TSTP Solution File: ITP062^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP062^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 22:16:07 EDT 2024

% Result   : Theorem 2.47s 0.81s
% Output   : CNFRefutation 2.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   91 (  68 unt;  19 typ;   0 def)
%            Number of atoms       :   79 (  44 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives : 1045 (  14   ~;   5   |;   0   &;1024   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   8 con; 0-2 aty)
%            Number of variables   :  105 (  12   ^  93   !;   0   ?; 105   :)

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

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

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

thf(decl_23,type,
    genClo1144207539le_rho: real ).

thf(decl_29,type,
    abs_abs_real: real > real ).

thf(decl_31,type,
    minus_minus_real: real > real > real ).

thf(decl_33,type,
    one_one_real: real ).

thf(decl_36,type,
    plus_plus_real: real > real > real ).

thf(decl_39,type,
    times_times_real: real > real > real ).

thf(decl_41,type,
    bit0: num > num ).

thf(decl_42,type,
    one: num ).

thf(decl_44,type,
    numeral_numeral_real: num > real ).

thf(decl_47,type,
    ord_less_eq_real: real > real > $o ).

thf(decl_50,type,
    c: nat > real > real ).

thf(decl_51,type,
    d: nat > real > real ).

thf(decl_52,type,
    p: nat ).

thf(decl_53,type,
    q: nat ).

thf(decl_54,type,
    s: real ).

thf(decl_55,type,
    t: real ).

thf(conj_0,conjecture,
    ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_4_Eq4,axiom,
    ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
    = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Eq4) ).

thf(fact_84_one__add__one,axiom,
    ( ( plus_plus_real @ one_one_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_one__add__one) ).

thf(fact_5_Eq3,axiom,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Eq3) ).

thf(fact_167_mult_Oassoc,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( times_times_real @ ( times_times_real @ X1 @ X2 ) @ X4 )
      = ( times_times_real @ X1 @ ( times_times_real @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mult_Oassoc) ).

thf(fact_224_mult__2,axiom,
    ! [X8: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X8 )
      = ( plus_plus_real @ X8 @ X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mult__2) ).

thf(fact_3_Eq1,axiom,
    ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
    = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Eq1) ).

thf(fact_163_mult_Oleft__commute,axiom,
    ! [X2: real,X1: real,X4: real] :
      ( ( times_times_real @ X2 @ ( times_times_real @ X1 @ X4 ) )
      = ( times_times_real @ X1 @ ( times_times_real @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult_Oleft__commute) ).

thf(fact_152_add__diff__eq,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( plus_plus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X2 ) @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__diff__eq) ).

thf(fact_151_diff__diff__eq2,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( minus_minus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X4 ) @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_diff__diff__eq2) ).

thf(fact_149_diff__add__eq__diff__diff__swap,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( minus_minus_real @ X1 @ ( plus_plus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( minus_minus_real @ X1 @ X4 ) @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_diff__add__eq__diff__diff__swap) ).

thf(fact_147_diff__diff__add,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ X1 @ X2 ) @ X4 )
      = ( minus_minus_real @ X1 @ ( plus_plus_real @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_diff__diff__add) ).

thf(fact_165_mult_Ocommute,axiom,
    ( times_times_real
    = ( ^ [X76: real,X77: real] : ( times_times_real @ X77 @ X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult_Ocommute) ).

thf(fact_9_Eq2,axiom,
    ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Eq2) ).

thf(fact_150_diff__add__eq,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ X1 @ X2 ) @ X4 )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X4 ) @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_diff__add__eq) ).

thf(fact_103_add_Ocommute,axiom,
    ( plus_plus_real
    = ( ^ [X76: real,X77: real] : ( plus_plus_real @ X77 @ X76 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add_Ocommute) ).

thf(fact_303_order_Otrans,axiom,
    ! [X1: real,X2: real,X4: real] :
      ( ( ord_less_eq_real @ X1 @ X2 )
     => ( ( ord_less_eq_real @ X2 @ X4 )
       => ( ord_less_eq_real @ X1 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order_Otrans) ).

