TSTP Solution File: ITP179^1 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP179^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 22:16:41 EDT 2024

% Result   : Theorem 1.38s 0.69s
% Output   : CNFRefutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   73 (  30 unt;  39 typ;   0 def)
%            Number of atoms       :   54 (  33 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  598 (  14   ~;  10   |;  10   &; 564   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :   14 (  13 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  26 usr;   9 con; 0-3 aty)
%            Number of variables   :   29 (   0   ^  29   !;   0   ?;  29   :)

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

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

thf(decl_sort3,type,
    labele431970251um_a_b: $tType ).

thf(decl_sort4,type,
    set_Pr1647387645at_nat: $tType ).

thf(decl_sort5,type,
    set_Pr409224873um_a_b: $tType ).

thf(decl_sort6,type,
    set_Pr1174980151um_a_b: $tType ).

thf(decl_sort7,type,
    labele935650037_a_nat: $tType ).

thf(decl_sort8,type,
    set_nat: $tType ).

thf(decl_sort9,type,
    product_prod_nat_nat: $tType ).

thf(decl_sort10,type,
    produc1032616263at_nat: $tType ).

thf(decl_sort11,type,
    produc1124793815um_a_b: $tType ).

thf(decl_sort12,type,
    sum_sum_a_b: $tType ).

thf(decl_sort13,type,
    set_Sum_sum_a_b: $tType ).

thf(decl_22,type,
    zero_zero_nat: nat ).

thf(decl_24,type,
    standard_S_Idt_a: standard_Constant_a ).

thf(decl_27,type,
    edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).

thf(decl_40,type,
    labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).

thf(decl_45,type,
    labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).

thf(decl_46,type,
    labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).

thf(decl_47,type,
    labele1810595089_a_nat: labele935650037_a_nat > set_nat ).

thf(decl_48,type,
    labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).

thf(decl_49,type,
    restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).

thf(decl_50,type,
    restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).

thf(decl_53,type,
    unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).

thf(decl_57,type,
    bot_bot_set_nat: set_nat ).

thf(decl_58,type,
    bot_bo810816657at_nat: set_Pr1647387645at_nat ).

thf(decl_64,type,
    bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).

thf(decl_82,type,
    ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).

thf(decl_83,type,
    produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).

thf(decl_88,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(decl_90,type,
    produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).

thf(decl_103,type,
    domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).

thf(decl_114,type,
    image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).

thf(decl_134,type,
    insert_nat: nat > set_nat > set_nat ).

thf(decl_135,type,
    insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).

thf(decl_138,type,
    insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).

thf(decl_165,type,
    g: labele431970251um_a_b ).

thf(decl_166,type,
    f: set_Pr1174980151um_a_b ).

thf(decl_168,type,
    v: sum_sum_a_b ).

thf(conj_0,conjecture,
    ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
      = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    & ( g
      = ( restri1162247455um_a_b @ g ) )
    & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
    & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(fact_135_labeled__graph_Osel_I2_J,axiom,
    ! [X48: set_Pr1647387645at_nat,X49: set_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X48 @ X49 ) )
      = X49 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_labeled__graph_Osel_I2_J) ).

thf(fact_5_d,axiom,
    ( ( domain1368163076um_a_b @ f )
    = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_d) ).

thf(fact_4_f,axiom,
    ( f
    = ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f) ).

thf(fact_9_u,axiom,
    unival2092813468um_a_b @ f,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_u) ).

thf(fact_137_labeled__graph_Osel_I1_J,axiom,
    ! [X48: set_Pr1647387645at_nat,X49: set_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X48 @ X49 ) )
      = X48 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_labeled__graph_Osel_I1_J) ).

thf(fact_3_r,axiom,
    ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_r) ).

thf(fact_7_graph__single,axiom,
    ! [X1: standard_Constant_a,X4: nat,X5: nat] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_graph__single) ).

thf(fact_252_insert__absorb2,axiom,
    ! [X517: nat,X61: set_nat] :
      ( ( insert_nat @ X517 @ ( insert_nat @ X517 @ X61 ) )
      = ( insert_nat @ X517 @ X61 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__absorb2) ).

thf(fact_0_g,axiom,
    ( g
    = ( restri1162247455um_a_b @ g ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_g) ).

thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
    edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062) ).

thf(c_0_11,negated_conjecture,
    ~ ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
      & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
      & ( g
        = ( restri1162247455um_a_b @ g ) )
      & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
      & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
      & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(c_0_12,negated_conjecture,
    ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
     != ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    | ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
     != ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    | ( g
     != ( restri1162247455um_a_b @ g ) )
    | ~ ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
    | ~ ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    | ~ ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

thf(c_0_13,plain,
    ! [X1944: set_Pr1647387645at_nat,X1945: set_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1944 @ X1945 ) )
      = X1945 ),
    inference(variable_rename,[status(thm)],[fact_135_labeled__graph_Osel_I2_J]) ).

