TSTP Solution File: ALG249^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG249^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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 18:05:51 EDT 2024

% Result   : Theorem 0.18s 0.49s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   38 (  10 unt;  17 typ;   0 def)
%            Number of atoms       :   57 (  14 equ;   0 cnn)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  246 (  11   ~;   8   |;   7   &; 185   @)
%                                         (   9 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   9 con; 0-4 aty)
%            Number of variables   :   70 (   8   ^  62   !;   0   ?;  70   :)

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

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

thf(decl_25,type,
    sub: term > subst > term ).

thf(decl_27,type,
    sh: subst ).

thf(decl_28,type,
    push: term > subst > subst ).

thf(decl_29,type,
    comp: subst > subst > subst ).

thf(decl_30,type,
    var: term > $o ).

thf(decl_80,type,
    pushprop_lem2v2: $o ).

thf(decl_82,type,
    axclos: $o ).

thf(decl_126,type,
    pushprop_lem2v2_lthm: $o ).

thf(decl_136,type,
    axshiftcons: $o ).

thf(decl_141,type,
    pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).

thf(decl_144,type,
    epred1_0: term > $o ).

thf(decl_145,type,
    epred2_0: term > $o ).

thf(decl_146,type,
    esk1_0: term ).

thf(decl_147,type,
    esk2_0: subst ).

thf(decl_148,type,
    esk3_0: term ).

thf(pushprop_p_and_p_prime,axiom,
    ( pushprop_p_and_p_prime
    = ( ^ [X1: term,X3: subst,X6: term > $o,X9: term > $o] :
        ! [X10: term] :
          ( ( X9 @ X10 )
        <=> ( X6 @ ( sub @ X10 @ ( push @ X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_p_and_p_prime) ).

thf(pushprop_lem2v2,axiom,
    ( pushprop_lem2v2
  <=> ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
        ( ( pushprop_p_and_p_prime @ X1 @ X3 @ X6 @ X9 )
       => ( ! [X2: term] :
              ( ( var @ X2 )
             => ( X6 @ ( sub @ X2 @ X3 ) ) )
         => ! [X7: term] :
              ( ( var @ X7 )
             => ( ( X9 @ X7 )
               => ( X9 @ ( sub @ X7 @ sh ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2) ).

thf(pushprop_lem2v2_lthm,axiom,
    ( pushprop_lem2v2_lthm
  <=> ( axclos
     => ( axshiftcons
       => pushprop_lem2v2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2_lthm) ).

thf(axclos,axiom,
    ( axclos
  <=> ! [X1: term,X3: subst,X4: subst] :
        ( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
        = ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axclos) ).

thf(axshiftcons,axiom,
    ( axshiftcons
  <=> ! [X1: term,X3: subst] :
        ( ( comp @ sh @ ( push @ X1 @ X3 ) )
        = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).

thf(thm,conjecture,
    pushprop_lem2v2_lthm,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(c_0_6,plain,
    ( pushprop_p_and_p_prime
    = ( ^ [Z0: term,Z1: subst,Z2: term > $o,Z3: term > $o] :
        ! [X10: term] :
          ( ( Z3 @ X10 )
        <=> ( Z2 @ ( sub @ X10 @ ( push @ Z0 @ Z1 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[pushprop_p_and_p_prime]) ).

thf(c_0_7,axiom,
    ( pushprop_lem2v2
    = ( ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
          ( ! [X1716: term] :
              ( ( X9 @ X1716 )
            <=> ( X6 @ ( sub @ X1716 @ ( push @ X1 @ X3 ) ) ) )
         => ( ! [X2: term] :
                ( ( var @ X2 )
               => ( X6 @ ( sub @ X2 @ X3 ) ) )
           => ! [X7: term] :
                ( ( var @ X7 )
               => ( ( X9 @ X7 )
                 => ( X9 @ ( sub @ X7 @ sh ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[pushprop_lem2v2,c_0_6]) ).

