TSTP Solution File: ITP072^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : Mon May 20 22:16:10 EDT 2024

% Result   : Theorem 0.74s 0.63s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   28 (   7 unt;   8 typ;   0 def)
%            Number of atoms       :   45 (  21 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  118 (  20   ~;  14   |;   4   &;  73   @)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    hF_Mirabelle_hf: $tType ).

thf(decl_37,type,
    zero_z189798548lle_hf: hF_Mirabelle_hf ).

thf(decl_42,type,
    hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(decl_43,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(decl_79,type,
    z: hF_Mirabelle_hf ).

thf(decl_80,type,
    esk1_0: hF_Mirabelle_hf ).

thf(decl_82,type,
    esk3_1: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(decl_83,type,
    esk4_1: hF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(fact_4_hmem__hinsert,axiom,
    ! [X6: hF_Mirabelle_hf,X10: hF_Mirabelle_hf,X11: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ X6 @ ( hF_Mirabelle_hinsert @ X10 @ X11 ) )
    <=> ( ( X6 = X10 )
        | ( hF_Mirabelle_hmem @ X6 @ X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_hmem__hinsert) ).

thf(fact_3_hf__cases,axiom,
    ! [X7: hF_Mirabelle_hf] :
      ( ( X7 != zero_z189798548lle_hf )
     => ~ ! [X8: hF_Mirabelle_hf,X9: hF_Mirabelle_hf] :
            ( ( X7
              = ( hF_Mirabelle_hinsert @ X8 @ X9 ) )
           => ( hF_Mirabelle_hmem @ X8 @ X9 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hf__cases) ).

thf(conj_0,conjecture,
    ( ( z = zero_z189798548lle_hf )
  <=> ! [X5: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ X5 @ z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_1_hemptyE,axiom,
    ! [X6: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ X6 @ zero_z189798548lle_hf ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_hemptyE) ).

thf(c_0_4,plain,
    ! [X1504: hF_Mirabelle_hf,X1505: hF_Mirabelle_hf,X1506: hF_Mirabelle_hf] :
      ( ( ~ ( hF_Mirabelle_hmem @ X1504 @ ( hF_Mirabelle_hinsert @ X1505 @ X1506 ) )
        | ( X1504 = X1505 )
        | ( hF_Mirabelle_hmem @ X1504 @ X1506 ) )
      & ( ( X1504 != X1505 )
        | ( hF_Mirabelle_hmem @ X1504 @ ( hF_Mirabelle_hinsert @ X1505 @ X1506 ) ) )
      & ( ~ ( hF_Mirabelle_hmem @ X1504 @ X1506 )
        | ( hF_Mirabelle_hmem @ X1504 @ ( hF_Mirabelle_hinsert @ X1505 @ X1506 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_hmem__hinsert])])])]) ).

thf(c_0_5,plain,
    ! [X7: hF_Mirabelle_hf] :
      ( ( X7 != zero_z189798548lle_hf )
     => ~ ! [X8: hF_Mirabelle_hf,X9: hF_Mirabelle_hf] :
            ( ( X7
              = ( hF_Mirabelle_hinsert @ X8 @ X9 ) )
           => ( hF_Mirabelle_hmem @ X8 @ X9 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_3_hf__cases]) ).

thf(c_0_6,negated_conjecture,
    ~ ( ( z = zero_z189798548lle_hf )
    <=> ! [X5: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ X5 @ z ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_7,plain,
    ! [X1: hF_Mirabelle_hf,X3: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_hmem @ X1 @ ( hF_Mirabelle_hinsert @ X2 @ X3 ) )
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_8,plain,
    ! [X1501: hF_Mirabelle_hf] :
      ( ( ( X1501
          = ( hF_Mirabelle_hinsert @ ( esk3_1 @ X1501 ) @ ( esk4_1 @ X1501 ) ) )
        | ( X1501 = zero_z189798548lle_hf ) )
      & ( ~ ( hF_Mirabelle_hmem @ ( esk3_1 @ X1501 ) @ ( esk4_1 @ X1501 ) )
        | ( X1501 = zero_z189798548lle_hf ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).

