TSTP Solution File: ITP101^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP101^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 08:06:57 EDT 2024

% Result   : Theorem 0.42s 0.61s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   24 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   44 (  18 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  219 (  16   ~;  11   |;   9   &; 171   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :    5 (   0   ^   5   !;   0   ?;   5   :)

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

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

thf(decl_sort3,type,
    list_a: $tType ).

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

thf(decl_43,type,
    nth_a: list_a > nat > a ).

thf(decl_45,type,
    size_size_list_a: list_a > nat ).

thf(decl_46,type,
    ord_less_nat: nat > nat > $o ).

thf(decl_52,type,
    f: nat > a ).

thf(decl_53,type,
    g: nat > a ).

thf(decl_54,type,
    x: nat ).

thf(decl_55,type,
    xs: list_a ).

thf(decl_56,type,
    ys: list_a ).

thf(conj_1,hypothesis,
    ! [X156: nat] :
      ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
       => ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( nth_a @ xs @ X156 )
              = ( nth_a @ ys @ X156 ) ) )
          & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
              = ( nth_a @ ys @ X156 ) ) ) ) )
      & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
       => ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( nth_a @ xs @ X156 )
              = ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) )
          & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
              = ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oHnJdRHhDc/E---3.1_10684.p',conj_1) ).

thf(conj_3,conjecture,
    ( ( nth_a @ xs @ x )
    = ( nth_a @ ys @ x ) ),
    file('/export/starexec/sandbox/tmp/tmp.oHnJdRHhDc/E---3.1_10684.p',conj_3) ).

thf(conj_2,hypothesis,
    ord_less_nat @ x @ ( size_size_list_a @ ys ),
    file('/export/starexec/sandbox/tmp/tmp.oHnJdRHhDc/E---3.1_10684.p',conj_2) ).

thf(c_0_3,hypothesis,
    ! [X156: nat] :
      ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
       => ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( nth_a @ xs @ X156 )
              = ( nth_a @ ys @ X156 ) ) )
          & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
              = ( nth_a @ ys @ X156 ) ) ) ) )
      & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
       => ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( nth_a @ xs @ X156 )
              = ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) )
          & ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
           => ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
              = ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[conj_1]) ).

thf(c_0_4,hypothesis,
    ! [X1998: nat] :
      ( ( ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
        | ( ( nth_a @ xs @ X1998 )
          = ( nth_a @ ys @ X1998 ) )
        | ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
      & ( ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
        | ( ( f @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ xs ) ) )
          = ( nth_a @ ys @ X1998 ) )
        | ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
      & ( ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
        | ( ( nth_a @ xs @ X1998 )
          = ( g @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) )
        | ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
      & ( ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
        | ( ( f @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ xs ) ) )
          = ( g @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) )
        | ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

thf(c_0_5,negated_conjecture,
    ( ( nth_a @ xs @ x )
   != ( nth_a @ ys @ x ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_3])]) ).

thf(c_0_6,hypothesis,
    ! [X3: nat] :
      ( ( ( nth_a @ xs @ X3 )
        = ( nth_a @ ys @ X3 ) )
      | ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) )
      | ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_7,negated_conjecture,
    ( ( nth_a @ xs @ x )
   != ( nth_a @ ys @ x ) ),
    inference(fof_nnf,[status(thm)],[c_0_5]) ).

thf(c_0_8,hypothesis,
    ! [X3: nat] :
      ( ( ( nth_a @ ys @ X3 )
        = ( nth_a @ xs @ X3 ) )
      | ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) ) ),
    inference(cn,[status(thm)],[c_0_6]) ).

thf(c_0_9,hypothesis,
    ord_less_nat @ x @ ( size_size_list_a @ ys ),
    inference(split_conjunct,[status(thm)],[conj_2]) ).