thf(c_0_17,negated_conjecture,
    ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_18,plain,
    ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
    = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(split_conjunct,[status(thm)],[fact_4_Eq4]) ).

thf(c_0_19,plain,
    ( ( plus_plus_real @ one_one_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    inference(split_conjunct,[status(thm)],[fact_84_one__add__one]) ).

thf(c_0_20,negated_conjecture,
    ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_17]) ).

thf(c_0_21,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
    inference(split_conjunct,[status(thm)],[fact_5_Eq3]) ).

thf(c_0_22,plain,
    ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
    = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_23,plain,
    ! [X1750: real,X1751: real,X1752: real] :
      ( ( times_times_real @ ( times_times_real @ X1750 @ X1751 ) @ X1752 )
      = ( times_times_real @ X1750 @ ( times_times_real @ X1751 @ X1752 ) ) ),
    inference(variable_rename,[status(thm)],[fact_167_mult_Oassoc]) ).

thf(c_0_24,plain,
    ! [X1785: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X1785 )
      = ( plus_plus_real @ X1785 @ X1785 ) ),
    inference(variable_rename,[status(thm)],[fact_224_mult__2]) ).

thf(c_0_25,negated_conjecture,
    ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,plain,
    ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
    = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
    inference(split_conjunct,[status(thm)],[fact_3_Eq1]) ).

thf(c_0_27,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_28,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( times_times_real @ ( times_times_real @ X1 @ X2 ) @ X4 )
      = ( times_times_real @ X1 @ ( times_times_real @ X2 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_29,plain,
    ! [X1747: real,X1748: real,X1749: real] :
      ( ( times_times_real @ X1747 @ ( times_times_real @ X1748 @ X1749 ) )
      = ( times_times_real @ X1748 @ ( times_times_real @ X1747 @ X1749 ) ) ),
    inference(variable_rename,[status(thm)],[fact_163_mult_Oleft__commute]) ).

thf(c_0_30,plain,
    ! [X1: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X1 )
      = ( plus_plus_real @ X1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_31,plain,
    ! [X1821: real,X1822: real,X1823: real] :
      ( ( plus_plus_real @ X1821 @ ( minus_minus_real @ X1822 @ X1823 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1821 @ X1822 ) @ X1823 ) ),
    inference(variable_rename,[status(thm)],[fact_152_add__diff__eq]) ).

thf(c_0_32,plain,
    ! [X1818: real,X1819: real,X1820: real] :
      ( ( minus_minus_real @ X1818 @ ( minus_minus_real @ X1819 @ X1820 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1818 @ X1820 ) @ X1819 ) ),
    inference(variable_rename,[status(thm)],[fact_151_diff__diff__eq2]) ).

thf(c_0_33,plain,
    ! [X1812: real,X1813: real,X1814: real] :
      ( ( minus_minus_real @ X1812 @ ( plus_plus_real @ X1813 @ X1814 ) )
      = ( minus_minus_real @ ( minus_minus_real @ X1812 @ X1814 ) @ X1813 ) ),
    inference(variable_rename,[status(thm)],[fact_149_diff__add__eq__diff__diff__swap]) ).

thf(c_0_34,plain,
    ! [X1809: real,X1810: real,X1811: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ X1809 @ X1810 ) @ X1811 )
      = ( minus_minus_real @ X1809 @ ( plus_plus_real @ X1810 @ X1811 ) ) ),
    inference(variable_rename,[status(thm)],[fact_147_diff__diff__add]) ).

thf(c_0_35,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).

thf(c_0_36,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_37,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( times_times_real @ X1 @ ( times_times_real @ X2 @ X4 ) )
      = ( times_times_real @ X2 @ ( times_times_real @ X1 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_38,plain,
    ! [X1: real] :
      ( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ X1 )
      = ( plus_plus_real @ X1 @ X1 ) ),
    inference(rw,[status(thm)],[c_0_30,c_0_19]) ).

thf(c_0_39,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( plus_plus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X2 ) @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

thf(c_0_40,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( minus_minus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X4 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_41,plain,
    ( times_times_real
    = ( ^ [Z0: real,Z1: real] : ( times_times_real @ Z1 @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_165_mult_Ocommute]) ).