thf(c_0_9,negated_conjecture,
    ! [X1491: hF_Mirabelle_hf] :
      ( ( ( z != zero_z189798548lle_hf )
        | ( hF_Mirabelle_hmem @ esk1_0 @ z ) )
      & ( ( z = zero_z189798548lle_hf )
        | ~ ( hF_Mirabelle_hmem @ X1491 @ z ) ) ),
    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_6])])])])]) ).

thf(c_0_10,plain,
    ! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ X1 @ ( hF_Mirabelle_hinsert @ X1 @ X2 ) ),
    inference(er,[status(thm)],[c_0_7]) ).

thf(c_0_11,plain,
    ! [X1: hF_Mirabelle_hf] :
      ( ( X1
        = ( hF_Mirabelle_hinsert @ ( esk3_1 @ X1 ) @ ( esk4_1 @ X1 ) ) )
      | ( X1 = zero_z189798548lle_hf ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,plain,
    ! [X6: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ X6 @ zero_z189798548lle_hf ),
    inference(fof_simplification,[status(thm)],[fact_1_hemptyE]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: hF_Mirabelle_hf] :
      ( ( z = zero_z189798548lle_hf )
      | ~ ( hF_Mirabelle_hmem @ X1 @ z ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,plain,
    ! [X1: hF_Mirabelle_hf] :
      ( ( X1 = zero_z189798548lle_hf )
      | ( hF_Mirabelle_hmem @ ( esk3_1 @ X1 ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_15,plain,
    ! [X1499: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ X1499 @ zero_z189798548lle_hf ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).

