TSTP Solution File: NUM926+8 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : NUM926+8 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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 01:28:37 EDT 2024

% Result   : Theorem 117.79s 15.82s
% Output   : CNFRefutation 117.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   76 (  66 unt;   0 def)
%            Number of atoms       :   94 (  72 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (  16   ~;  10   |;   0   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  15 con; 0-4 aty)
%            Number of variables   :   76 (   4 sgn  41   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_2897_succ__pred,axiom,
    ! [X10] : hAPP(int,int,succ,hAPP(int,int,pred,X10)) = ti(int,X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2897_succ__pred) ).

fof(fact_89_number__of__is__id,axiom,
    ! [X19] : hAPP(int,int,number_number_of(int),X19) = ti(int,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_number__of__is__id) ).

fof(fact_131_zmult__1,axiom,
    ! [X16] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X16) = ti(int,X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zmult__1) ).

fof(fact_2898_pred__Bit1,axiom,
    ! [X19] : hAPP(int,int,pred,hAPP(int,int,bit1,X19)) = hAPP(int,int,bit0,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2898_pred__Bit1) ).

fof(conj_0,conjecture,
    ? [X6,X7] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X6),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X7),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_1128_nat__number__of__def,axiom,
    ! [X14] : hAPP(int,nat,number_number_of(nat),X14) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_nat__number__of__def) ).

fof(fact_161_one__is__num__one,axiom,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_one__is__num__one) ).

fof(fact_123_Bit0__Pls,axiom,
    hAPP(int,int,bit0,pls) = pls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Bit0__Pls) ).

fof(fact_1590_succ__Pls,axiom,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1590_succ__Pls) ).

fof(tsy_v_m_res,hypothesis,
    ti(int,m) = m,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m_res) ).

fof(fact_1593_succ__def,axiom,
    ! [X19] : hAPP(int,int,succ,X19) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X19),one_one(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1593_succ__def) ).

fof(fact_2899_pred__Bit0,axiom,
    ! [X19] : hAPP(int,int,pred,hAPP(int,int,bit0,X19)) = hAPP(int,int,bit1,hAPP(int,int,pred,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2899_pred__Bit0) ).

fof(fact_1592_succ__Bit1,axiom,
    ! [X19] : hAPP(int,int,succ,hAPP(int,int,bit1,X19)) = hAPP(int,int,bit0,hAPP(int,int,succ,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1592_succ__Bit1) ).

fof(fact_125_mult__Bit0,axiom,
    ! [X19,X52] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,X19)),X52) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X19),X52)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mult__Bit0) ).

fof(fact_1591_succ__Bit0,axiom,
    ! [X19] : hAPP(int,int,succ,hAPP(int,int,bit0,X19)) = hAPP(int,int,bit1,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1591_succ__Bit0) ).

fof(fact_1568_xt1_I12_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X8,X9] :
          ( ti(X1,X8) != ti(X1,X9)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X9),X8))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X9),X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1568_xt1_I12_J) ).

fof(tsy_v_t_____res,axiom,
    ti(int,t) = t,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).

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)
   => ? [X6,X7] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X6),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X7),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,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_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,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))
   => ? [X6,X7] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X6),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X7),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,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_0_tpos,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X3,X1,X4,X5] : ti(X3,hAPP(X1,X3,X4,X5)) = hAPP(X1,X3,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

fof(arity_Int_Oint___Orderings_Oorder,axiom,
    order(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).

fof(c_0_22,plain,
    ! [X11429] : hAPP(int,int,succ,hAPP(int,int,pred,X11429)) = ti(int,X11429),
    inference(variable_rename,[status(thm)],[fact_2897_succ__pred]) ).

fof(c_0_23,plain,
    ! [X719] : hAPP(int,int,number_number_of(int),X719) = ti(int,X719),
    inference(variable_rename,[status(thm)],[fact_89_number__of__is__id]) ).

fof(c_0_24,plain,
    ! [X472] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X472) = ti(int,X472),
    inference(variable_rename,[status(thm)],[fact_131_zmult__1]) ).

cnf(c_0_25,plain,
    hAPP(int,int,succ,hAPP(int,int,pred,X1)) = ti(int,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,plain,
    hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_27,plain,
    ! [X11481] : hAPP(int,int,pred,hAPP(int,int,bit1,X11481)) = hAPP(int,int,bit0,X11481),
    inference(variable_rename,[status(thm)],[fact_2898_pred__Bit1]) ).