thf(c_0_42,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    inference(split_conjunct,[status(thm)],[fact_9_Eq2]) ).

thf(c_0_43,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( minus_minus_real @ X1 @ ( plus_plus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ ( minus_minus_real @ X1 @ X4 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_44,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ X1 @ X2 ) @ X4 )
      = ( minus_minus_real @ X1 @ ( plus_plus_real @ X2 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_45,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ) ),
    inference(rw,[status(thm)],[c_0_35,c_0_28]) ).

thf(c_0_46,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

thf(c_0_47,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( minus_minus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) )
      = ( plus_plus_real @ X1 @ ( minus_minus_real @ X4 @ X2 ) ) ),
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_48,plain,
    ( times_times_real
    = ( ^ [Z0: real,Z1: real] : ( times_times_real @ Z1 @ Z0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

thf(c_0_49,plain,
    ! [X1815: real,X1816: real,X1817: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ X1815 @ X1816 ) @ X1817 )
      = ( minus_minus_real @ ( plus_plus_real @ X1815 @ X1817 ) @ X1816 ) ),
    inference(variable_rename,[status(thm)],[fact_150_diff__add__eq]) ).

thf(c_0_50,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( c @ p @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

thf(c_0_51,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( minus_minus_real @ X1 @ ( plus_plus_real @ X2 @ X4 ) )
      = ( minus_minus_real @ X1 @ ( plus_plus_real @ X4 @ X2 ) ) ),
    inference(rw,[status(thm)],[c_0_44,c_0_43]) ).

thf(c_0_52,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( c @ p @ s ) ) ) @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ) ),
    inference(rw,[status(thm)],[c_0_45,c_0_43]) ).

thf(c_0_53,plain,
    ( plus_plus_real
    = ( ^ [Z0: real,Z1: real] : ( plus_plus_real @ Z1 @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_103_add_Ocommute]) ).

thf(c_0_54,plain,
    ! [X1704: real,X1705: real,X1706: real] :
      ( ~ ( ord_less_eq_real @ X1704 @ X1705 )
      | ~ ( ord_less_eq_real @ X1705 @ X1706 )
      | ( ord_less_eq_real @ X1704 @ X1706 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_303_order_Otrans])])]) ).

thf(c_0_55,plain,
    ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ s ) @ ( d @ q @ t ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

thf(c_0_56,plain,
    ! [X2: real,X1: real] :
      ( ( times_times_real @ X1 @ X2 )
      = ( times_times_real @ X2 @ X1 ) ),
    inference(arg_cong,[status(thm)],[c_0_48]) ).

thf(c_0_57,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ X1 @ X2 ) @ X4 )
      = ( minus_minus_real @ ( plus_plus_real @ X1 @ X4 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

thf(c_0_58,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ X1 @ X2 ) @ X4 )
      = ( plus_plus_real @ X1 @ ( minus_minus_real @ X2 @ X4 ) ) ),
    inference(rw,[status(thm)],[c_0_40,c_0_47]) ).

thf(c_0_59,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    inference(rw,[status(thm)],[c_0_50,c_0_51]) ).

thf(c_0_60,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ) ),
    inference(rw,[status(thm)],[c_0_52,c_0_51]) ).

thf(c_0_61,plain,
    ( plus_plus_real
    = ( ^ [Z0: real,Z1: real] : ( plus_plus_real @ Z1 @ Z0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

thf(c_0_62,plain,
    ! [X2: real,X1: real,X4: real] :
      ( ( ord_less_eq_real @ X1 @ X4 )
      | ~ ( ord_less_eq_real @ X1 @ X2 )
      | ~ ( ord_less_eq_real @ X2 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

thf(c_0_63,plain,
    ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) @ ( minus_minus_real @ ( d @ q @ s ) @ ( d @ q @ t ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(rw,[status(thm)],[c_0_55,c_0_56]) ).

thf(c_0_64,plain,
    ! [X4: real,X1: real,X2: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ X1 @ X2 ) @ X4 )
      = ( plus_plus_real @ X1 @ ( minus_minus_real @ X4 @ X2 ) ) ),
    inference(rw,[status(thm)],[c_0_57,c_0_58]) ).