thf(c_0_16,negated_conjecture,
    ( ( hF_Mirabelle_hmem @ esk1_0 @ z )
    | ( z != zero_z189798548lle_hf ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_17,negated_conjecture,
    z = zero_z189798548lle_hf,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_18,plain,
    ! [X1: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.36  % Computer : n004.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Sat May 18 18:19:52 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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
% 0.74/0.63  # Version: 3.1.0-ho
% 0.74/0.63  # Preprocessing class: HSLSSMSMSSMNHFA.
% 0.74/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.63  # Starting new_ho_3 with 1500s (5) cores
% 0.74/0.63  # Starting sh7 with 300s (1) cores
% 0.74/0.63  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.74/0.63  # Starting pre_casc_7 with 300s (1) cores
% 0.74/0.63  # new_ho_3 with pid 14962 completed with status 0
% 0.74/0.63  # Result found by new_ho_3
% 0.74/0.63  # Preprocessing class: HSLSSMSMSSMNHFA.
% 0.74/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.63  # Starting new_ho_3 with 1500s (5) cores
% 0.74/0.63  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.74/0.63  # Search class: HGHSM-FSLM32-MHFFFSBN
% 0.74/0.63  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.63  # Starting sh9 with 811s (1) cores
% 0.74/0.63  # Starting new_ho_3 with 151s (1) cores
% 0.74/0.63  # Starting almost_fo_1 with 136s (1) cores
% 0.74/0.63  # Starting lpo6_lambda_fix with 136s (1) cores
% 0.74/0.63  # Starting sh6 with 136s (1) cores
% 0.74/0.63  # sh6 with pid 14970 completed with status 0
% 0.74/0.63  # Result found by sh6
% 0.74/0.63  # Preprocessing class: HSLSSMSMSSMNHFA.
% 0.74/0.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.63  # Starting new_ho_3 with 1500s (5) cores
% 0.74/0.63  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.74/0.63  # Search class: HGHSM-FSLM32-MHFFFSBN
% 0.74/0.63  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.63  # Starting sh9 with 811s (1) cores
% 0.74/0.63  # Starting new_ho_3 with 151s (1) cores
% 0.74/0.63  # Starting almost_fo_1 with 136s (1) cores
% 0.74/0.63  # Starting lpo6_lambda_fix with 136s (1) cores
% 0.74/0.63  # Starting sh6 with 136s (1) cores
% 0.74/0.63  # Preprocessing time       : 0.008 s
% 0.74/0.63  # Presaturation interreduction done
% 0.74/0.63  
% 0.74/0.63  # Proof found!
% 0.74/0.63  # SZS status Theorem
% 0.74/0.63  # SZS output start CNFRefutation
% See solution above
% 0.74/0.63  # Parsed axioms                        : 415
% 0.74/0.63  # Removed by relevancy pruning/SinE    : 100
% 0.74/0.63  # Initial clauses                      : 748
% 0.74/0.63  # Removed in clause preprocessing      : 24
% 0.74/0.63  # Initial clauses in saturation        : 724
% 0.74/0.63  # Processed clauses                    : 1025
% 0.74/0.63  # ...of these trivial                  : 8
% 0.74/0.63  # ...subsumed                          : 252
% 0.74/0.63  # ...remaining for further processing  : 765
% 0.74/0.63  # Other redundant clauses eliminated   : 83
% 0.74/0.63  # Clauses deleted for lack of memory   : 0
% 0.74/0.63  # Backward-subsumed                    : 3
% 0.74/0.63  # Backward-rewritten                   : 6
% 0.74/0.63  # Generated clauses                    : 548
% 0.74/0.63  # ...of the previous two non-redundant : 412
% 0.74/0.63  # ...aggressively subsumed             : 0
% 0.74/0.63  # Contextual simplify-reflections      : 2
% 0.74/0.63  # Paramodulations                      : 462
% 0.74/0.63  # Factorizations                       : 0
% 0.74/0.63  # NegExts                              : 2
% 0.74/0.63  # Equation resolutions                 : 86
% 0.74/0.63  # Disequality decompositions           : 0
% 0.74/0.63  # Total rewrite steps                  : 145
% 0.74/0.63  # ...of those cached                   : 96
% 0.74/0.63  # Propositional unsat checks           : 0
% 0.74/0.63  #    Propositional check models        : 0
% 0.74/0.63  #    Propositional check unsatisfiable : 0
% 0.74/0.63  #    Propositional clauses             : 0
% 0.74/0.63  #    Propositional clauses after purity: 0
% 0.74/0.63  #    Propositional unsat core size     : 0
% 0.74/0.63  #    Propositional preprocessing time  : 0.000
% 0.74/0.63  #    Propositional encoding time       : 0.000
% 0.74/0.63  #    Propositional solver time         : 0.000
% 0.74/0.63  #    Success case prop preproc time    : 0.000
% 0.74/0.63  #    Success case prop encoding time   : 0.000
% 0.74/0.63  #    Success case prop solver time     : 0.000
% 0.74/0.63  # Current number of processed clauses  : 178
% 0.74/0.63  #    Positive orientable unit clauses  : 47
% 0.74/0.63  #    Positive unorientable unit clauses: 3
% 0.74/0.63  #    Negative unit clauses             : 14
% 0.74/0.63  #    Non-unit-clauses                  : 114
% 0.74/0.63  # Current number of unprocessed clauses: 620
% 0.74/0.63  # ...number of literals in the above   : 1814
% 0.74/0.63  # Current number of archived formulas  : 0
% 0.74/0.63  # Current number of archived clauses   : 519
% 0.74/0.63  # Clause-clause subsumption calls (NU) : 39945
% 0.74/0.63  # Rec. Clause-clause subsumption calls : 15809
% 0.74/0.63  # Non-unit clause-clause subsumptions  : 176
% 0.74/0.63  # Unit Clause-clause subsumption calls : 132
% 0.74/0.63  # Rewrite failures with RHS unbound    : 0
% 0.74/0.63  # BW rewrite match attempts            : 35
% 0.74/0.63  # BW rewrite match successes           : 17
% 0.74/0.63  # Condensation attempts                : 0
% 0.74/0.63  # Condensation successes               : 0
% 0.74/0.63  # Termbank termtop insertions          : 65656
% 0.74/0.63  # Search garbage collected termcells   : 17417
% 0.74/0.63  
% 0.74/0.63  # -------------------------------------------------
% 0.74/0.63  # User time                : 0.078 s
% 0.74/0.63  # System time              : 0.013 s
% 0.74/0.63  # Total time               : 0.091 s
% 0.74/0.63  # Maximum resident set size: 5560 pages
% 0.74/0.63  
% 0.74/0.63  # -------------------------------------------------
% 0.74/0.63  # User time                : 0.376 s
% 0.74/0.63  # System time              : 0.042 s
% 0.74/0.63  # Total time               : 0.417 s
% 0.74/0.63  # Maximum resident set size: 2668 pages
% 0.74/0.63  % E---3.1 exiting
% 0.74/0.63  % E exiting
%------------------------------------------------------------------------------