TSTP Solution File: ITP103^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP103^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 : Sat May  4 08:06:58 EDT 2024

% Result   : Theorem 0.37s 0.66s
% Output   : CNFRefutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   54 (  26 unt;  11 typ;   0 def)
%            Number of atoms       :   70 (  31 equ;   0 cnn)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  226 (  31   ~;  17   |;   2   &; 168   @)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   50 (   2   ^  48   !;   0   ?;  50   :)

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

thf(decl_sort2,type,
    list_a: $tType ).

thf(decl_22,type,
    times_times_nat: nat > nat > nat ).

thf(decl_23,type,
    zero_zero_nat: nat ).

thf(decl_28,type,
    suc: nat > nat ).

thf(decl_33,type,
    size_size_list_a: list_a > nat ).

thf(decl_34,type,
    ord_less_nat: nat > nat > $o ).

thf(decl_36,type,
    divide_divide_nat: nat > nat > nat ).

thf(decl_37,type,
    k: nat ).

thf(decl_38,type,
    n: nat ).

thf(decl_39,type,
    xs: list_a ).

thf(conj_2,conjecture,
    ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',conj_2) ).

thf(fact_133_mult_Ocommute,axiom,
    ( times_times_nat
    = ( ^ [X40: nat,X41: nat] : ( times_times_nat @ X41 @ X40 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_133_mult_Ocommute) ).

thf(fact_93_Euclidean__Division_Oless__mult__imp__div__less,axiom,
    ! [X2: nat,X27: nat,X1: nat] :
      ( ( ord_less_nat @ X2 @ ( times_times_nat @ X27 @ X1 ) )
     => ( ord_less_nat @ ( divide_divide_nat @ X2 @ X1 ) @ X27 ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_93_Euclidean__Division_Oless__mult__imp__div__less) ).

thf(fact_29_linorder__neqE__nat,axiom,
    ! [X11: nat,X12: nat] :
      ( ( X11 != X12 )
     => ( ~ ( ord_less_nat @ X11 @ X12 )
       => ( ord_less_nat @ X12 @ X11 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_29_linorder__neqE__nat) ).

thf(fact_32_less__irrefl__nat,axiom,
    ! [X1: nat] :
      ~ ( ord_less_nat @ X1 @ X1 ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_32_less__irrefl__nat) ).

thf(conj_0,hypothesis,
    ( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
    = ( suc @ n ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',conj_0) ).

thf(fact_68_less__Suc__eq,axiom,
    ! [X2: nat,X1: nat] :
      ( ( ord_less_nat @ X2 @ ( suc @ X1 ) )
    <=> ( ( ord_less_nat @ X2 @ X1 )
        | ( X2 = X1 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_68_less__Suc__eq) ).

thf(fact_99_nonzero__mult__div__cancel__left,axiom,
    ! [X8: nat,X10: nat] :
      ( ( X8 != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ X8 @ X10 ) @ X8 )
        = X10 ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_99_nonzero__mult__div__cancel__left) ).

thf(fact_27_n__not__Suc__n,axiom,
    ! [X1: nat] :
      ( X1
     != ( suc @ X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',fact_27_n__not__Suc__n) ).

thf(conj_1,hypothesis,
    k != zero_zero_nat,
    file('/export/starexec/sandbox/tmp/tmp.WqtBu33tpL/E---3.1_1063.p',conj_1) ).

thf(c_0_10,negated_conjecture,
    ~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_2])]) ).

thf(c_0_11,plain,
    ! [X461: nat,X462: nat] :
      ( ( times_times_nat @ X461 @ X462 )
      = ( times_times_nat @ X462 @ X461 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_133_mult_Ocommute])]) ).

thf(c_0_12,plain,
    ! [X715: nat,X716: nat,X717: nat] :
      ( ~ ( ord_less_nat @ X715 @ ( times_times_nat @ X716 @ X717 ) )
      | ( ord_less_nat @ ( divide_divide_nat @ X715 @ X717 ) @ X716 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_Euclidean__Division_Oless__mult__imp__div__less])])]) ).