thf(c_0_65,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ s ) @ ( d @ q @ t ) ) ),
    inference(rw,[status(thm)],[c_0_59,c_0_47]) ).

thf(c_0_66,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ t @ s ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_37]),c_0_38]) ).

thf(c_0_67,plain,
    ! [X2: real,X1: real] :
      ( ( plus_plus_real @ X1 @ X2 )
      = ( plus_plus_real @ X2 @ X1 ) ),
    inference(arg_cong,[status(thm)],[c_0_61]) ).

thf(c_0_68,plain,
    ! [X1: real] :
      ( ( ord_less_eq_real @ X1 @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ t @ ( minus_minus_real @ t @ ( plus_plus_real @ s @ s ) ) ) ) )
      | ~ ( ord_less_eq_real @ X1 @ ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) @ ( minus_minus_real @ ( d @ q @ s ) @ ( d @ q @ t ) ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_43]) ).

thf(c_0_69,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) @ ( minus_minus_real @ ( d @ q @ s ) @ ( d @ q @ t ) ) ),
    inference(rw,[status(thm)],[c_0_65,c_0_56]) ).

thf(c_0_70,negated_conjecture,
    ~ ( ord_less_eq_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( plus_plus_real @ ( c @ p @ s ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( plus_plus_real @ t @ ( minus_minus_real @ t @ ( plus_plus_real @ s @ s ) ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_64]),c_0_43]) ).