thf(c_0_10,negated_conjecture,
    ( ( nth_a @ xs @ x )
   != ( nth_a @ ys @ x ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_11,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : ITP101^1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.15  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 12:37:35 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.18/0.48  Running higher-order theorem proving
% 0.18/0.48  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.oHnJdRHhDc/E---3.1_10684.p
% 0.42/0.61  # Version: 3.1.0-ho
% 0.42/0.61  # Preprocessing class: HSLSSMSSSSSNHFA.
% 0.42/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.42/0.61  # Starting new_ho_10 with 1500s (5) cores
% 0.42/0.61  # Starting new_ho_10_unif with 300s (1) cores
% 0.42/0.61  # Starting sh10 with 300s (1) cores
% 0.42/0.61  # Starting lpo5_rw_fix with 300s (1) cores
% 0.42/0.61  # new_ho_10_unif with pid 10763 completed with status 0
% 0.42/0.61  # Result found by new_ho_10_unif
% 0.42/0.61  # Preprocessing class: HSLSSMSSSSSNHFA.
% 0.42/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.42/0.61  # Starting new_ho_10 with 1500s (5) cores
% 0.42/0.61  # Starting new_ho_10_unif with 300s (1) cores
% 0.42/0.61  # No SInE strategy applied
% 0.42/0.61  # Search class: HGHSM-FSLF32-MHFFFSBC
% 0.42/0.61  # partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.42/0.61  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.42/0.61  # Starting additional_ho_6 with 163s (1) cores
% 0.42/0.61  # additional_ho_6 with pid 10771 completed with status 0
% 0.42/0.61  # Result found by additional_ho_6
% 0.42/0.61  # Preprocessing class: HSLSSMSSSSSNHFA.
% 0.42/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.42/0.61  # Starting new_ho_10 with 1500s (5) cores
% 0.42/0.61  # Starting new_ho_10_unif with 300s (1) cores
% 0.42/0.61  # No SInE strategy applied
% 0.42/0.61  # Search class: HGHSM-FSLF32-MHFFFSBC
% 0.42/0.61  # partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.42/0.61  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.42/0.61  # Starting additional_ho_6 with 163s (1) cores
% 0.42/0.61  # Preprocessing time       : 0.011 s
% 0.42/0.61  # Presaturation interreduction done
% 0.42/0.61  
% 0.42/0.61  # Proof found!
% 0.42/0.61  # SZS status Theorem
% 0.42/0.61  # SZS output start CNFRefutation
% See solution above
% 0.42/0.61  # Parsed axioms                        : 308
% 0.42/0.61  # Removed by relevancy pruning/SinE    : 0
% 0.42/0.61  # Initial clauses                      : 708
% 0.42/0.61  # Removed in clause preprocessing      : 74
% 0.42/0.61  # Initial clauses in saturation        : 634
% 0.42/0.61  # Processed clauses                    : 709
% 0.42/0.61  # ...of these trivial                  : 3
% 0.42/0.61  # ...subsumed                          : 184
% 0.42/0.61  # ...remaining for further processing  : 522
% 0.42/0.61  # Other redundant clauses eliminated   : 71
% 0.42/0.61  # Clauses deleted for lack of memory   : 0
% 0.42/0.61  # Backward-subsumed                    : 0
% 0.42/0.61  # Backward-rewritten                   : 0
% 0.42/0.61  # Generated clauses                    : 75
% 0.42/0.61  # ...of the previous two non-redundant : 55
% 0.42/0.61  # ...aggressively subsumed             : 0
% 0.42/0.61  # Contextual simplify-reflections      : 1
% 0.42/0.61  # Paramodulations                      : 7
% 0.42/0.61  # Factorizations                       : 0
% 0.42/0.61  # NegExts                              : 0
% 0.42/0.61  # Equation resolutions                 : 71
% 0.42/0.61  # Disequality decompositions           : 0
% 0.42/0.61  # Total rewrite steps                  : 34
% 0.42/0.61  # ...of those cached                   : 23
% 0.42/0.61  # Propositional unsat checks           : 0
% 0.42/0.61  #    Propositional check models        : 0
% 0.42/0.61  #    Propositional check unsatisfiable : 0
% 0.42/0.61  #    Propositional clauses             : 0
% 0.42/0.61  #    Propositional clauses after purity: 0
% 0.42/0.61  #    Propositional unsat core size     : 0
% 0.42/0.61  #    Propositional preprocessing time  : 0.000
% 0.42/0.61  #    Propositional encoding time       : 0.000
% 0.42/0.61  #    Propositional solver time         : 0.000
% 0.42/0.61  #    Success case prop preproc time    : 0.000
% 0.42/0.61  #    Success case prop encoding time   : 0.000
% 0.42/0.61  #    Success case prop solver time     : 0.000
% 0.42/0.61  # Current number of processed clauses  : 25
% 0.42/0.61  #    Positive orientable unit clauses  : 8
% 0.42/0.61  #    Positive unorientable unit clauses: 0
% 0.42/0.61  #    Negative unit clauses             : 10
% 0.42/0.61  #    Non-unit-clauses                  : 7
% 0.42/0.61  # Current number of unprocessed clauses: 409
% 0.42/0.61  # ...number of literals in the above   : 1763
% 0.42/0.61  # Current number of archived formulas  : 0
% 0.42/0.61  # Current number of archived clauses   : 429
% 0.42/0.61  # Clause-clause subsumption calls (NU) : 75719
% 0.42/0.61  # Rec. Clause-clause subsumption calls : 13585
% 0.42/0.61  # Non-unit clause-clause subsumptions  : 163
% 0.42/0.61  # Unit Clause-clause subsumption calls : 105
% 0.42/0.61  # Rewrite failures with RHS unbound    : 0
% 0.42/0.61  # BW rewrite match attempts            : 1
% 0.42/0.61  # BW rewrite match successes           : 0
% 0.42/0.61  # Condensation attempts                : 0
% 0.42/0.61  # Condensation successes               : 0
% 0.42/0.61  # Termbank termtop insertions          : 74593
% 0.42/0.61  # Search garbage collected termcells   : 12806
% 0.42/0.61  
% 0.42/0.61  # -------------------------------------------------
% 0.42/0.61  # User time                : 0.106 s
% 0.42/0.61  # System time              : 0.009 s
% 0.42/0.61  # Total time               : 0.115 s
% 0.42/0.61  # Maximum resident set size: 4748 pages
% 0.42/0.61  
% 0.42/0.61  # -------------------------------------------------
% 0.42/0.61  # User time                : 0.116 s
% 0.42/0.61  # System time              : 0.010 s
% 0.42/0.61  # Total time               : 0.126 s
% 0.42/0.61  # Maximum resident set size: 2312 pages
% 0.42/0.61  % E---3.1 exiting
% 0.42/0.62  % E exiting
%------------------------------------------------------------------------------