thf(c_0_13,negated_conjecture,
    ~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
    inference(fof_nnf,[status(thm)],[c_0_10]) ).

thf(c_0_14,plain,
    ! [X801: nat,X802: nat] :
      ( ( times_times_nat @ X801 @ X802 )
      = ( times_times_nat @ X802 @ X801 ) ),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

thf(c_0_15,plain,
    ! [X11: nat,X12: nat] :
      ( ( X11 != X12 )
     => ( ~ ( ord_less_nat @ X11 @ X12 )
       => ( ord_less_nat @ X12 @ X11 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_29_linorder__neqE__nat]) ).

thf(c_0_16,plain,
    ! [X1: nat] :
      ~ ( ord_less_nat @ X1 @ X1 ),
    inference(fof_simplification,[status(thm)],[fact_32_less__irrefl__nat]) ).

thf(c_0_17,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ord_less_nat @ ( divide_divide_nat @ X1 @ X3 ) @ X2 )
      | ~ ( ord_less_nat @ X1 @ ( times_times_nat @ X2 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_18,hypothesis,
    ( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
    = ( suc @ n ) ),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

thf(c_0_19,negated_conjecture,
    ~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_20,plain,
    ! [X2: nat,X1: nat] :
      ( ( times_times_nat @ X1 @ X2 )
      = ( times_times_nat @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_21,plain,
    ! [X528: nat,X529: nat] :
      ( ( X528 = X529 )
      | ( ord_less_nat @ X528 @ X529 )
      | ( ord_less_nat @ X529 @ X528 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).

thf(c_0_22,plain,
    ! [X538: nat] :
      ~ ( ord_less_nat @ X538 @ X538 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).

thf(c_0_23,plain,
    ! [X626: nat,X627: nat] :
      ( ( ~ ( ord_less_nat @ X626 @ ( suc @ X627 ) )
        | ( ord_less_nat @ X626 @ X627 )
        | ( X626 = X627 ) )
      & ( ~ ( ord_less_nat @ X626 @ X627 )
        | ( ord_less_nat @ X626 @ ( suc @ X627 ) ) )
      & ( ( X626 != X627 )
        | ( ord_less_nat @ X626 @ ( suc @ X627 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_less__Suc__eq])])])]) ).

thf(c_0_24,plain,
    ! [X8: nat,X10: nat] :
      ( ( X8 != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ X8 @ X10 ) @ X8 )
        = X10 ) ),
    inference(fof_simplification,[status(thm)],[fact_99_nonzero__mult__div__cancel__left]) ).

thf(c_0_25,hypothesis,
    ! [X1: nat] :
      ( ( ord_less_nat @ ( suc @ n ) @ X1 )
      | ~ ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ X1 @ k ) ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_26,negated_conjecture,
    ~ ( ord_less_nat @ ( times_times_nat @ k @ n ) @ ( size_size_list_a @ xs ) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_27,plain,
    ! [X2: nat,X1: nat] :
      ( ( X1 = X2 )
      | ( ord_less_nat @ X1 @ X2 )
      | ( ord_less_nat @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_28,plain,
    ! [X1: nat] :
      ~ ( ord_less_nat @ X1 @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_29,plain,
    ! [X1: nat,X2: nat] :
      ( ( ord_less_nat @ X1 @ ( suc @ X2 ) )
      | ~ ( ord_less_nat @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_30,plain,
    ! [X1: nat] :
      ( X1
     != ( suc @ X1 ) ),
    inference(fof_simplification,[status(thm)],[fact_27_n__not__Suc__n]) ).

thf(c_0_31,hypothesis,
    k != zero_zero_nat,
    inference(fof_simplification,[status(thm)],[conj_1]) ).

thf(c_0_32,plain,
    ! [X729: nat,X730: nat] :
      ( ( X729 = zero_zero_nat )
      | ( ( divide_divide_nat @ ( times_times_nat @ X729 @ X730 ) @ X729 )
        = X730 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).