fof(c_0_28,negated_conjecture,
    ~ ? [X6,X7] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X6),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X7),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_29,plain,
    ! [X4881] : hAPP(int,nat,number_number_of(nat),X4881) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X4881)),
    inference(variable_rename,[status(thm)],[fact_1128_nat__number__of__def]) ).

cnf(c_0_30,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X1) = ti(int,X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
    inference(split_conjunct,[status(thm)],[fact_161_one__is__num__one]) ).

cnf(c_0_32,plain,
    hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,plain,
    hAPP(int,int,pred,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    hAPP(int,int,bit0,pls) = pls,
    inference(split_conjunct,[status(thm)],[fact_123_Bit0__Pls]) ).

cnf(c_0_35,plain,
    hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
    inference(split_conjunct,[status(thm)],[fact_1590_succ__Pls]) ).

cnf(c_0_36,hypothesis,
    ti(int,m) = m,
    inference(split_conjunct,[status(thm)],[tsy_v_m_res]) ).

fof(c_0_37,plain,
    ! [X11417] : hAPP(int,int,succ,X11417) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X11417),one_one(int)),
    inference(variable_rename,[status(thm)],[fact_1593_succ__def]) ).

fof(c_0_38,negated_conjecture,
    ! [X230,X231] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X230),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X231),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).

cnf(c_0_39,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_29]) ).

fof(c_0_40,plain,
    ! [X11482] : hAPP(int,int,pred,hAPP(int,int,bit0,X11482)) = hAPP(int,int,bit1,hAPP(int,int,pred,X11482)),
    inference(variable_rename,[status(thm)],[fact_2899_pred__Bit0]) ).

fof(c_0_41,plain,
    ! [X11416] : hAPP(int,int,succ,hAPP(int,int,bit1,X11416)) = hAPP(int,int,bit0,hAPP(int,int,succ,X11416)),
    inference(variable_rename,[status(thm)],[fact_1592_succ__Bit1]) ).

fof(c_0_42,plain,
    ! [X751,X752] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,X751)),X752) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X751),X752)),
    inference(variable_rename,[status(thm)],[fact_125_mult__Bit0]) ).

cnf(c_0_43,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),X1) = hAPP(int,int,number_number_of(int),X1),
    inference(rw,[status(thm)],[c_0_30,c_0_26]) ).

cnf(c_0_44,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_31,c_0_32]),c_0_33]),c_0_34]),c_0_35]) ).

cnf(c_0_45,hypothesis,
    hAPP(int,int,number_number_of(int),m) = m,
    inference(rw,[status(thm)],[c_0_36,c_0_26]) ).

cnf(c_0_46,plain,
    hAPP(int,int,succ,X1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_47,plain,
    ! [X11415] : hAPP(int,int,succ,hAPP(int,int,bit0,X11415)) = hAPP(int,int,bit1,X11415),
    inference(variable_rename,[status(thm)],[fact_1591_succ__Bit0]) ).

fof(c_0_48,plain,
    ! [X1] :
      ( order(X1)
     => ! [X8,X9] :
          ( ti(X1,X8) != ti(X1,X9)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X9),X8))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X9),X8)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_1568_xt1_I12_J]) ).

cnf(c_0_49,plain,
    ti(int,t) = t,
    inference(split_conjunct,[status(thm)],[tsy_v_t_____res]) ).

fof(c_0_50,plain,
    ( t != one_one(int)
    | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk35_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk36_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) ),
    inference(fof_nnf,[status(thm)],[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_51,negated_conjecture,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_52,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_39,c_0_32]) ).

cnf(c_0_53,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_40]) ).

cnf(c_0_54,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_41]) ).

cnf(c_0_55,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,X1)),X2) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_56,plain,
    hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,pls)),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_32]),c_0_44]) ).

cnf(c_0_57,hypothesis,
    hAPP(int,int,succ,hAPP(int,int,pred,m)) = m,
    inference(rw,[status(thm)],[c_0_45,c_0_32]) ).

cnf(c_0_58,plain,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),hAPP(int,int,bit1,pls)) = hAPP(int,int,succ,X1),
    inference(rw,[status(thm)],[c_0_46,c_0_44]) ).