thf(c_0_14,plain,
    ( ( domain1368163076um_a_b @ f )
    = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
    inference(split_conjunct,[status(thm)],[fact_5_d]) ).

thf(c_0_15,plain,
    ( f
    = ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
    inference(split_conjunct,[status(thm)],[fact_4_f]) ).

thf(c_0_16,plain,
    unival2092813468um_a_b @ f,
    inference(split_conjunct,[status(thm)],[fact_9_u]) ).

thf(c_0_17,plain,
    ! [X1948: set_Pr1647387645at_nat,X1949: set_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1948 @ X1949 ) )
      = X1948 ),
    inference(variable_rename,[status(thm)],[fact_137_labeled__graph_Osel_I1_J]) ).

thf(c_0_18,plain,
    ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
    inference(split_conjunct,[status(thm)],[fact_3_r]) ).

thf(c_0_19,plain,
    ! [X1527: standard_Constant_a,X1528: nat,X1529: nat] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1527 @ ( product_Pair_nat_nat @ X1528 @ X1529 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1528 @ ( insert_nat @ X1529 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1527 @ ( product_Pair_nat_nat @ X1528 @ X1529 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1528 @ ( insert_nat @ X1529 @ bot_bot_set_nat ) ) ) ) ),
    inference(variable_rename,[status(thm)],[fact_7_graph__single]) ).

thf(c_0_20,plain,
    ! [X2233: nat,X2234: set_nat] :
      ( ( insert_nat @ X2233 @ ( insert_nat @ X2233 @ X2234 ) )
      = ( insert_nat @ X2233 @ X2234 ) ),
    inference(variable_rename,[status(thm)],[fact_252_insert__absorb2]) ).

thf(c_0_21,negated_conjecture,
    ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
     != ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    | ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
     != ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    | ( g
     != ( restri1162247455um_a_b @ g ) )
    | ~ ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
    | ~ ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    | ~ ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_22,plain,
    ( g
    = ( restri1162247455um_a_b @ g ) ),
    inference(split_conjunct,[status(thm)],[fact_0_g]) ).

thf(c_0_23,plain,
    ! [X8: set_Pr1647387645at_nat,X39: set_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X8 @ X39 ) )
      = X39 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_24,plain,
    ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_25,plain,
    unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ),
    inference(rw,[status(thm)],[c_0_16,c_0_15]) ).

thf(c_0_26,plain,
    ! [X39: set_nat,X8: set_Pr1647387645at_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X8 @ X39 ) )
      = X8 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_27,plain,
    edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
    inference(split_conjunct,[status(thm)],[fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062]) ).

thf(c_0_28,plain,
    ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
    inference(rw,[status(thm)],[c_0_18,c_0_15]) ).

thf(c_0_29,plain,
    ! [X1: standard_Constant_a,X4: nat,X5: nat] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_30,plain,
    ! [X4: nat,X39: set_nat] :
      ( ( insert_nat @ X4 @ ( insert_nat @ X4 @ X39 ) )
      = ( insert_nat @ X4 @ X39 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_31,negated_conjecture,
    ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
   != ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_23]),c_0_28])]) ).

