TSTP Solution File: NUM415^1 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 : Tue May 21 01:13:50 EDT 2024

% Result   : Theorem 10.86s 1.84s
% Output   : CNFRefutation 10.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  110 (  96 unt;  14 typ;   0 def)
%            Number of atoms       :   96 (  95 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  591 (   5   ~;   0   |;   0   &; 586   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  222 ( 222   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   1 con; 0-4 aty)
%            Number of variables   :  190 (  31   ^ 159   !;   0   ?; 190   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    one: ( $i > $i ) > $i > $i ).

thf(decl_24,type,
    two: ( $i > $i ) > $i > $i ).

thf(decl_25,type,
    three: ( $i > $i ) > $i > $i ).

thf(decl_26,type,
    four: ( $i > $i ) > $i > $i ).

thf(decl_27,type,
    five: ( $i > $i ) > $i > $i ).

thf(decl_28,type,
    six: ( $i > $i ) > $i > $i ).

thf(decl_29,type,
    seven: ( $i > $i ) > $i > $i ).

thf(decl_30,type,
    eight: ( $i > $i ) > $i > $i ).

thf(decl_31,type,
    nine: ( $i > $i ) > $i > $i ).

thf(decl_32,type,
    ten: ( $i > $i ) > $i > $i ).

thf(decl_33,type,
    succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(decl_34,type,
    plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(decl_35,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(decl_1315,type,
    esk1280_1: $i > $i ).

thf(four_ax,axiom,
    ( four
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',four_ax) ).

thf(three_ax,axiom,
    ( three
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',three_ax) ).

thf(two_ax,axiom,
    ( two
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',two_ax) ).

thf(five_ax,axiom,
    ( five
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',five_ax) ).

thf(six_ax,axiom,
    ( six
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',six_ax) ).

thf(seven_ax,axiom,
    ( seven
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',seven_ax) ).

thf(eight_ax,axiom,
    ( eight
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',eight_ax) ).

thf(nine_ax,axiom,
    ( nine
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',nine_ax) ).

thf(ten_ax,axiom,
    ( ten
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',ten_ax) ).

thf(succ_ax,axiom,
    ( succ
    = ( ^ [X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',succ_ax) ).

thf(plus_ax,axiom,
    ( plus
    = ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ X1 @ ( X3 @ X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',plus_ax) ).

thf(thm,conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
    = ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(mult_ax,axiom,
    ( mult
    = ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',mult_ax) ).

thf(one_ax,axiom,
    ( one
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',one_ax) ).

thf(c_0_14,plain,
    ! [X13: $i > $i,X14: $i] :
      ( ( four @ X13 @ X14 )
      = ( X13 @ ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[four_ax])]) ).

thf(c_0_15,plain,
    ! [X11: $i > $i,X12: $i] :
      ( ( three @ X11 @ X12 )
      = ( X11 @ ( X11 @ ( X11 @ X12 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).

thf(c_0_16,plain,
    ! [X9: $i > $i,X10: $i] :
      ( ( two @ X9 @ X10 )
      = ( X9 @ ( X9 @ X10 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).

thf(c_0_17,plain,
    ! [X15: $i > $i,X16: $i] :
      ( ( five @ X15 @ X16 )
      = ( X15 @ ( X15 @ ( X15 @ ( X15 @ ( X15 @ X16 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).

thf(c_0_18,plain,
    ! [X46: $i > $i,X47: $i] :
      ( ( four @ X46 @ X47 )
      = ( X46 @ ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

thf(c_0_19,plain,
    ! [X44: $i > $i,X45: $i] :
      ( ( three @ X44 @ X45 )
      = ( X44 @ ( X44 @ ( X44 @ X45 ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

thf(c_0_20,plain,
    ! [X42: $i > $i,X43: $i] :
      ( ( two @ X42 @ X43 )
      = ( X42 @ ( X42 @ X43 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_16]) ).

thf(c_0_21,plain,
    ! [X17: $i > $i,X18: $i] :
      ( ( six @ X17 @ X18 )
      = ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ X18 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).

thf(c_0_22,plain,
    ! [X48: $i > $i,X49: $i] :
      ( ( five @ X48 @ X49 )
      = ( X48 @ ( X48 @ ( X48 @ ( X48 @ ( X48 @ X49 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

thf(c_0_23,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( four @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_24,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_25,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ X1 @ X2 )
      = ( X1 @ ( X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,plain,
    ! [X19: $i > $i,X20: $i] :
      ( ( seven @ X19 @ X20 )
      = ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ X20 ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[seven_ax])]) ).