thf(c_0_8,axiom,
    ( pushprop_lem2v2_lthm
    = ( ! [X3138: term,X3139: subst,X3140: subst] :
          ( ( sub @ ( sub @ X3138 @ X3139 ) @ X3140 )
          = ( sub @ X3138 @ ( comp @ X3139 @ X3140 ) ) )
     => ( ! [X3141: term,X3142: subst] :
            ( ( comp @ sh @ ( push @ X3141 @ X3142 ) )
            = X3142 )
       => ! [X3143: term > $o,X3144: term > $o,X3145: term,X3146: subst] :
            ( ! [X3147: term] :
                ( ( X3144 @ X3147 )
              <=> ( X3143 @ ( sub @ X3147 @ ( push @ X3145 @ X3146 ) ) ) )
           => ( ! [X3148: term] :
                  ( ( var @ X3148 )
                 => ( X3143 @ ( sub @ X3148 @ X3146 ) ) )
             => ! [X3149: term] :
                  ( ( var @ X3149 )
                 => ( ( X3144 @ X3149 )
                   => ( X3144 @ ( sub @ X3149 @ sh ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pushprop_lem2v2_lthm,axclos]),axshiftcons]),c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ~ ( ! [X3373: term,X3374: subst,X3375: subst] :
          ( ( sub @ ( sub @ X3373 @ X3374 ) @ X3375 )
          = ( sub @ X3373 @ ( comp @ X3374 @ X3375 ) ) )
     => ( ! [X3376: term,X3377: subst] :
            ( ( comp @ sh @ ( push @ X3376 @ X3377 ) )
            = X3377 )
       => ! [X3378: term > $o,X3379: term > $o,X3380: term,X3381: subst] :
            ( ! [X3382: term] :
                ( ( X3379 @ X3382 )
              <=> ( X3378 @ ( sub @ X3382 @ ( push @ X3380 @ X3381 ) ) ) )
           => ( ! [X3383: term] :
                  ( ( var @ X3383 )
                 => ( X3378 @ ( sub @ X3383 @ X3381 ) ) )
             => ! [X3384: term] :
                  ( ( var @ X3384 )
                 => ( ( X3379 @ X3384 )
                   => ( X3379 @ ( sub @ X3384 @ sh ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ! [X3397: term,X3398: subst,X3399: subst,X3400: term,X3401: subst,X3406: term,X3407: term] :
      ( ( ( sub @ ( sub @ X3397 @ X3398 ) @ X3399 )
        = ( sub @ X3397 @ ( comp @ X3398 @ X3399 ) ) )
      & ( ( comp @ sh @ ( push @ X3400 @ X3401 ) )
        = X3401 )
      & ( ~ ( epred2_0 @ X3406 )
        | ( epred1_0 @ ( sub @ X3406 @ ( push @ esk1_0 @ esk2_0 ) ) ) )
      & ( ~ ( epred1_0 @ ( sub @ X3406 @ ( push @ esk1_0 @ esk2_0 ) ) )
        | ( epred2_0 @ X3406 ) )
      & ( ~ ( var @ X3407 )
        | ( epred1_0 @ ( sub @ X3407 @ esk2_0 ) ) )
      & ( var @ esk3_0 )
      & ( epred2_0 @ esk3_0 )
      & ~ ( epred2_0 @ ( sub @ esk3_0 @ sh ) ) ),
    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_9])])])])]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: term] :
      ( ( epred2_0 @ X1 )
      | ~ ( epred1_0 @ ( sub @ X1 @ ( push @ esk1_0 @ esk2_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ! [X1: term,X3: subst,X4: subst] :
      ( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
      = ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: term,X3: subst] :
      ( ( epred2_0 @ ( sub @ X1 @ X3 ) )
      | ~ ( epred1_0 @ ( sub @ X1 @ ( comp @ X3 @ ( push @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: term,X3: subst] :
      ( ( comp @ sh @ ( push @ X1 @ X3 ) )
      = X3 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: term] :
      ( ( epred2_0 @ ( sub @ X1 @ sh ) )
      | ~ ( epred1_0 @ ( sub @ X1 @ esk2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: term] :
      ( ( epred1_0 @ ( sub @ X1 @ esk2_0 ) )
      | ~ ( var @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_17,negated_conjecture,
    ~ ( epred2_0 @ ( sub @ esk3_0 @ sh ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: term] :
      ( ( epred2_0 @ ( sub @ X1 @ sh ) )
      | ~ ( var @ X1 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_19,negated_conjecture,
    var @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : ALG249^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 23:23:22 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.18/0.44  Running higher-order theorem proving
% 0.18/0.45  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
% 0.18/0.49  # Version: 3.1.0-ho
% 0.18/0.49  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.49  # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.49  # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.49  # post_as_ho1 with pid 21726 completed with status 0
% 0.18/0.49  # Result found by post_as_ho1
% 0.18/0.49  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.49  # No SInE strategy applied
% 0.18/0.49  # Search class: HHUSM-FFSF32-SHFMMFNN
