TSTP Solution File: NUM925+8 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 18:58:01 EDT 2023

% Result   : Theorem 72.59s 12.23s
% Output   : CNFRefutation 72.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   88 (  80 unt;   0 def)
%            Number of atoms       :  135 (  85 equ)
%            Maximal formula atoms :   19 (   1 avg)
%            Number of connectives :   84 (  37   ~;  33   |;   8   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  12 con; 0-4 aty)
%            Number of variables   :   65 (   2 sgn;  41   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_2924_succ__pred,axiom,
    ! [X11] : hAPP(int,int,succ,hAPP(int,int,pred,X11)) = ti(int,X11),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2924_succ__pred) ).

fof(fact_123_number__of__is__id,axiom,
    ! [X21] : hAPP(int,int,number_number_of(int),X21) = ti(int,X21),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_123_number__of__is__id) ).

fof(fact_1006_transfer__nat__int__numerals_I2_J,axiom,
    one_one(nat) = hAPP(int,nat,nat_1,one_one(int)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1006_transfer__nat__int__numerals_I2_J) ).

fof(fact_1382_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1382_One__nat__def) ).

fof(fact_998_transfer__nat__int__numerals_I1_J,axiom,
    zero_zero(nat) = hAPP(int,nat,nat_1,zero_zero(int)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_998_transfer__nat__int__numerals_I1_J) ).

fof(fact_76_Pls__def,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_76_Pls__def) ).

fof(fact_2926_pred__Bit1,axiom,
    ! [X21] : hAPP(int,int,pred,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,X21),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2926_pred__Bit1) ).

fof(fact_37_one__is__num__one,axiom,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_37_one__is__num__one) ).

fof(fact_72_Bit0__Pls,axiom,
    hAPP(int,int,bit0,pls) = pls,
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_72_Bit0__Pls) ).

fof(fact_284_succ__Pls,axiom,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_284_succ__Pls) ).

fof(fact_1004_nat__number__of__def,axiom,
    ! [X10] : hAPP(int,nat,number_number_of(nat),X10) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X10)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1004_nat__number__of__def) ).

fof(conj_0,conjecture,
    hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',conj_0) ).

fof(fact_1484_semiring__norm_I115_J,axiom,
    hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1484_semiring__norm_I115_J) ).

fof(fact_1450_int__Suc,axiom,
    ! [X15] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X15)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X15)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1450_int__Suc) ).

fof(fact_2925_pred__Bit0,axiom,
    ! [X21] : hAPP(int,int,pred,hAPP(int,int,bit0,X21)) = hAPP(int,int,bit1,hAPP(int,int,pred,X21)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2925_pred__Bit0) ).

fof(fact_285_succ__Bit1,axiom,
    ! [X21] : hAPP(int,int,succ,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,hAPP(int,int,succ,X21)),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_285_succ__Bit1) ).

fof(fact_1503_nat__2,axiom,
    hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1503_nat__2) ).

fof(fact_534_not__less__iff__gr__or__eq,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
            | ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_534_not__less__iff__gr__or__eq) ).

fof(fact_188_power__eq__0__iff,axiom,
    ! [X1] :
      ( ( power(X1)
        & mult_zero(X1)
        & no_zero_divisors(X1)
        & zero_neq_one(X1) )
     => ! [X8,X18] :
          ( hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X8),X18) = zero_zero(X1)
        <=> ( ti(X1,X8) = zero_zero(X1)
            & X18 != zero_zero(nat) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_188_power__eq__0__iff) ).

fof(fact_21_int__power,axiom,
    ! [X15,X16] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X15),X16)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X15)),X16),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_21_int__power) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X2,X1,X4,X5] : ti(X2,hAPP(X1,X2,X4,X5)) = hAPP(X1,X2,X4,X5),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',tsy_c_hAPP_res) ).

fof(fact_0_n1pos,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_0_n1pos) ).

fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
    zero_neq_one(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Ozero__neq__one) ).