thf(c_0_27,plain,
    ! [X50: $i > $i,X51: $i] :
      ( ( six @ X50 @ X51 )
      = ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ X51 ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_21]) ).

thf(c_0_28,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( five @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_29,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( three @ X1 @ X2 ) )
      = ( four @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_30,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( X1 @ ( two @ X1 @ X2 ) ) )
      = ( two @ ( two @ X1 ) @ X2 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_25]) ).

thf(c_0_31,plain,
    ! [X21: $i > $i,X22: $i] :
      ( ( eight @ X21 @ X22 )
      = ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ X22 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[eight_ax])]) ).

thf(c_0_32,plain,
    ! [X52: $i > $i,X53: $i] :
      ( ( seven @ X52 @ X53 )
      = ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ X53 ) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_26]) ).

thf(c_0_33,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( six @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_34,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( four @ X1 @ X2 ) )
      = ( five @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_24]),c_0_29]) ).

thf(c_0_35,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ ( two @ X1 ) @ X2 )
      = ( four @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_24]),c_0_29]) ).

thf(c_0_36,plain,
    ! [X23: $i > $i,X24: $i] :
      ( ( nine @ X23 @ X24 )
      = ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ X24 ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[nine_ax])]) ).

thf(c_0_37,plain,
    ! [X54: $i > $i,X55: $i] :
      ( ( eight @ X54 @ X55 )
      = ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ X55 ) ) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_31]) ).

thf(c_0_38,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( seven @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_39,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( five @ X1 @ X2 ) )
      = ( six @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_24]),c_0_29]),c_0_34]) ).

thf(c_0_40,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
      = ( five @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_24]),c_0_29]),c_0_34]) ).

thf(c_0_41,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ ( X1 @ X2 ) )
      = ( four @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_30]),c_0_35]) ).

thf(c_0_42,plain,
    ! [X25: $i > $i,X26: $i] :
      ( ( ten @ X25 @ X26 )
      = ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ X26 ) ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ten_ax])]) ).

thf(c_0_43,plain,
    ! [X56: $i > $i,X57: $i] :
      ( ( nine @ X56 @ X57 )
      = ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ X57 ) ) ) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_36]) ).

thf(c_0_44,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( eight @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_45,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( six @ X1 @ X2 ) )
      = ( seven @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_24]),c_0_29]),c_0_34]),c_0_39]) ).

thf(c_0_46,plain,
    ! [X27: ( $i > $i ) > $i > $i,X28: $i > $i,X29: $i] :
      ( ( succ @ X27 @ X28 @ X29 )
      = ( X28 @ ( X27 @ X28 @ X29 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[succ_ax])]) ).

thf(c_0_47,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( four @ X1 @ ( X1 @ X2 ) )
      = ( five @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[c_0_40,c_0_41]) ).

thf(c_0_48,plain,
    ! [X58: $i > $i,X59: $i] :
      ( ( ten @ X58 @ X59 )
      = ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ X59 ) ) ) ) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_42]) ).

thf(c_0_49,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( nine @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

thf(c_0_50,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( seven @ X1 @ X2 ) )
      = ( eight @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]) ).

thf(c_0_51,plain,
    ! [X60: ( $i > $i ) > $i > $i,X61: $i > $i,X62: $i] :
      ( ( succ @ X60 @ X61 @ X62 )
      = ( X61 @ ( X60 @ X61 @ X62 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_46]) ).

thf(c_0_52,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( X1 @ ( two @ X1 @ X2 ) ) )
      = ( four @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[c_0_30,c_0_35]) ).

thf(c_0_53,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
      = ( four @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_25]),c_0_35]) ).

thf(c_0_54,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( five @ X1 @ ( X1 @ X2 ) )
      = ( three @ ( two @ X1 ) @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_35]),c_0_47]) ).

thf(c_0_55,plain,
    ! [X30: ( $i > $i ) > $i > $i,X31: ( $i > $i ) > $i > $i,X32: $i > $i,X33: $i] :
      ( ( plus @ X30 @ X31 @ X32 @ X33 )
      = ( X30 @ X32 @ ( X31 @ X32 @ X33 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).

thf(c_0_56,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( ten @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

thf(c_0_57,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( eight @ X1 @ X2 ) )
      = ( nine @ X1 @ X2 ) ),
    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_49,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]),c_0_50]) ).

thf(c_0_58,plain,
    ! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( succ @ X3 @ X1 @ X2 )
      = ( X1 @ ( X3 @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

thf(c_0_59,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ ( two @ X1 ) @ X2 )
      = ( six @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34]),c_0_39]),c_0_47]),c_0_54]) ).

