TSTP Solution File: NUM926+5 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:41:38 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   62 (  20 unt;  33 typ;   0 def)
%            Number of atoms       :   45 (  29 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   33 (  17   ~;  10   |;   3   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  22   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-3 aty)
%            Number of variables   :   37 (   6 sgn;  16   !;   8   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    semiring_1: $i > $o ).

tff(decl_23,type,
    one_one: $i > $i ).

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

tff(decl_25,type,
    comm_semiring_1: $i > $o ).

tff(decl_26,type,
    plus_plus: ( $i * $i * $i ) > $i ).

tff(decl_27,type,
    monoid_mult: $i > $o ).

tff(decl_28,type,
    times_times: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    undefined: $i > $i ).

tff(decl_30,type,
    int: $i ).

tff(decl_31,type,
    zprime: $i > $o ).

tff(decl_32,type,
    bit0: $i > $i ).

tff(decl_33,type,
    bit1: $i > $i ).

tff(decl_34,type,
    pls: $i ).

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

tff(decl_36,type,
    number_number_of: ( $i * $i ) > $i ).

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

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

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

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

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

tff(decl_42,type,
    twoSqu33214720sum2sq: $i > $o ).

tff(decl_43,type,
    m: $i ).

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

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

tff(decl_46,type,
    number_semiring: $i > $o ).

tff(decl_47,type,
    number_ring: $i > $o ).

tff(decl_48,type,
    linordered_idom: $i > $o ).

tff(decl_49,type,
    ring_char_0: $i > $o ).

tff(decl_50,type,
    esk1_0: $i ).

tff(decl_51,type,
    esk2_0: $i ).

tff(decl_52,type,
    esk3_0: $i ).

tff(decl_53,type,
    esk4_0: $i ).

tff(decl_54,type,
    esk5_0: $i ).

fof(conj_0,conjecture,
    ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(fact_86_number__of__is__id,axiom,
    ! [X18] : number_number_of(int,X18) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).

fof(fact_89_zadd__commute,axiom,
    ! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).

fof(fact_85_zmult__commute,axiom,
    ! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).

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)
   => ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/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_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)
   => ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/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_22_zless__le,axiom,
    ! [X16,X17] :
      ( ord_less(int,X16,X17)
    <=> ( ord_less_eq(int,X16,X17)
        & X16 != X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).

fof(fact_0_tpos,axiom,
    ord_less_eq(int,one_one(int),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).

fof(c_0_8,negated_conjecture,
    ~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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_9,negated_conjecture,
    ! [X308,X309] : plus_plus(int,power_power(int,X308,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X309,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_8])]) ).

fof(c_0_10,plain,
    ! [X285] : number_number_of(int,X285) = X285,
    inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).

fof(c_0_11,plain,
    ! [X292,X293] : plus_plus(int,X292,X293) = plus_plus(int,X293,X292),
    inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).

cnf(c_0_12,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_9]) ).

cnf(c_0_13,plain,
    number_number_of(int,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,plain,
    ! [X283,X284] : times_times(int,X283,X284) = times_times(int,X284,X283),
    inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).

fof(c_0_16,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_17,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,bit0(bit0(bit1(pls))),m)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_18,plain,
    times_times(int,X1,X2) = times_times(int,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,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_20,plain,
    ! [X126,X127] :
      ( ( ord_less_eq(int,X126,X127)
        | ~ ord_less(int,X126,X127) )
      & ( X126 != X127
        | ~ ord_less(int,X126,X127) )
      & ( ~ ord_less_eq(int,X126,X127)
        | X126 = X127
        | ord_less(int,X126,X127) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_zless__le])])]) ).

cnf(c_0_21,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_16]) ).

cnf(c_0_22,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)],[c_0_17,c_0_18]) ).

cnf(c_0_23,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_19]) ).

cnf(c_0_24,plain,
    ( X1 = X2
    | ord_less(int,X1,X2)
    | ~ ord_less_eq(int,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    ord_less_eq(int,one_one(int),t),
    inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).

cnf(c_0_26,plain,
    one_one(int) != t,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_13]),c_0_18]),c_0_14]),c_0_22]) ).

cnf(c_0_27,plain,
    ~ ord_less(int,one_one(int),t),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_18]),c_0_14]),c_0_22]) ).

cnf(c_0_28,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 16:23:50 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.021000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.027000 s
%------------------------------------------------------------------------------