,type,
    esk1_0: $i ).

thf(decl_31,type,
    esk2_0: $i ).

thf(decl_32,type,
    epred1_0: $i > $i > $o ).

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

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

thf(setOfPairsIsBReln,conjecture,
    ( dpsetconstrSub
   => ! [X1: $i,X2: $i,X4: $i > $i > $o] :
        ( breln @ X1 @ X2
        @ ( dpsetconstr @ X1 @ X2
          @ ^ [X6: $i,X7: $i] : ( X4 @ X6 @ X7 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).

thf(c_0_3,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_4,plain,
    ( dpsetconstrSub
  <=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
        ( subset
        @ ( dpsetconstr @ X1 @ X2
          @ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) )
        @ ( cartprod @ X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).

thf(c_0_5,negated_conjecture,
    ~ ( ! [X14: $i,X15: $i,X16: $i > $i > $o] : ( subset @ ( dpsetconstr @ X14 @ X15 @ X16 ) @ ( cartprod @ X14 @ X15 ) )
     => ! [X1: $i,X2: $i,X4: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X2 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ),
    inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[setOfPairsIsBReln])]),c_0_3]),c_0_4])]) ).

thf(c_0_6,negated_conjecture,
    ! [X17: $i,X18: $i,X19: $i > $i > $o] :
      ( ( subset @ ( dpsetconstr @ X17 @ X18 @ X19 ) @ ( cartprod @ X17 @ X18 ) )
      & ~ ( subset @ ( dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0 ) @ ( cartprod @ esk1_0 @ esk2_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_5])])])])]) ).