thf(c_0_60,plain,
    ! [X63: ( $i > $i ) > $i > $i,X64: ( $i > $i ) > $i > $i,X65: $i > $i,X66: $i] :
      ( ( plus @ X63 @ X64 @ X65 @ X66 )
      = ( X63 @ X65 @ ( X64 @ X65 @ X66 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_55]) ).

thf(c_0_61,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( X1 @ ( nine @ X1 @ X2 ) )
      = ( ten @ X1 @ X2 ) ),
    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_56,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]),c_0_50]),c_0_57]) ).

thf(c_0_62,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( succ @ three @ X1 @ X2 )
      = ( four @ X1 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_58]) ).

thf(c_0_63,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( four @ ( two @ X1 ) @ X2 )
      = ( eight @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_59]),c_0_45]),c_0_50]) ).

thf(c_0_64,negated_conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
   != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thm])]) ).

thf(c_0_65,plain,
    ! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( plus @ X3 @ X4 @ X1 @ X2 )
      = ( X3 @ X1 @ ( X4 @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_66,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ ( seven @ X1 @ X2 ) )
      = ( ten @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_57]),c_0_61]) ).

thf(c_0_67,plain,
    ! [X34: ( $i > $i ) > $i > $i,X35: ( $i > $i ) > $i > $i,X36: $i > $i,X37: $i] :
      ( ( mult @ X34 @ X35 @ X36 @ X37 )
      = ( X34 @ ( X35 @ X36 ) @ X37 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).

thf(c_0_68,plain,
    ! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( succ @ ( succ @ X3 ) @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
    inference(spm,[status(thm)],[c_0_58,c_0_58]) ).

thf(c_0_69,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ ( five @ X1 @ X2 ) )
      = ( eight @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_45]),c_0_50]) ).

thf(c_0_70,plain,
    ( ( succ @ three )
    = four ),
    inference(pos_ext,[status(thm)],[c_0_62]) ).

thf(c_0_71,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( succ @ four @ X1 @ X2 )
      = ( five @ X1 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_58]) ).

thf(c_0_72,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( five @ ( two @ X1 ) @ X2 )
      = ( ten @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_63]),c_0_57]),c_0_61]) ).

thf(c_0_73,negated_conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
   != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_64]) ).

thf(c_0_74,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( plus @ three @ seven @ X1 @ X2 )
      = ( ten @ X1 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

thf(c_0_75,plain,
    ! [X67: ( $i > $i ) > $i > $i,X68: ( $i > $i ) > $i > $i,X69: $i > $i,X70: $i] :
      ( ( mult @ X67 @ X68 @ X69 @ X70 )
      = ( X67 @ ( X68 @ X69 ) @ X70 ) ),
    inference(variable_rename,[status(thm)],[c_0_67]) ).

thf(c_0_76,plain,
    ! [X7: $i > $i,X8: $i] :
      ( ( one @ X7 @ X8 )
      = ( X7 @ X8 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).

thf(c_0_77,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ ( five @ X1 ) @ X2 )
      = ( ten @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71]),c_0_25]),c_0_57]),c_0_61]) ).

thf(c_0_78,plain,
    ! [X1: $i > $i] :
      ( ( five @ ( two @ X1 ) )
      = ( ten @ X1 ) ),
    inference(pos_ext,[status(thm)],[c_0_72]) ).

thf(c_0_79,plain,
    ! [X1: $i > $i] :
      ( ( two @ ( two @ X1 ) )
      = ( four @ X1 ) ),
    inference(pos_ext,[status(thm)],[c_0_35]) ).

thf(c_0_80,negated_conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
   != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_73]) ).

thf(c_0_81,plain,
    ( ( plus @ three @ seven )
    = ten ),
    inference(pos_ext,[status(thm)],[c_0_74]) ).

thf(c_0_82,plain,
    ! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( mult @ X3 @ X4 @ X1 @ X2 )
      = ( X3 @ ( X4 @ X1 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

thf(c_0_83,plain,
    ! [X40: $i > $i,X41: $i] :
      ( ( one @ X40 @ X41 )
      = ( X40 @ X41 ) ),
    inference(variable_rename,[status(thm)],[c_0_76]) ).

thf(c_0_84,plain,
    ! [X1: $i > $i] :
      ( ( two @ ( five @ X1 ) )
      = ( ten @ X1 ) ),
    inference(pos_ext,[status(thm)],[c_0_77]) ).