thf(c_0_71,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem    : ITP062^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.10  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Sat May 18 17:00:22 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.42  Running higher-order theorem proving
% 0.15/0.42  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
% 2.47/0.81  # Version: 3.1.0-ho
% 2.47/0.81  # Preprocessing class: HSLSSMSMSSSNHFA.
% 2.47/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.81  # Starting new_ho_10 with 1500s (5) cores
% 2.47/0.81  # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.47/0.81  # Starting full_lambda_6 with 300s (1) cores
% 2.47/0.81  # Starting full_lambda_9 with 300s (1) cores
% 2.47/0.81  # full_lambda_6 with pid 25533 completed with status 0
% 2.47/0.81  # Result found by full_lambda_6
% 2.47/0.81  # Preprocessing class: HSLSSMSMSSSNHFA.
% 2.47/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.81  # Starting new_ho_10 with 1500s (5) cores
% 2.47/0.81  # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.47/0.81  # Starting full_lambda_6 with 300s (1) cores
% 2.47/0.81  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 2.47/0.81  # Search class: HGUSM-FSLM33-DHFFFFBN
% 2.47/0.81  # partial match(1): HGUSM-FSLM32-DHFFFFBN
% 2.47/0.81  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.47/0.81  # Starting new_ho_10 with 163s (1) cores
% 2.47/0.81  # new_ho_10 with pid 25535 completed with status 0
% 2.47/0.81  # Result found by new_ho_10
% 2.47/0.81  # Preprocessing class: HSLSSMSMSSSNHFA.
% 2.47/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.81  # Starting new_ho_10 with 1500s (5) cores
% 2.47/0.81  # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.47/0.81  # Starting full_lambda_6 with 300s (1) cores
% 2.47/0.81  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 2.47/0.81  # Search class: HGUSM-FSLM33-DHFFFFBN
% 2.47/0.81  # partial match(1): HGUSM-FSLM32-DHFFFFBN
% 2.47/0.81  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.47/0.81  # Starting new_ho_10 with 163s (1) cores
% 2.47/0.81  # Preprocessing time       : 0.010 s
% 2.47/0.81  # Presaturation interreduction done
% 2.47/0.81  
% 2.47/0.81  # Proof found!
% 2.47/0.81  # SZS status Theorem
% 2.47/0.81  # SZS output start CNFRefutation
% See solution above
% 2.47/0.81  # Parsed axioms                        : 391
% 2.47/0.81  # Removed by relevancy pruning/SinE    : 50
% 2.47/0.81  # Initial clauses                      : 625
% 2.47/0.81  # Removed in clause preprocessing      : 19
% 2.47/0.81  # Initial clauses in saturation        : 606
% 2.47/0.81  # Processed clauses                    : 1542
% 2.47/0.81  # ...of these trivial                  : 77
% 2.47/0.81  # ...subsumed                          : 517
% 2.47/0.81  # ...remaining for further processing  : 948
% 2.47/0.81  # Other redundant clauses eliminated   : 126
% 2.47/0.81  # Clauses deleted for lack of memory   : 0
% 2.47/0.81  # Backward-subsumed                    : 6
% 2.47/0.81  # Backward-rewritten                   : 55
% 2.47/0.81  # Generated clauses                    : 10901
% 2.47/0.81  # ...of the previous two non-redundant : 9511
% 2.47/0.81  # ...aggressively subsumed             : 0
% 2.47/0.81  # Contextual simplify-reflections      : 0
% 2.47/0.81  # Paramodulations                      : 10706
% 2.47/0.81  # Factorizations                       : 6
% 2.47/0.81  # NegExts                              : 0
% 2.47/0.81  # Equation resolutions                 : 142
% 2.47/0.81  # Disequality decompositions           : 0
% 2.47/0.81  # Total rewrite steps                  : 6169
% 2.47/0.81  # ...of those cached                   : 4367
% 2.47/0.81  # Propositional unsat checks           : 0
% 2.47/0.81  #    Propositional check models        : 0
% 2.47/0.81  #    Propositional check unsatisfiable : 0
% 2.47/0.81  #    Propositional clauses             : 0
% 2.47/0.81  #    Propositional clauses after purity: 0
% 2.47/0.81  #    Propositional unsat core size     : 0
% 2.47/0.81  #    Propositional preprocessing time  : 0.000
% 2.47/0.81  #    Propositional encoding time       : 0.000
% 2.47/0.81  #    Propositional solver time         : 0.000
% 2.47/0.81  #    Success case prop preproc time    : 0.000
% 2.47/0.81  #    Success case prop encoding time   : 0.000
% 2.47/0.81  #    Success case prop solver time     : 0.000
% 2.47/0.81  # Current number of processed clauses  : 527
% 2.47/0.81  #    Positive orientable unit clauses  : 184
% 2.47/0.81  #    Positive unorientable unit clauses: 17
% 2.47/0.81  #    Negative unit clauses             : 25
% 2.47/0.81  #    Non-unit-clauses                  : 301
% 2.47/0.81  # Current number of unprocessed clauses: 8817
% 2.47/0.81  # ...number of literals in the above   : 18197
% 2.47/0.81  # Current number of archived formulas  : 0
% 2.47/0.81  # Current number of archived clauses   : 346
% 2.47/0.81  # Clause-clause subsumption calls (NU) : 35047
% 2.47/0.81  # Rec. Clause-clause subsumption calls : 26050
% 2.47/0.81  # Non-unit clause-clause subsumptions  : 402
% 2.47/0.81  # Unit Clause-clause subsumption calls : 3774
% 2.47/0.81  # Rewrite failures with RHS unbound    : 0
% 2.47/0.81  # BW rewrite match attempts            : 578
% 2.47/0.81  # BW rewrite match successes           : 218
% 2.47/0.81  # Condensation attempts                : 1542
% 2.47/0.81  # Condensation successes               : 36
% 2.47/0.81  # Termbank termtop insertions          : 212605
% 2.47/0.81  # Search garbage collected termcells   : 10257
% 2.47/0.81  
% 2.47/0.81  # -------------------------------------------------
% 2.47/0.81  # User time                : 0.326 s
% 2.47/0.81  # System time              : 0.022 s
% 2.47/0.81  # Total time               : 0.348 s
% 2.47/0.81  # Maximum resident set size: 4644 pages
% 2.47/0.81  
% 2.47/0.81  # -------------------------------------------------
% 2.47/0.81  # User time                : 0.337 s
% 2.47/0.81  # System time              : 0.026 s
% 2.47/0.81  # Total time               : 0.363 s
% 2.47/0.81  # Maximum resident set size: 2504 pages
% 2.47/0.81  % E---3.1 exiting
% 2.47/0.81  % E exiting
%------------------------------------------------------------------------------