thf(c_0_7,negated_conjecture,
    ~ ( subset @ ( dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0 ) @ ( cartprod @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X4: $i > $i > $o,X2: $i] : ( subset @ ( dpsetconstr @ X1 @ X2 @ X4 ) @ ( cartprod @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SEU667^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sun May 19 16:08:53 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.18/0.44  Running higher-order theorem proving
% 0.18/0.44  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
% 0.18/0.45  # Version: 3.1.0-ho
% 0.18/0.45  # Preprocessing class: HSSSSMSSSLMNHSN.
% 0.18/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.18/0.45  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.18/0.45  # Starting sh2l with 300s (1) cores
% 0.18/0.45  # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.18/0.45  # sh2l with pid 1207 completed with status 0
% 0.18/0.45  # Result found by sh2l
% 0.18/0.45  # Preprocessing class: HSSSSMSSSLMNHSN.
% 0.18/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.18/0.45  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.18/0.45  # Starting sh2l with 300s (1) cores
% 0.18/0.45  # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.18/0.45  # Search class: HUUNF-FFSF32-SHSFMFBN
% 0.18/0.45  # partial match(2): HUUNF-FFSF00-SHSFMFBN
% 0.18/0.45  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.45  # Starting sh3 with 163s (1) cores
% 0.18/0.45  # sh3 with pid 1211 completed with status 0
% 0.18/0.45  # Result found by sh3
% 0.18/0.45  # Preprocessing class: HSSSSMSSSLMNHSN.
% 0.18/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.18/0.45  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.18/0.45  # Starting sh2l with 300s (1) cores
% 0.18/0.45  # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.18/0.45  # Search class: HUUNF-FFSF32-SHSFMFBN
% 0.18/0.45  # partial match(2): HUUNF-FFSF00-SHSFMFBN
% 0.18/0.45  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.45  # Starting sh3 with 163s (1) cores
% 0.18/0.45  # Preprocessing time       : 0.001 s
% 0.18/0.45  # Presaturation interreduction done
% 0.18/0.45  
% 0.18/0.45  # Proof found!
% 0.18/0.45  # SZS status Theorem
% 0.18/0.45  # SZS output start CNFRefutation
% See solution above
% 0.18/0.45  # Parsed axioms                        : 12
% 0.18/0.45  # Removed by relevancy pruning/SinE    : 9
% 0.18/0.45  # Initial clauses                      : 2
% 0.18/0.45  # Removed in clause preprocessing      : 0
% 0.18/0.45  # Initial clauses in saturation        : 2
% 0.18/0.45  # Processed clauses                    : 2
% 0.18/0.45  # ...of these trivial                  : 0
% 0.18/0.45  # ...subsumed                          : 0
% 0.18/0.45  # ...remaining for further processing  : 2
% 0.18/0.45  # Other redundant clauses eliminated   : 0
% 0.18/0.45  # Clauses deleted for lack of memory   : 0
% 0.18/0.45  # Backward-subsumed                    : 0
% 0.18/0.45  # Backward-rewritten                   : 1
% 0.18/0.45  # Generated clauses                    : 0
% 0.18/0.45  # ...of the previous two non-redundant : 0
% 0.18/0.45  # ...aggressively subsumed             : 0
% 0.18/0.45  # Contextual simplify-reflections      : 0
% 0.18/0.45  # Paramodulations                      : 0
% 0.18/0.45  # Factorizations                       : 0
% 0.18/0.45  # NegExts                              : 0
% 0.18/0.45  # Equation resolutions                 : 0
% 0.18/0.45  # Disequality decompositions           : 0
% 0.18/0.45  # Total rewrite steps                  : 1
% 0.18/0.45  # ...of those cached                   : 0
% 0.18/0.45  # Propositional unsat checks           : 0
% 0.18/0.45  #    Propositional check models        : 0
% 0.18/0.45  #    Propositional check unsatisfiable : 0
% 0.18/0.45  #    Propositional clauses             : 0
% 0.18/0.45  #    Propositional clauses after purity: 0
% 0.18/0.45  #    Propositional unsat core size     : 0
% 0.18/0.45  #    Propositional preprocessing time  : 0.000
% 0.18/0.45  #    Propositional encoding time       : 0.000
% 0.18/0.45  #    Propositional solver time         : 0.000
% 0.18/0.45  #    Success case prop preproc time    : 0.000
% 0.18/0.45  #    Success case prop encoding time   : 0.000
% 0.18/0.45  #    Success case prop solver time     : 0.000
% 0.18/0.45  # Current number of processed clauses  : 1
% 0.18/0.45  #    Positive orientable unit clauses  : 1
% 0.18/0.45  #    Positive unorientable unit clauses: 0
% 0.18/0.45  #    Negative unit clauses             : 0
% 0.18/0.45  #    Non-unit-clauses                  : 0
% 0.18/0.45  # Current number of unprocessed clauses: 0
% 0.18/0.45  # ...number of literals in the above   : 0
% 0.18/0.45  # Current number of archived formulas  : 0
% 0.18/0.45  # Current number of archived clauses   : 1
% 0.18/0.45  # Clause-clause subsumption calls (NU) : 0
% 0.18/0.45  # Rec. Clause-clause subsumption calls : 0
% 0.18/0.45  # Non-unit clause-clause subsumptions  : 0
% 0.18/0.45  # Unit Clause-clause subsumption calls : 0
% 0.18/0.45  # Rewrite failures with RHS unbound    : 0
% 0.18/0.45  # BW rewrite match attempts            : 1
% 0.18/0.45  # BW rewrite match successes           : 1
% 0.18/0.45  # Condensation attempts                : 0
% 0.18/0.45  # Condensation successes               : 0
% 0.18/0.45  # Termbank termtop insertions          : 356
% 0.18/0.45  # Search garbage collected termcells   : 145
% 0.18/0.45  
% 0.18/0.45  # -------------------------------------------------
% 0.18/0.45  # User time                : 0.004 s
% 0.18/0.45  # System time              : 0.000 s
% 0.18/0.45  # Total time               : 0.004 s
% 0.18/0.45  # Maximum resident set size: 1800 pages
% 0.18/0.45  
% 0.18/0.45  # -------------------------------------------------
% 0.18/0.45  # User time                : 0.004 s
% 0.18/0.45  # System time              : 0.003 s
% 0.18/0.45  # Total time               : 0.007 s
% 0.18/0.45  # Maximum resident set size: 1732 pages
% 0.18/0.45  % E---3.1 exiting
% 0.18/0.46  % E exiting
%------------------------------------------------------------------------------