thf(c_0_85,plain,
    ! [X1: $i > $i] :
      ( ( ten @ ( two @ X1 ) )
      = ( five @ ( four @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

thf(c_0_86,negated_conjecture,
    ( ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) )
   != ( mult @ two @ ten ) ),
    inference(rw,[status(thm)],[c_0_80,c_0_81]) ).

thf(c_0_87,plain,
    ! [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
      ( ( mult @ X3 @ X4 @ X1 )
      = ( X3 @ ( X4 @ X1 ) ) ),
    inference(pos_ext,[status(thm)],[c_0_82]) ).

thf(c_0_88,plain,
    ! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( plus @ X3 @ X3 @ X1 @ X2 )
      = ( two @ ( X3 @ X1 ) @ X2 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_65]) ).

thf(c_0_89,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( one @ X1 @ X2 )
      = ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

thf(c_0_90,plain,
    ! [X1: $i > $i] :
      ( ( five @ ( four @ X1 ) )
      = ( two @ ( ten @ X1 ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_78]),c_0_85]) ).

thf(c_0_91,negated_conjecture,
    ( ( ten @ ( plus @ one @ one @ esk1280_1 ) )
   != ( two @ ( ten @ esk1280_1 ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_86]),c_0_87]),c_0_87]),c_0_84]),c_0_87]) ).

thf(c_0_92,plain,
    ! [X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
      ( ( plus @ X3 @ X3 @ X1 )
      = ( two @ ( X3 @ X1 ) ) ),
    inference(pos_ext,[status(thm)],[c_0_88]) ).

thf(c_0_93,plain,
    ! [X1: $i > $i] :
      ( ( one @ X1 )
      = X1 ),
    inference(pos_ext,[status(thm)],[c_0_89]) ).

thf(c_0_94,plain,
    ! [X1: $i > $i] :
      ( ( ten @ ( two @ X1 ) )
      = ( two @ ( ten @ X1 ) ) ),
    inference(rw,[status(thm)],[c_0_85,c_0_90]) ).