fof(arity_Int_Oint___Rings_Omult__zero,axiom,
    mult_zero(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Omult__zero) ).

fof(arity_Int_Oint___Rings_Ono__zero__divisors,axiom,
    no_zero_divisors(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).

fof(arity_Int_Oint___Power_Opower,axiom,
    power(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Power_Opower) ).

fof(fact_2928_pred__Pls,axiom,
    hAPP(int,int,pred,pls) = min,
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2928_pred__Pls) ).

fof(fact_686_succ__Min,axiom,
    hAPP(int,int,succ,min) = pls,
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_686_succ__Min) ).

fof(arity_Int_Oint___Orderings_Olinorder,axiom,
    linorder(int),
    file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Orderings_Olinorder) ).

fof(c_0_29,plain,
    ! [X9861] : hAPP(int,int,succ,hAPP(int,int,pred,X9861)) = ti(int,X9861),
    inference(variable_rename,[status(thm)],[fact_2924_succ__pred]) ).

fof(c_0_30,plain,
    ! [X561] : hAPP(int,int,number_number_of(int),X561) = ti(int,X561),
    inference(variable_rename,[status(thm)],[fact_123_number__of__is__id]) ).

cnf(c_0_31,plain,
    one_one(nat) = hAPP(int,nat,nat_1,one_one(int)),
    inference(split_conjunct,[status(thm)],[fact_1006_transfer__nat__int__numerals_I2_J]) ).

cnf(c_0_32,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(split_conjunct,[status(thm)],[fact_1382_One__nat__def]) ).

cnf(c_0_33,plain,
    zero_zero(nat) = hAPP(int,nat,nat_1,zero_zero(int)),
    inference(split_conjunct,[status(thm)],[fact_998_transfer__nat__int__numerals_I1_J]) ).

cnf(c_0_34,plain,
    pls = zero_zero(int),
    inference(split_conjunct,[status(thm)],[fact_76_Pls__def]) ).

cnf(c_0_35,plain,
    hAPP(int,int,succ,hAPP(int,int,pred,X1)) = ti(int,X1),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_36,plain,
    hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_37,plain,
    ! [X9863] : hAPP(int,int,pred,hAPP(int,int,bit1,X9863)) = hAPP(int,int,bit0,X9863),
    inference(variable_rename,[status(thm)],[fact_2926_pred__Bit1]) ).

cnf(c_0_38,plain,
    hAPP(int,nat,nat_1,one_one(int)) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_39,plain,
    zero_zero(nat) = hAPP(int,nat,nat_1,pls),
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,plain,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).

cnf(c_0_41,plain,
    hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_42,plain,
    hAPP(int,int,pred,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_43,plain,
    hAPP(int,int,bit0,pls) = pls,
    inference(split_conjunct,[status(thm)],[fact_72_Bit0__Pls]) ).

cnf(c_0_44,plain,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    inference(split_conjunct,[status(thm)],[fact_284_succ__Pls]) ).

fof(c_0_45,plain,
    ! [X3049] : hAPP(int,nat,number_number_of(nat),X3049) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X3049)),
    inference(variable_rename,[status(thm)],[fact_1004_nat__number__of__def]) ).

fof(c_0_46,negated_conjecture,
    hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(c_0_47,plain,
    hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
    inference(split_conjunct,[status(thm)],[fact_1484_semiring__norm_I115_J]) ).

cnf(c_0_48,plain,
    hAPP(int,nat,nat_1,one_one(int)) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls)),
    inference(rw,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_49,plain,
    one_one(int) = hAPP(int,int,bit1,pls),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),c_0_44]) ).

fof(c_0_50,plain,
    ! [X1354] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1354)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1354)),
    inference(variable_rename,[status(thm)],[fact_1450_int__Suc]) ).

cnf(c_0_51,plain,
    hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X1)),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_52,plain,
    ! [X9862] : hAPP(int,int,pred,hAPP(int,int,bit0,X9862)) = hAPP(int,int,bit1,hAPP(int,int,pred,X9862)),
    inference(variable_rename,[status(thm)],[fact_2925_pred__Bit0]) ).