% 0.18/0.49  # partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.49  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.49  # new_ho_10 with pid 21734 completed with status 0
% 0.18/0.49  # Result found by new_ho_10
% 0.18/0.49  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.49  # No SInE strategy applied
% 0.18/0.49  # Search class: HHUSM-FFSF32-SHFMMFNN
% 0.18/0.49  # partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.49  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.49  # Preprocessing time       : 0.001 s
% 0.18/0.49  # Presaturation interreduction done
% 0.18/0.49  
% 0.18/0.49  # Proof found!
% 0.18/0.49  # SZS status Theorem
% 0.18/0.49  # SZS output start CNFRefutation
% See solution above
% 0.18/0.49  # Parsed axioms                        : 238
% 0.18/0.49  # Removed by relevancy pruning/SinE    : 0
% 0.18/0.49  # Initial clauses                      : 134
% 0.18/0.49  # Removed in clause preprocessing      : 124
% 0.18/0.49  # Initial clauses in saturation        : 10
% 0.18/0.49  # Processed clauses                    : 36
% 0.18/0.49  # ...of these trivial                  : 0
% 0.18/0.49  # ...subsumed                          : 5
% 0.18/0.49  # ...remaining for further processing  : 31
% 0.18/0.49  # Other redundant clauses eliminated   : 0
% 0.18/0.49  # Clauses deleted for lack of memory   : 0
% 0.18/0.49  # Backward-subsumed                    : 0
% 0.18/0.49  # Backward-rewritten                   : 0
% 0.18/0.49  # Generated clauses                    : 42
% 0.18/0.49  # ...of the previous two non-redundant : 34
% 0.18/0.49  # ...aggressively subsumed             : 0
% 0.18/0.49  # Contextual simplify-reflections      : 0
% 0.18/0.49  # Paramodulations                      : 38
% 0.18/0.49  # Factorizations                       : 0
% 0.18/0.49  # NegExts                              : 0
% 0.18/0.49  # Equation resolutions                 : 0
% 0.18/0.49  # Disequality decompositions           : 0
% 0.18/0.49  # Total rewrite steps                  : 18
% 0.18/0.49  # ...of those cached                   : 3
% 0.18/0.49  # Propositional unsat checks           : 0
% 0.18/0.49  #    Propositional check models        : 0
% 0.18/0.49  #    Propositional check unsatisfiable : 0
% 0.18/0.49  #    Propositional clauses             : 0
% 0.18/0.49  #    Propositional clauses after purity: 0
% 0.18/0.49  #    Propositional unsat core size     : 0
% 0.18/0.49  #    Propositional preprocessing time  : 0.000
% 0.18/0.49  #    Propositional encoding time       : 0.000
% 0.18/0.49  #    Propositional solver time         : 0.000
% 0.18/0.49  #    Success case prop preproc time    : 0.000
% 0.18/0.49  #    Success case prop encoding time   : 0.000
% 0.18/0.49  #    Success case prop solver time     : 0.000
% 0.18/0.49  # Current number of processed clauses  : 21
% 0.18/0.49  #    Positive orientable unit clauses  : 8
% 0.18/0.49  #    Positive unorientable unit clauses: 3
% 0.18/0.49  #    Negative unit clauses             : 1
% 0.18/0.49  #    Non-unit-clauses                  : 9
% 0.18/0.49  # Current number of unprocessed clauses: 18
% 0.18/0.49  # ...number of literals in the above   : 27
% 0.18/0.49  # Current number of archived formulas  : 0
% 0.18/0.49  # Current number of archived clauses   : 10
% 0.18/0.49  # Clause-clause subsumption calls (NU) : 10
% 0.18/0.49  # Rec. Clause-clause subsumption calls : 10
% 0.18/0.49  # Non-unit clause-clause subsumptions  : 0
% 0.18/0.49  # Unit Clause-clause subsumption calls : 9
% 0.18/0.49  # Rewrite failures with RHS unbound    : 0
% 0.18/0.49  # BW rewrite match attempts            : 3
% 0.18/0.49  # BW rewrite match successes           : 2
% 0.18/0.49  # Condensation attempts                : 36
% 0.18/0.49  # Condensation successes               : 0
% 0.18/0.49  # Termbank termtop insertions          : 27192
% 0.18/0.49  # Search garbage collected termcells   : 1856
% 0.18/0.49  
% 0.18/0.49  # -------------------------------------------------
% 0.18/0.49  # User time                : 0.025 s
% 0.18/0.49  # System time              : 0.010 s
% 0.18/0.49  # Total time               : 0.034 s
% 0.18/0.49  # Maximum resident set size: 5800 pages
% 0.18/0.49  
% 0.18/0.49  # -------------------------------------------------
% 0.18/0.49  # User time                : 0.030 s
% 0.18/0.49  # System time              : 0.011 s
% 0.18/0.49  # Total time               : 0.041 s
% 0.18/0.49  # Maximum resident set size: 2076 pages
% 0.18/0.49  % E---3.1 exiting
% 0.18/0.49  % E exiting
%------------------------------------------------------------------------------