TSTP Solution File: NUM926+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 : Thu Aug 31 10:41:35 EDT 2023

% Result   : Theorem 0.18s 0.64s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   66 (  21 unt;  27 typ;   0 def)
%            Number of atoms       :   62 (  34 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (  22   ~;  16   |;   1   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  16   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  11 con; 0-2 aty)
%            Number of variables   :   47 (   6 sgn;  22   !;   8   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    one_one_int: $i ).

tff(decl_23,type,
    t: $i ).

tff(decl_24,type,
    ord_less_eq_int: ( $i * $i ) > $o ).

tff(decl_25,type,
    pls: $i ).

tff(decl_26,type,
    bit1: $i > $i ).

tff(decl_27,type,
    bit0: $i > $i ).

tff(decl_28,type,
    number_number_of_nat: $i > $i ).

tff(decl_29,type,
    power_power_int: ( $i * $i ) > $i ).

tff(decl_30,type,
    plus_plus_int: ( $i * $i ) > $i ).

tff(decl_31,type,
    number_number_of_int: $i > $i ).

tff(decl_32,type,
    m: $i ).

tff(decl_33,type,
    times_times_int: ( $i * $i ) > $i ).

tff(decl_34,type,
    ord_less_int: ( $i * $i ) > $o ).

tff(decl_35,type,
    zprime: $i > $o ).

tff(decl_36,type,
    s: $i ).

tff(decl_37,type,
    twoSqu526106917sum2sq: $i > $o ).

tff(decl_38,type,
    plus_plus_nat: ( $i * $i ) > $i ).

tff(decl_39,type,
    power_power_nat: ( $i * $i ) > $i ).

tff(decl_40,type,
    times_times_nat: ( $i * $i ) > $i ).

tff(decl_41,type,
    one_one_nat: $i ).

tff(decl_42,type,
    ord_less_eq_nat: ( $i * $i ) > $o ).

tff(decl_43,type,
    ord_less_nat: ( $i * $i ) > $o ).

tff(decl_44,type,
    esk1_0: $i ).

tff(decl_45,type,
    esk2_0: $i ).

tff(decl_46,type,
    esk3_0: $i ).

tff(decl_47,type,
    esk4_0: $i ).

tff(decl_48,type,
    esk5_0: $i ).

fof(conj_0,conjecture,
    ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
    ( ord_less_int(one_one_int,t)
   => ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(fact_111_number__of__is__id,axiom,
    ! [X21] : number_number_of_int(X21) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).

fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X82,X83] : plus_plus_int(X82,X83) = plus_plus_int(X83,X82),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X64,X65] : times_times_int(X64,X65) = times_times_int(X65,X64),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_38_le__number__of__eq__not__less,axiom,
    ! [X28,X18] :
      ( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
    <=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__number__of__eq__not__less) ).

fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
    ( t = one_one_int
   => ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(fact_31_zle__antisym,axiom,
    ! [X16,X15] :
      ( ord_less_eq_int(X16,X15)
     => ( ord_less_eq_int(X15,X16)
       => X16 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zle__antisym) ).

fof(fact_0_tpos,axiom,
    ord_less_eq_int(one_one_int,t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).

fof(c_0_9,negated_conjecture,
    ~ ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_10,plain,
    ( ~ ord_less_int(one_one_int,t)
    | plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).

fof(c_0_11,plain,
    ! [X308] : number_number_of_int(X308) = X308,
    inference(variable_rename,[status(thm)],[fact_111_number__of__is__id]) ).

fof(c_0_12,negated_conjecture,
    ! [X329,X330] : plus_plus_int(power_power_int(X329,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X330,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

cnf(c_0_13,plain,
    ( plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
    | ~ ord_less_int(one_one_int,t) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    number_number_of_int(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,plain,
    ! [X289,X290] : plus_plus_int(X289,X290) = plus_plus_int(X290,X289),
    inference(variable_rename,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

cnf(c_0_16,negated_conjecture,
    plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,plain,
    ! [X253,X254] : times_times_int(X253,X254) = times_times_int(X254,X253),
    inference(variable_rename,[status(thm)],[fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(c_0_18,plain,
    ! [X28,X18] :
      ( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
    <=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
    inference(fof_simplification,[status(thm)],[fact_38_le__number__of__eq__not__less]) ).

cnf(c_0_19,plain,
    ( plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)
    | ~ ord_less_int(one_one_int,t) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),
    inference(rw,[status(thm)],[c_0_16,c_0_14]) ).

cnf(c_0_22,plain,
    times_times_int(X1,X2) = times_times_int(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_23,plain,
    ! [X138,X139] :
      ( ( ~ ord_less_eq_int(number_number_of_int(X138),number_number_of_int(X139))
        | ~ ord_less_int(number_number_of_int(X139),number_number_of_int(X138)) )
      & ( ord_less_int(number_number_of_int(X139),number_number_of_int(X138))
        | ord_less_eq_int(number_number_of_int(X138),number_number_of_int(X139)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

fof(c_0_24,plain,
    ( t != one_one_int
    | plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).

cnf(c_0_25,plain,
    ( plus_plus_int(one_one_int,times_times_int(bit0(bit0(bit1(pls))),m)) = plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls)))))
    | ~ ord_less_int(one_one_int,t) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).

cnf(c_0_27,plain,
    ( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
    | ord_less_eq_int(number_number_of_int(X2),number_number_of_int(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,plain,
    ( plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
    | t != one_one_int ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_29,plain,
    ! [X123,X124] :
      ( ~ ord_less_eq_int(X123,X124)
      | ~ ord_less_eq_int(X124,X123)
      | X123 = X124 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_zle__antisym])]) ).

cnf(c_0_30,plain,
    ~ ord_less_int(one_one_int,t),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).

cnf(c_0_31,plain,
    ( ord_less_eq_int(X2,X1)
    | ord_less_int(X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).

cnf(c_0_32,plain,
    ( plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)
    | t != one_one_int ),
    inference(rw,[status(thm)],[c_0_28,c_0_14]) ).

cnf(c_0_33,plain,
    ( X1 = X2
    | ~ ord_less_eq_int(X1,X2)
    | ~ ord_less_eq_int(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_34,plain,
    ord_less_eq_int(t,one_one_int),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    ord_less_eq_int(one_one_int,t),
    inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).

cnf(c_0_36,plain,
    ( plus_plus_int(one_one_int,times_times_int(bit0(bit0(bit1(pls))),m)) = plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls)))))
    | t != one_one_int ),
    inference(rw,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_37,plain,
    t = one_one_int,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).

cnf(c_0_38,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_22]),c_0_37])]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri Aug 25 09:29:00 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.18/0.61  start to proof: theBenchmark
% 0.18/0.64  % Version  : CSE_E---1.5
% 0.18/0.64  % Problem  : theBenchmark.p
% 0.18/0.64  % Proof found
% 0.18/0.64  % SZS status Theorem for theBenchmark.p
% 0.18/0.64  % SZS output start Proof
% See solution above
% 0.18/0.65  % Total time : 0.024000 s
% 0.18/0.65  % SZS output end Proof
% 0.18/0.65  % Total time : 0.029000 s
%------------------------------------------------------------------------------