TSTP Solution File: ITP042^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP042^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 08:06:45 EDT 2024

% Result   : Theorem 0.43s 0.63s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   35 (   3 unt;  18 typ;   0 def)
%            Number of atoms       :   64 (  17 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  169 (   7   ~;   3   |;  13   &; 142   @)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   36 (  11   ^  12   !;  13   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    sum_su1965225555um_c_b: $tType ).

thf(decl_sort2,type,
    set_Su111624115um_c_b: $tType ).

thf(decl_sort3,type,
    denota723907260t_unit: $tType ).

thf(decl_sort4,type,
    a: $tType ).

thf(decl_sort5,type,
    trm_a_b: $tType ).

thf(decl_sort6,type,
    set_a: $tType ).

thf(decl_22,type,
    denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o ).

thf(decl_83,type,
    collec1166375742um_c_b: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b ).

thf(decl_90,type,
    static_SIGT_a_b: trm_a_b > set_a ).

thf(decl_92,type,
    sum_In811702836um_c_b: a > sum_su1965225555um_c_b ).

thf(decl_95,type,
    times_a_b: trm_a_b > trm_a_b > trm_a_b ).

thf(decl_110,type,
    member_a: a > set_a > $o ).

thf(decl_111,type,
    i: denota723907260t_unit ).

thf(decl_112,type,
    j: denota723907260t_unit ).

thf(decl_115,type,
    theta_1: trm_a_b ).

thf(decl_116,type,
    theta_2: trm_a_b ).

thf(decl_137,type,
    epred1_0: sum_su1965225555um_c_b > $o ).

thf(decl_140,type,
    epred4_0: sum_su1965225555um_c_b > $o ).

thf(conj_0,conjecture,
    ( denota896875430_a_c_b @ i @ j
    @ ( collec1166375742um_c_b
      @ ^ [X3: sum_su1965225555um_c_b] :
        ? [X4: a] :
          ( ( X3
            = ( sum_In811702836um_c_b @ X4 ) )
          & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',conj_0) ).

thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
    ! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
      ( ( denota896875430_a_c_b @ X1 @ X2
        @ ( collec1166375742um_c_b
          @ ^ [X3: sum_su1965225555um_c_b] :
            ? [X4: a] :
              ( ( X3
                = ( sum_In811702836um_c_b @ X4 ) )
              & ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
     => ( denota896875430_a_c_b @ X1 @ X2
        @ ( collec1166375742um_c_b
          @ ^ [X3: sum_su1965225555um_c_b] :
            ? [X4: a] :
              ( ( X3
                = ( sum_In811702836um_c_b @ X4 ) )
              & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062) ).

thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
    ( denota896875430_a_c_b @ i @ j
    @ ( collec1166375742um_c_b
      @ ^ [X3: sum_su1965225555um_c_b] :
        ? [X4: a] :
          ( ( X3
            = ( sum_In811702836um_c_b @ X4 ) )
          & ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',fact_3_dfree__Times_Oprems_I2_J) ).

thf(c_0_3,negated_conjecture,
    ~ ( denota896875430_a_c_b @ i @ j
      @ ( collec1166375742um_c_b
        @ ^ [Z0: sum_su1965225555um_c_b] :
          ? [X4: a] :
            ( ( Z0
              = ( sum_In811702836um_c_b @ X4 ) )
            & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).

thf(c_0_4,plain,
    ! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
      ( ( denota896875430_a_c_b @ X1 @ X2
        @ ( collec1166375742um_c_b
          @ ^ [Z0: sum_su1965225555um_c_b] :
            ? [X4: a] :
              ( ( Z0
                = ( sum_In811702836um_c_b @ X4 ) )
              & ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
     => ( denota896875430_a_c_b @ X1 @ X2
        @ ( collec1166375742um_c_b
          @ ^ [Z0: sum_su1965225555um_c_b] :
            ? [X4: a] :
              ( ( Z0
                = ( sum_In811702836um_c_b @ X4 ) )
              & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062]) ).

thf(c_0_5,negated_conjecture,
    ~ ( denota896875430_a_c_b @ i @ j
      @ ( collec1166375742um_c_b
        @ ^ [Z0: sum_su1965225555um_c_b] :
          ? [X4: a] :
            ( ( Z0
              = ( sum_In811702836um_c_b @ X4 ) )
            & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_3]) ).