fof(c_0_53,plain,
    ! [X9932] : hAPP(int,int,succ,hAPP(int,int,bit1,X9932)) = hAPP(int,int,bit0,hAPP(int,int,succ,X9932)),
    inference(variable_rename,[status(thm)],[fact_285_succ__Bit1]) ).

cnf(c_0_54,negated_conjecture,
    hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_55,plain,
    hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls))),
    inference(rw,[status(thm)],[c_0_47,c_0_39]) ).

cnf(c_0_56,plain,
    hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls)) = hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls)),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_57,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,plain,
    hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[fact_1503_nat__2]) ).

cnf(c_0_59,plain,
    hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,X1))),
    inference(rw,[status(thm)],[c_0_51,c_0_41]) ).

cnf(c_0_60,plain,
    hAPP(int,int,pred,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,hAPP(int,int,pred,X1)),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_61,plain,
    hAPP(int,int,succ,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,hAPP(int,int,succ,X1)),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

fof(c_0_62,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
            | ti(X1,X6) = ti(X1,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_534_not__less__iff__gr__or__eq]) ).

fof(c_0_63,plain,
    ! [X11679,X11680,X11681] :
      ( ( ti(X11679,X11680) = zero_zero(X11679)
        | hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) != zero_zero(X11679)
        | ~ power(X11679)
        | ~ mult_zero(X11679)
        | ~ no_zero_divisors(X11679)
        | ~ zero_neq_one(X11679) )
      & ( X11681 != zero_zero(nat)
        | hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) != zero_zero(X11679)
        | ~ power(X11679)
        | ~ mult_zero(X11679)
        | ~ no_zero_divisors(X11679)
        | ~ zero_neq_one(X11679) )
      & ( ti(X11679,X11680) != zero_zero(X11679)
        | X11681 = zero_zero(nat)
        | hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) = zero_zero(X11679)
        | ~ power(X11679)
        | ~ mult_zero(X11679)
        | ~ no_zero_divisors(X11679)
        | ~ zero_neq_one(X11679) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_power__eq__0__iff])])])]) ).

fof(c_0_64,plain,
    ! [X1222,X1223] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1222),X1223)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X1222)),X1223),
    inference(variable_rename,[status(thm)],[fact_21_int__power]) ).

fof(c_0_65,plain,
    ! [X2121,X2122,X2123,X2124] : ti(X2121,hAPP(X2122,X2121,X2123,X2124)) = hAPP(X2122,X2121,X2123,X2124),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).

cnf(c_0_66,negated_conjecture,
    hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls)))) = pls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_49]),c_0_55]),c_0_56]),c_0_34]) ).

cnf(c_0_67,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)),
    inference(rw,[status(thm)],[c_0_57,c_0_49]) ).

cnf(c_0_68,plain,
    hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
    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)],[inference(rw,[status(thm)],[c_0_58,c_0_51]),c_0_59]),c_0_60]),c_0_42]),c_0_43]),c_0_61]),c_0_44]),c_0_39]),c_0_56]) ).

fof(c_0_69,plain,
    ! [X11323,X11324,X11325] :
      ( ( hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
        | hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11325),X11324))
        | ti(X11323,X11324) = ti(X11323,X11325)
        | ~ linorder(X11323) )
      & ( ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11325),X11324))
        | ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
        | ~ linorder(X11323) )
      & ( ti(X11323,X11324) != ti(X11323,X11325)
        | ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
        | ~ linorder(X11323) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).

cnf(c_0_70,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).

cnf(c_0_71,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
    | ~ power(X1)
    | ~ mult_zero(X1)
    | ~ no_zero_divisors(X1)
    | ~ zero_neq_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_72,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),X2),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_73,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_74,plain,
    zero_neq_one(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).

cnf(c_0_75,plain,
    mult_zero(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Omult__zero]) ).