thf(c_0_33,hypothesis,
    ! [X1: nat] :
      ( ( ord_less_nat @ ( suc @ n ) @ X1 )
      | ~ ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ k @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

thf(c_0_34,negated_conjecture,
    ( ( ( times_times_nat @ k @ n )
      = ( size_size_list_a @ xs ) )
    | ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ k @ n ) ) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_35,plain,
    ! [X1: nat] :
      ~ ( ord_less_nat @ ( suc @ X1 ) @ X1 ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_36,plain,
    ! [X525: nat] :
      ( X525
     != ( suc @ X525 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).

thf(c_0_37,hypothesis,
    k != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[c_0_31]) ).

thf(c_0_38,plain,
    ! [X1: nat,X2: nat] :
      ( ( X1 = zero_zero_nat )
      | ( ( divide_divide_nat @ ( times_times_nat @ X1 @ X2 ) @ X1 )
        = X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_39,negated_conjecture,
    ( ( times_times_nat @ k @ n )
    = ( size_size_list_a @ xs ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

thf(c_0_40,plain,
    ! [X1: nat] :
      ( X1
     != ( suc @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_41,hypothesis,
    k != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_42,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_18]),c_0_40]),c_0_41]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.16  % Problem    : ITP103^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.17  % Command    : run_E %s %d THM
% 0.17/0.39  % Computer : n017.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Fri May  3 12:22:21 EDT 2024
% 0.17/0.39  % CPUTime    : 
% 0.23/0.54  Running higher-order theorem proving
% 0.23/0.54  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/tmp/tmp.WqtBu33tpL/E---3.1_1063.p
% 0.37/0.66  # Version: 3.1.0-ho
% 0.37/0.66  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.37/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.66  # Starting new_ho_11 with 1500s (5) cores
% 0.37/0.66  # Starting post_as_ho6 with 300s (1) cores
% 0.37/0.66  # Starting sh9 with 300s (1) cores
% 0.37/0.66  # Starting sh5l with 300s (1) cores
% 0.37/0.66  # new_ho_11 with pid 1157 completed with status 0
% 0.37/0.66  # Result found by new_ho_11
% 0.37/0.66  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.37/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.66  # Starting new_ho_11 with 1500s (5) cores
% 0.37/0.66  # No SInE strategy applied
% 0.37/0.66  # Search class: HGHSM-FSLF31-MSFFFSBN
% 0.37/0.66  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.66  # Starting new_ho_10 with 811s (1) cores
% 0.37/0.66  # Starting new_ho_11 with 151s (1) cores
% 0.37/0.66  # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.37/0.66  # Starting sh3l with 136s (1) cores
% 0.37/0.66  # Starting ehoh_best3_rw with 136s (1) cores
% 0.37/0.66  # sh3l with pid 1186 completed with status 0
% 0.37/0.66  # Result found by sh3l
% 0.37/0.66  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.37/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.66  # Starting new_ho_11 with 1500s (5) cores
% 0.37/0.66  # No SInE strategy applied
% 0.37/0.66  # Search class: HGHSM-FSLF31-MSFFFSBN
% 0.37/0.66  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.66  # Starting new_ho_10 with 811s (1) cores
% 0.37/0.66  # Starting new_ho_11 with 151s (1) cores
% 0.37/0.66  # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.37/0.66  # Starting sh3l with 136s (1) cores
% 0.37/0.66  # Preprocessing time       : 0.006 s
% 0.37/0.66  # Presaturation interreduction done
% 0.37/0.66  
% 0.37/0.66  # Proof found!
% 0.37/0.66  # SZS status Theorem
% 0.37/0.66  # SZS output start CNFRefutation
% See solution above
% 0.37/0.66  # Parsed axioms                        : 210