thf(c_0_6,plain,
    ! [X1345: sum_su1965225555um_c_b] :
      ( ( epred1_0 @ X1345 )
    <=> ? [X1344: a] :
          ( ( X1345
            = ( sum_In811702836um_c_b @ X1344 ) )
          & ( member_a @ X1344 @ ( static_SIGT_a_b @ theta_1 ) ) ) ),
    introduced(definition) ).

thf(c_0_7,plain,
    ! [X1091: denota723907260t_unit,X1092: denota723907260t_unit] :
      ( ~ ( denota896875430_a_c_b @ X1091 @ X1092
          @ ( collec1166375742um_c_b
            @ ^ [Z0: sum_su1965225555um_c_b] :
              ? [X4: a] :
                ( ( Z0
                  = ( sum_In811702836um_c_b @ X4 ) )
                & ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
      | ( denota896875430_a_c_b @ X1091 @ X1092
        @ ( collec1166375742um_c_b
          @ ^ [Z0: sum_su1965225555um_c_b] :
            ? [X4: a] :
              ( ( Z0
                = ( sum_In811702836um_c_b @ X4 ) )
              & ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

thf(c_0_8,plain,
    ! [X1353: sum_su1965225555um_c_b] :
      ( ( epred4_0 @ X1353 )
    <=> ? [X1352: a] :
          ( ( X1353
            = ( sum_In811702836um_c_b @ X1352 ) )
          & ( member_a @ X1352 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ),
    introduced(definition) ).

thf(c_0_9,plain,
    ( denota896875430_a_c_b @ i @ j
    @ ( collec1166375742um_c_b
      @ ^ [Z0: sum_su1965225555um_c_b] :
        ? [X4: a] :
          ( ( Z0
            = ( sum_In811702836um_c_b @ X4 ) )
          & ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_3_dfree__Times_Oprems_I2_J]) ).

thf(c_0_10,negated_conjecture,
    ( ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred1_0 ) )
   != $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]),c_0_6]) ).

thf(c_0_11,plain,
    ! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
      ( ( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred1_0 ) )
        = $true )
      | ( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred4_0 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]),c_0_8]),c_0_6]) ).

thf(c_0_12,plain,
    ( ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred4_0 ) )
    = $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]),c_0_8]) ).

thf(c_0_13,negated_conjecture,
    ~ ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred1_0 ) ),
    inference(cn,[status(thm)],[c_0_10]) ).

thf(c_0_14,plain,
    ! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
      ( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred1_0 ) )
      | ~ ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred4_0 ) ) ),
    inference(cn,[status(thm)],[c_0_11]) ).

thf(c_0_15,plain,
    denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred4_0 ),
    inference(cn,[status(thm)],[c_0_12]) ).