cnf(c_0_76,plain,
    no_zero_divisors(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ono__zero__divisors]) ).

cnf(c_0_77,plain,
    power(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Power_Opower]) ).

cnf(c_0_78,negated_conjecture,
    hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_79,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_80,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_34]),c_0_49]),c_0_67]) ).

cnf(c_0_81,plain,
    hAPP(int,int,pred,pls) = min,
    inference(split_conjunct,[status(thm)],[fact_2928_pred__Pls]) ).

cnf(c_0_82,plain,
    hAPP(int,int,succ,min) = pls,
    inference(split_conjunct,[status(thm)],[fact_686_succ__Min]) ).

cnf(c_0_83,plain,
    linorder(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]) ).

cnf(c_0_84,plain,
    ( hAPP(nat,int,semiring_1_of_nat(int),X1) = pls
    | hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) != pls ),
    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(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_34]),c_0_34]),c_0_74]),c_0_75]),c_0_76]),c_0_77])]) ).

cnf(c_0_85,negated_conjecture,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = pls,
    inference(rw,[status(thm)],[c_0_78,c_0_72]) ).

cnf(c_0_86,plain,
    hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) != pls,
    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(spm,[status(thm)],[c_0_79,c_0_80]),c_0_36]),c_0_41]),c_0_81]),c_0_82]),c_0_73]),c_0_83])]) ).