thf(c_0_32,plain,
    ! [X1: standard_Constant_a,X4: nat] :
      ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X4 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
      = ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X4 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : ITP179^1 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 17:52:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 1.38/0.69  # Version: 3.1.0-ho
% 1.38/0.69  # Preprocessing class: HSLMSMSMSSMNSFA.
% 1.38/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.38/0.69  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.38/0.69  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 1.38/0.69  # Starting full_lambda_6 with 300s (1) cores
% 1.38/0.69  # Starting ehoh_best_sine with 300s (1) cores
% 1.38/0.69  # ho_unfolding_3 with pid 23850 completed with status 0
% 1.38/0.69  # Result found by ho_unfolding_3
% 1.38/0.69  # Preprocessing class: HSLMSMSMSSMNSFA.
% 1.38/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.38/0.69  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.38/0.69  # No SInE strategy applied
% 1.38/0.69  # Search class: HGHSM-FSLM31-DSFFFFBN
% 1.38/0.69  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.38/0.69  # Starting lpo8_lambda_fix with 541s (1) cores
% 1.38/0.69  # Starting ho_unfolding_3 with 151s (1) cores
% 1.38/0.69  # Starting new_ho_2_cnf4 with 226s (1) cores
% 1.38/0.69  # Starting full_lambda_5 with 226s (1) cores
% 1.38/0.69  # Starting sh5l with 136s (1) cores
% 1.38/0.69  # full_lambda_5 with pid 23860 completed with status 0
% 1.38/0.69  # Result found by full_lambda_5
% 1.38/0.69  # Preprocessing class: HSLMSMSMSSMNSFA.
% 1.38/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.38/0.69  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.38/0.69  # No SInE strategy applied
% 1.38/0.69  # Search class: HGHSM-FSLM31-DSFFFFBN
% 1.38/0.69  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.38/0.69  # Starting lpo8_lambda_fix with 541s (1) cores
% 1.38/0.69  # Starting ho_unfolding_3 with 151s (1) cores
% 1.38/0.69  # Starting new_ho_2_cnf4 with 226s (1) cores
% 1.38/0.69  # Starting full_lambda_5 with 226s (1) cores
% 1.38/0.69  # Preprocessing time       : 0.008 s
% 1.38/0.69  # Presaturation interreduction done
% 1.38/0.69  
% 1.38/0.69  # Proof found!
% 1.38/0.69  # SZS status Theorem
% 1.38/0.69  # SZS output start CNFRefutation
% See solution above
% 1.38/0.69  # Parsed axioms                        : 554
% 1.38/0.69  # Removed by relevancy pruning/SinE    : 0
% 1.38/0.69  # Initial clauses                      : 779
% 1.38/0.69  # Removed in clause preprocessing      : 205
% 1.38/0.69  # Initial clauses in saturation        : 574
% 1.38/0.69  # Processed clauses                    : 2217
% 1.38/0.69  # ...of these trivial                  : 80
% 1.38/0.69  # ...subsumed                          : 855
% 1.38/0.69  # ...remaining for further processing  : 1282
% 1.38/0.69  # Other redundant clauses eliminated   : 200
% 1.38/0.69  # Clauses deleted for lack of memory   : 0
% 1.38/0.69  # Backward-subsumed                    : 6
% 1.38/0.69  # Backward-rewritten                   : 26
% 1.38/0.69  # Generated clauses                    : 3846
% 1.38/0.69  # ...of the previous two non-redundant : 3128
% 1.38/0.69  # ...aggressively subsumed             : 0
% 1.38/0.69  # Contextual simplify-reflections      : 4
% 1.38/0.69  # Paramodulations                      : 3592
% 1.38/0.69  # Factorizations                       : 2
% 1.38/0.69  # NegExts                              : 0
% 1.38/0.69  # Equation resolutions                 : 244
% 1.38/0.69  # Disequality decompositions           : 0
% 1.38/0.69  # Total rewrite steps                  : 1285
% 1.38/0.69  # ...of those cached                   : 1050
% 1.38/0.69  # Propositional unsat checks           : 0
% 1.38/0.69  #    Propositional check models        : 0
% 1.38/0.69  #    Propositional check unsatisfiable : 0
% 1.38/0.69  #    Propositional clauses             : 0
% 1.38/0.69  #    Propositional clauses after purity: 0
% 1.38/0.69  #    Propositional unsat core size     : 0
% 1.38/0.69  #    Propositional preprocessing time  : 0.000
% 1.38/0.69  #    Propositional encoding time       : 0.000
% 1.38/0.69  #    Propositional solver time         : 0.000
% 1.38/0.69  #    Success case prop preproc time    : 0.000
% 1.38/0.69  #    Success case prop encoding time   : 0.000
% 1.38/0.69  #    Success case prop solver time     : 0.000
% 1.38/0.69  # Current number of processed clauses  : 743
% 1.38/0.69  #    Positive orientable unit clauses  : 154
% 1.38/0.69  #    Positive unorientable unit clauses: 0
% 1.38/0.69  #    Negative unit clauses             : 13
% 1.38/0.69  #    Non-unit-clauses                  : 576
% 1.38/0.69  # Current number of unprocessed clauses: 1831
% 1.38/0.69  # ...number of literals in the above   : 4468
% 1.38/0.69  # Current number of archived formulas  : 0
% 1.38/0.69  # Current number of archived clauses   : 452
% 1.38/0.69  # Clause-clause subsumption calls (NU) : 194525
% 1.38/0.69  # Rec. Clause-clause subsumption calls : 80784
% 1.38/0.69  # Non-unit clause-clause subsumptions  : 681
% 1.38/0.69  # Unit Clause-clause subsumption calls : 14731
% 1.38/0.69  # Rewrite failures with RHS unbound    : 0
% 1.38/0.69  # BW rewrite match attempts            : 76
% 1.38/0.69  # BW rewrite match successes           : 24
% 1.38/0.69  # Condensation attempts                : 0
% 1.38/0.69  # Condensation successes               : 0
% 1.38/0.69  # Termbank termtop insertions          : 94169
% 1.38/0.69  # Search garbage collected termcells   : 11397
% 1.38/0.69  
% 1.38/0.69  # -------------------------------------------------
% 1.38/0.69  # User time                : 0.183 s
% 1.38/0.69  # System time              : 0.010 s
% 1.38/0.69  # Total time               : 0.193 s
% 1.38/0.69  # Maximum resident set size: 5272 pages
% 1.38/0.69  
% 1.38/0.69  # -------------------------------------------------
% 1.38/0.69  # User time                : 0.768 s
% 1.38/0.69  # System time              : 0.037 s
% 1.38/0.69  # Total time               : 0.805 s
% 1.38/0.69  # Maximum resident set size: 2740 pages
% 1.38/0.69  % E---3.1 exiting
% 1.38/0.69  % E exiting
%------------------------------------------------------------------------------