thf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17  % Problem    : ITP042^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.18  % Command    : run_E %s %d THM
% 0.18/0.40  % Computer : n010.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit   : 300
% 0.18/0.40  % WCLimit    : 300
% 0.18/0.40  % DateTime   : Fri May  3 12:13:03 EDT 2024
% 0.18/0.40  % CPUTime    : 
% 0.25/0.57  Running higher-order theorem proving
% 0.25/0.57  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/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p
% 0.43/0.63  # Version: 3.1.0-ho
% 0.43/0.63  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63  # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63  # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63  # Starting post_as_ho6 with 300s (1) cores
% 0.43/0.63  # Starting ho_unfolding_1 with 300s (1) cores
% 0.43/0.63  # Starting full_lambda_4 with 300s (1) cores
% 0.43/0.63  # Starting pre_casc_5 with 300s (1) cores
% 0.43/0.63  # new_bool_8 with pid 7597 completed with status 0
% 0.43/0.63  # Result found by new_bool_8
% 0.43/0.63  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63  # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63  # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.43/0.63  # Search class: HGUSM-FFLM32-MHSFFSBN
% 0.43/0.63  # partial match(1): HGUSM-FSLM32-MHSFFSBN
% 0.43/0.63  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.63  # Starting lpo8_s with 163s (1) cores
% 0.43/0.63  # lpo8_s with pid 7605 completed with status 0
% 0.43/0.63  # Result found by lpo8_s
% 0.43/0.63  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63  # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63  # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.43/0.63  # Search class: HGUSM-FFLM32-MHSFFSBN
% 0.43/0.63  # partial match(1): HGUSM-FSLM32-MHSFFSBN
% 0.43/0.63  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.63  # Starting lpo8_s with 163s (1) cores
% 0.43/0.63  # Preprocessing time       : 0.004 s
% 0.43/0.63  # Presaturation interreduction done
% 0.43/0.63  
% 0.43/0.63  # Proof found!
% 0.43/0.63  # SZS status Theorem
% 0.43/0.63  # SZS output start CNFRefutation
% See solution above
% 0.43/0.63  # Parsed axioms                        : 482
% 0.43/0.63  # Removed by relevancy pruning/SinE    : 365
% 0.43/0.63  # Initial clauses                      : 182
% 0.43/0.63  # Removed in clause preprocessing      : 6
% 0.43/0.63  # Initial clauses in saturation        : 176
% 0.43/0.63  # Processed clauses                    : 211
% 0.43/0.63  # ...of these trivial                  : 13
% 0.43/0.63  # ...subsumed                          : 52
% 0.43/0.63  # ...remaining for further processing  : 146
% 0.43/0.63  # Other redundant clauses eliminated   : 28
% 0.43/0.63  # Clauses deleted for lack of memory   : 0
% 0.43/0.63  # Backward-subsumed                    : 0
% 0.43/0.63  # Backward-rewritten                   : 0
% 0.43/0.63  # Generated clauses                    : 42
% 0.43/0.63  # ...of the previous two non-redundant : 17
% 0.43/0.63  # ...aggressively subsumed             : 0
% 0.43/0.63  # Contextual simplify-reflections      : 0
% 0.43/0.63  # Paramodulations                      : 3
% 0.43/0.63  # Factorizations                       : 0
% 0.43/0.63  # NegExts                              : 2
% 0.43/0.63  # Equation resolutions                 : 28
% 0.43/0.63  # Disequality decompositions           : 0
% 0.43/0.63  # Total rewrite steps                  : 32
% 0.43/0.63  # ...of those cached                   : 19
% 0.43/0.63  # Propositional unsat checks           : 0
% 0.43/0.63  #    Propositional check models        : 0
% 0.43/0.63  #    Propositional check unsatisfiable : 0
% 0.43/0.63  #    Propositional clauses             : 0
% 0.43/0.63  #    Propositional clauses after purity: 0
% 0.43/0.63  #    Propositional unsat core size     : 0
% 0.43/0.63  #    Propositional preprocessing time  : 0.000
% 0.43/0.63  #    Propositional encoding time       : 0.000
% 0.43/0.63  #    Propositional solver time         : 0.000
% 0.43/0.63  #    Success case prop preproc time    : 0.000
% 0.43/0.63  #    Success case prop encoding time   : 0.000
% 0.43/0.63  #    Success case prop solver time     : 0.000
% 0.43/0.63  # Current number of processed clauses  : 24
% 0.43/0.63  #    Positive orientable unit clauses  : 12
% 0.43/0.63  #    Positive unorientable unit clauses: 0
% 0.43/0.63  #    Negative unit clauses             : 3
% 0.43/0.63  #    Non-unit-clauses                  : 9
% 0.43/0.63  # Current number of unprocessed clauses: 80
% 0.43/0.63  # ...number of literals in the above   : 180
% 0.43/0.63  # Current number of archived formulas  : 0
% 0.43/0.63  # Current number of archived clauses   : 103
% 0.43/0.63  # Clause-clause subsumption calls (NU) : 1512
% 0.43/0.63  # Rec. Clause-clause subsumption calls : 1205
% 0.43/0.63  # Non-unit clause-clause subsumptions  : 51
% 0.43/0.63  # Unit Clause-clause subsumption calls : 23
% 0.43/0.63  # Rewrite failures with RHS unbound    : 0
% 0.43/0.63  # BW rewrite match attempts            : 16
% 0.43/0.63  # BW rewrite match successes           : 0
% 0.43/0.63  # Condensation attempts                : 211
% 0.43/0.63  # Condensation successes               : 0
% 0.43/0.63  # Termbank termtop insertions          : 18218
% 0.43/0.63  # Search garbage collected termcells   : 5762
% 0.43/0.63  
% 0.43/0.63  # -------------------------------------------------
% 0.43/0.63  # User time                : 0.023 s
% 0.43/0.63  # System time              : 0.009 s
% 0.43/0.63  # Total time               : 0.032 s
% 0.43/0.63  # Maximum resident set size: 3496 pages
% 0.43/0.63  
% 0.43/0.63  # -------------------------------------------------
% 0.43/0.63  # User time                : 0.036 s
% 0.43/0.63  # System time              : 0.013 s
% 0.43/0.63  # Total time               : 0.049 s
% 0.43/0.63  # Maximum resident set size: 2676 pages
% 0.43/0.63  % E---3.1 exiting
% 0.43/0.64  % E exiting
%------------------------------------------------------------------------------