thf(c_0_95,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem    : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% 0.05/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 06:25:22 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.47  Running higher-order theorem proving
% 0.17/0.47  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/benchmark/theBenchmark.p
% 10.86/1.84  # Version: 3.1.0-ho
% 10.86/1.84  # Preprocessing class: HSSSSMSSMSSNHHN.
% 10.86/1.84  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.86/1.84  # Starting pre_casc_2 with 1500s (5) cores
% 10.86/1.84  # Starting sh2 with 300s (1) cores
% 10.86/1.84  # Starting sh3 with 300s (1) cores
% 10.86/1.84  # Starting new_ho_10 with 300s (1) cores
% 10.86/1.84  # pre_casc_2 with pid 12164 completed with status 0
% 10.86/1.84  # Result found by pre_casc_2
% 10.86/1.84  # Preprocessing class: HSSSSMSSMSSNHHN.
% 10.86/1.84  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.86/1.84  # Starting pre_casc_2 with 1500s (5) cores
% 10.86/1.84  # No SInE strategy applied
% 10.86/1.84  # Search class: HUUPM-FFSF32-DHHSFMNN
% 10.86/1.84  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 10.86/1.84  # Starting pre_casc_2 with 901s (1) cores
% 10.86/1.84  # Starting sh2 with 151s (1) cores
% 10.86/1.84  # Starting sh3 with 151s (1) cores
% 10.86/1.84  # Starting sh9 with 151s (1) cores
% 10.86/1.84  # Starting new_ho_10 with 146s (1) cores
% 10.86/1.84  # sh9 with pid 12174 completed with status 0
% 10.86/1.84  # Result found by sh9
% 10.86/1.84  # Preprocessing class: HSSSSMSSMSSNHHN.
% 10.86/1.84  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.86/1.84  # Starting pre_casc_2 with 1500s (5) cores
% 10.86/1.84  # No SInE strategy applied
% 10.86/1.84  # Search class: HUUPM-FFSF32-DHHSFMNN
% 10.86/1.84  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 10.86/1.84  # Starting pre_casc_2 with 901s (1) cores
% 10.86/1.84  # Starting sh2 with 151s (1) cores
% 10.86/1.84  # Starting sh3 with 151s (1) cores
% 10.86/1.84  # Starting sh9 with 151s (1) cores
% 10.86/1.84  # Preprocessing time       : 0.001 s
% 10.86/1.84  # Presaturation interreduction done
% 10.86/1.84  
% 10.86/1.84  # Proof found!
% 10.86/1.84  # SZS status Theorem
% 10.86/1.84  # SZS output start CNFRefutation
% See solution above
% 10.86/1.84  # Parsed axioms                        : 29
% 10.86/1.84  # Removed by relevancy pruning/SinE    : 0
% 10.86/1.84  # Initial clauses                      : 29
% 10.86/1.84  # Removed in clause preprocessing      : 14
% 10.86/1.84  # Initial clauses in saturation        : 15
% 10.86/1.84  # Processed clauses                    : 2504
% 10.86/1.84  # ...of these trivial                  : 771
% 10.86/1.84  # ...subsumed                          : 8
% 10.86/1.84  # ...remaining for further processing  : 1725
% 10.86/1.84  # Other redundant clauses eliminated   : 0
% 10.86/1.84  # Clauses deleted for lack of memory   : 0
% 10.86/1.84  # Backward-subsumed                    : 0
% 10.86/1.84  # Backward-rewritten                   : 476
% 10.86/1.84  # Generated clauses                    : 45751
% 10.86/1.84  # ...of the previous two non-redundant : 43064
% 10.86/1.84  # ...aggressively subsumed             : 0
% 10.86/1.84  # Contextual simplify-reflections      : 0
% 10.86/1.84  # Paramodulations                      : 43404
% 10.86/1.84  # Factorizations                       : 0
% 10.86/1.84  # NegExts                              : 2116
% 10.86/1.84  # Equation resolutions                 : 0
% 10.86/1.84  # Disequality decompositions           : 0
% 10.86/1.84  # Total rewrite steps                  : 57343
% 10.86/1.84  # ...of those cached                   : 44874
% 10.86/1.84  # Propositional unsat checks           : 0
% 10.86/1.84  #    Propositional check models        : 0
% 10.86/1.84  #    Propositional check unsatisfiable : 0
% 10.86/1.84  #    Propositional clauses             : 0
% 10.86/1.84  #    Propositional clauses after purity: 0
% 10.86/1.84  #    Propositional unsat core size     : 0
% 10.86/1.84  #    Propositional preprocessing time  : 0.000
% 10.86/1.84  #    Propositional encoding time       : 0.000
% 10.86/1.84  #    Propositional solver time         : 0.000
% 10.86/1.84  #    Success case prop preproc time    : 0.000
% 10.86/1.84  #    Success case prop encoding time   : 0.000
% 10.86/1.84  #    Success case prop solver time     : 0.000
% 10.86/1.84  # Current number of processed clauses  : 1234
% 10.86/1.84  #    Positive orientable unit clauses  : 484
% 10.86/1.84  #    Positive unorientable unit clauses: 27
% 10.86/1.84  #    Negative unit clauses             : 1
% 10.86/1.84  #    Non-unit-clauses                  : 722
% 10.86/1.84  # Current number of unprocessed clauses: 40356
% 10.86/1.84  # ...number of literals in the above   : 43103
% 10.86/1.84  # Current number of archived formulas  : 0
% 10.86/1.84  # Current number of archived clauses   : 491
% 10.86/1.84  # Clause-clause subsumption calls (NU) : 223515
% 10.86/1.84  # Rec. Clause-clause subsumption calls : 4317
% 10.86/1.84  # Non-unit clause-clause subsumptions  : 1
% 10.86/1.84  # Unit Clause-clause subsumption calls : 1074
% 10.86/1.84  # Rewrite failures with RHS unbound    : 0
% 10.86/1.84  # BW rewrite match attempts            : 90336
% 10.86/1.84  # BW rewrite match successes           : 523
% 10.86/1.84  # Condensation attempts                : 2504
% 10.86/1.84  # Condensation successes               : 0
% 10.86/1.84  # Termbank termtop insertions          : 2333460
% 10.86/1.84  # Search garbage collected termcells   : 78
% 10.86/1.84  
% 10.86/1.84  # -------------------------------------------------
% 10.86/1.84  # User time                : 1.238 s
% 10.86/1.84  # System time              : 0.050 s
% 10.86/1.84  # Total time               : 1.288 s
% 10.86/1.84  # Maximum resident set size: 1832 pages
% 10.86/1.84  
% 10.86/1.84  # -------------------------------------------------
% 10.86/1.84  # User time                : 6.429 s
% 10.86/1.84  # System time              : 0.184 s
% 10.86/1.84  # Total time               : 6.614 s
% 10.86/1.84  # Maximum resident set size: 1752 pages
% 10.86/1.84  % E---3.1 exiting
% 10.94/1.84  % E exiting
%------------------------------------------------------------------------------