cnf(c_0_87,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.29/1.30  % Problem    : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% 1.29/1.31  % Command    : run_E %s %d THM
% 1.31/1.51  % Computer : n028.cluster.edu
% 1.31/1.51  % Model    : x86_64 x86_64
% 1.31/1.51  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.31/1.51  % Memory   : 8042.1875MB
% 1.31/1.51  % OS       : Linux 3.10.0-693.el7.x86_64
% 1.31/1.51  % CPULimit   : 2400
% 1.31/1.51  % WCLimit    : 300
% 1.31/1.51  % DateTime   : Mon Oct  2 15:20:23 EDT 2023
% 1.31/1.51  % CPUTime    : 
% 2.56/2.81  Running first-order theorem proving
% 2.56/2.81  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p
% 72.59/12.23  # Version: 3.1pre001
% 72.59/12.23  # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23  # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23  # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23  # Starting sh5l with 300s (1) cores
% 72.59/12.23  # sh5l with pid 17729 completed with status 0
% 72.59/12.23  # Result found by sh5l
% 72.59/12.23  # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23  # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23  # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23  # Starting sh5l with 300s (1) cores
% 72.59/12.23  # SinE strategy is gf500_gu_R04_F100_L20000
% 72.59/12.23  # Search class: FGHSM-SMLM33-DFFFFFNN
% 72.59/12.23  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 72.59/12.23  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 72.59/12.23  # SAT001_MinMin_p005000_rr with pid 17735 completed with status 0
% 72.59/12.23  # Result found by SAT001_MinMin_p005000_rr
% 72.59/12.23  # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23  # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23  # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23  # Starting sh5l with 300s (1) cores
% 72.59/12.23  # SinE strategy is gf500_gu_R04_F100_L20000
% 72.59/12.23  # Search class: FGHSM-SMLM33-DFFFFFNN
% 72.59/12.23  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 72.59/12.23  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 72.59/12.23  # Preprocessing time       : 0.188 s
% 72.59/12.23  # Presaturation interreduction done
% 72.59/12.23  
% 72.59/12.23  # Proof found!
% 72.59/12.23  # SZS status Theorem
% 72.59/12.23  # SZS output start CNFRefutation
% See solution above
% 72.59/12.23  # Parsed axioms                        : 5747
% 72.59/12.23  # Removed by relevancy pruning/SinE    : 584
% 72.59/12.23  # Initial clauses                      : 7950
% 72.59/12.23  # Removed in clause preprocessing      : 208
% 72.59/12.23  # Initial clauses in saturation        : 7742
% 72.59/12.23  # Processed clauses                    : 20915
% 72.59/12.23  # ...of these trivial                  : 503
% 72.59/12.23  # ...subsumed                          : 9895
% 72.59/12.23  # ...remaining for further processing  : 10517
% 72.59/12.23  # Other redundant clauses eliminated   : 470
% 72.59/12.23  # Clauses deleted for lack of memory   : 0
% 72.59/12.23  # Backward-subsumed                    : 206
% 72.59/12.23  # Backward-rewritten                   : 369
% 72.59/12.23  # Generated clauses                    : 47924
% 72.59/12.23  # ...of the previous two non-redundant : 39610
% 72.59/12.23  # ...aggressively subsumed             : 0
% 72.59/12.23  # Contextual simplify-reflections      : 37
% 72.59/12.23  # Paramodulations                      : 47456
% 72.59/12.23  # Factorizations                       : 3
% 72.59/12.23  # NegExts                              : 0
% 72.59/12.23  # Equation resolutions                 : 486
% 72.59/12.23  # Total rewrite steps                  : 74293
% 72.59/12.23  # Propositional unsat checks           : 3
% 72.59/12.23  #    Propositional check models        : 2
% 72.59/12.23  #    Propositional check unsatisfiable : 0
% 72.59/12.23  #    Propositional clauses             : 0
% 72.59/12.23  #    Propositional clauses after purity: 0
% 72.59/12.23  #    Propositional unsat core size     : 0
% 72.59/12.23  #    Propositional preprocessing time  : 0.000
% 72.59/12.23  #    Propositional encoding time       : 0.151
% 72.59/12.23  #    Propositional solver time         : 0.045
% 72.59/12.23  #    Success case prop preproc time    : 0.000
% 72.59/12.23  #    Success case prop encoding time   : 0.000
% 72.59/12.23  #    Success case prop solver time     : 0.000
% 72.59/12.23  # Current number of processed clauses  : 3103
% 72.59/12.23  #    Positive orientable unit clauses  : 1633
% 72.59/12.23  #    Positive unorientable unit clauses: 44
% 72.59/12.23  #    Negative unit clauses             : 266
% 72.59/12.23  #    Non-unit-clauses                  : 1160
% 72.59/12.23  # Current number of unprocessed clauses: 32681
% 72.59/12.23  # ...number of literals in the above   : 61921
% 72.59/12.23  # Current number of archived formulas  : 0
% 72.59/12.23  # Current number of archived clauses   : 7112
% 72.59/12.23  # Clause-clause subsumption calls (NU) : 7398865
% 72.59/12.23  # Rec. Clause-clause subsumption calls : 1406062
% 72.59/12.23  # Non-unit clause-clause subsumptions  : 3561
% 72.59/12.23  # Unit Clause-clause subsumption calls : 10979
% 72.59/12.23  # Rewrite failures with RHS unbound    : 4
% 72.59/12.23  # BW rewrite match attempts            : 412041
% 72.59/12.23  # BW rewrite match successes           : 1266
% 72.59/12.23  # Condensation attempts                : 0
% 72.59/12.23  # Condensation successes               : 0
% 72.59/12.23  # Termbank termtop insertions          : 5474266
% 72.59/12.23  
% 72.59/12.23  # -------------------------------------------------
% 72.59/12.23  # User time                : 8.802 s
% 72.59/12.23  # System time              : 0.169 s
% 72.59/12.23  # Total time               : 8.971 s
% 72.59/12.23  # Maximum resident set size: 40616 pages
% 72.59/12.23  
% 72.59/12.23  # -------------------------------------------------
% 72.59/12.23  # User time                : 9.000 s
% 72.59/12.23  # System time              : 0.185 s
% 72.59/12.23  # Total time               : 9.185 s
% 72.59/12.23  # Maximum resident set size: 9936 pages
% 72.59/12.23  % E---3.1 exiting
% 72.59/12.23  % E---3.1 exiting
%------------------------------------------------------------------------------