% 0.37/0.66  # Removed by relevancy pruning/SinE    : 0
% 0.37/0.66  # Initial clauses                      : 349
% 0.37/0.66  # Removed in clause preprocessing      : 42
% 0.37/0.66  # Initial clauses in saturation        : 307
% 0.37/0.66  # Processed clauses                    : 586
% 0.37/0.66  # ...of these trivial                  : 13
% 0.37/0.66  # ...subsumed                          : 147
% 0.37/0.66  # ...remaining for further processing  : 426
% 0.37/0.66  # Other redundant clauses eliminated   : 89
% 0.37/0.66  # Clauses deleted for lack of memory   : 0
% 0.37/0.66  # Backward-subsumed                    : 1
% 0.37/0.66  # Backward-rewritten                   : 10
% 0.37/0.66  # Generated clauses                    : 2056
% 0.37/0.66  # ...of the previous two non-redundant : 1741
% 0.37/0.66  # ...aggressively subsumed             : 0
% 0.37/0.66  # Contextual simplify-reflections      : 1
% 0.37/0.66  # Paramodulations                      : 1916
% 0.37/0.66  # Factorizations                       : 2
% 0.37/0.66  # NegExts                              : 0
% 0.37/0.66  # Equation resolutions                 : 95
% 0.37/0.66  # Disequality decompositions           : 0
% 0.37/0.66  # Total rewrite steps                  : 437
% 0.37/0.66  # ...of those cached                   : 356
% 0.37/0.66  # Propositional unsat checks           : 0
% 0.37/0.66  #    Propositional check models        : 0
% 0.37/0.66  #    Propositional check unsatisfiable : 0
% 0.37/0.66  #    Propositional clauses             : 0
% 0.37/0.66  #    Propositional clauses after purity: 0
% 0.37/0.66  #    Propositional unsat core size     : 0
% 0.37/0.66  #    Propositional preprocessing time  : 0.000
% 0.37/0.66  #    Propositional encoding time       : 0.000
% 0.37/0.66  #    Propositional solver time         : 0.000
% 0.37/0.66  #    Success case prop preproc time    : 0.000
% 0.37/0.66  #    Success case prop encoding time   : 0.000
% 0.37/0.66  #    Success case prop solver time     : 0.000
% 0.37/0.66  # Current number of processed clauses  : 177
% 0.37/0.66  #    Positive orientable unit clauses  : 29
% 0.37/0.66  #    Positive unorientable unit clauses: 2
% 0.37/0.66  #    Negative unit clauses             : 11
% 0.37/0.66  #    Non-unit-clauses                  : 135
% 0.37/0.66  # Current number of unprocessed clauses: 1622
% 0.37/0.66  # ...number of literals in the above   : 4547
% 0.37/0.66  # Current number of archived formulas  : 0
% 0.37/0.66  # Current number of archived clauses   : 197
% 0.37/0.66  # Clause-clause subsumption calls (NU) : 5619
% 0.37/0.66  # Rec. Clause-clause subsumption calls : 4543
% 0.37/0.66  # Non-unit clause-clause subsumptions  : 65
% 0.37/0.66  # Unit Clause-clause subsumption calls : 75
% 0.37/0.66  # Rewrite failures with RHS unbound    : 0
% 0.37/0.66  # BW rewrite match attempts            : 29
% 0.37/0.66  # BW rewrite match successes           : 25
% 0.37/0.66  # Condensation attempts                : 0
% 0.37/0.66  # Condensation successes               : 0
% 0.37/0.66  # Termbank termtop insertions          : 84888
% 0.37/0.66  # Search garbage collected termcells   : 6431
% 0.37/0.66  
% 0.37/0.66  # -------------------------------------------------
% 0.37/0.66  # User time                : 0.091 s
% 0.37/0.66  # System time              : 0.011 s
% 0.37/0.66  # Total time               : 0.102 s
% 0.37/0.66  # Maximum resident set size: 3152 pages
% 0.37/0.66  
% 0.37/0.66  # -------------------------------------------------
% 0.37/0.66  # User time                : 0.421 s
% 0.37/0.66  # System time              : 0.039 s
% 0.37/0.66  # Total time               : 0.460 s
% 0.37/0.66  # Maximum resident set size: 1976 pages
% 0.37/0.66  % E---3.1 exiting
% 0.37/0.66  % E exiting
%------------------------------------------------------------------------------