cnf(c_0_59,plain,
    hAPP(int,int,succ,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,X1),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

fof(c_0_60,plain,
    ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))
    | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk37_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk38_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) ),
    inference(fof_nnf,[status(thm)],[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_61,plain,
    ! [X10829,X10830,X10831] :
      ( ~ order(X10829)
      | ti(X10829,X10830) = ti(X10829,X10831)
      | ~ hBOOL(hAPP(X10829,bool,hAPP(X10829,fun(X10829,bool),ord_less_eq(X10829),X10831),X10830))
      | hBOOL(hAPP(X10829,bool,hAPP(X10829,fun(X10829,bool),ord_less(X10829),X10831),X10830)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).

cnf(c_0_62,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
    inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).

cnf(c_0_63,plain,
    hAPP(int,int,number_number_of(int),t) = t,
    inference(rw,[status(thm)],[c_0_49,c_0_26]) ).

fof(c_0_64,plain,
    ! [X2092,X2093,X2094,X2095] : ti(X2092,hAPP(X2093,X2092,X2094,X2095)) = hAPP(X2093,X2092,X2094,X2095),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).

cnf(c_0_65,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk35_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk36_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))
    | t != one_one(int) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_66,negated_conjecture,
    hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X1),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X2),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,bit1,hAPP(int,int,bit0,m)),
    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)],[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)],[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_51,c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_32]),c_0_53]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_54]),c_0_35]),c_0_55]),c_0_55]),c_0_56]),c_0_57]),c_0_44]),c_0_58]),c_0_59]) ).

cnf(c_0_67,plain,
    ( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk37_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),esk38_0),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))
    | ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_68,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_69,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),t)),
    inference(rw,[status(thm)],[c_0_62,c_0_44]) ).

cnf(c_0_70,plain,
    hAPP(int,int,succ,hAPP(int,int,pred,t)) = t,
    inference(rw,[status(thm)],[c_0_63,c_0_32]) ).

cnf(c_0_71,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_72,plain,
    order(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Oorder]) ).

cnf(c_0_73,plain,
    hAPP(int,int,bit1,pls) != t,
    inference(sr,[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_32]),c_0_53]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_54]),c_0_35]),c_0_55]),c_0_55]),c_0_56]),c_0_57]),c_0_44]),c_0_58]),c_0_59]),c_0_44]),c_0_66]) ).

cnf(c_0_74,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),t)),
    inference(sr,[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_52]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_35]),c_0_32]),c_0_53]),c_0_53]),c_0_33]),c_0_34]),c_0_54]),c_0_54]),c_0_35]),c_0_55]),c_0_55]),c_0_56]),c_0_57]),c_0_44]),c_0_58]),c_0_59]),c_0_44]),c_0_66]) ).

cnf(c_0_75,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[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(spm,[status(thm)],[c_0_68,c_0_69]),c_0_26]),c_0_32]),c_0_70]),c_0_71]),c_0_72])]),c_0_73]),c_0_74]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM926+8 : TPTP v8.2.0. Released v5.3.0.
% 0.00/0.11  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n022.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   : Mon May 20 04:41:53 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.14/0.42  Running first-order model finding
% 0.14/0.42  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.79/15.82  # Version: 3.1.0
% 117.79/15.82  # Preprocessing class: FMLMSMSLSSSNFFN.
% 117.79/15.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.79/15.82  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 117.79/15.82  # Starting new_bool_3 with 600s (2) cores
% 117.79/15.82  # Starting new_bool_1 with 600s (2) cores
% 117.79/15.82  # Starting sh5l with 300s (1) cores
% 117.79/15.82  # sh5l with pid 5692 completed with status 0
% 117.79/15.82  # Result found by sh5l
% 117.79/15.82  # Preprocessing class: FMLMSMSLSSSNFFN.
% 117.79/15.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.79/15.82  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 117.79/15.82  # Starting new_bool_3 with 600s (2) cores
% 117.79/15.82  # Starting new_bool_1 with 600s (2) cores
% 117.79/15.82  # Starting sh5l with 300s (1) cores
% 117.79/15.82  # SinE strategy is gf500_gu_R04_F100_L20000
% 117.79/15.82  # Search class: FGHSM-SMLM33-DFFFFFNN
% 117.79/15.82  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 117.79/15.82  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 117.79/15.82  # SAT001_MinMin_p005000_rr with pid 5697 completed with status 0
% 117.79/15.82  # Result found by SAT001_MinMin_p005000_rr
% 117.79/15.82  # Preprocessing class: FMLMSMSLSSSNFFN.
% 117.79/15.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.79/15.82  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 117.79/15.82  # Starting new_bool_3 with 600s (2) cores
% 117.79/15.82  # Starting new_bool_1 with 600s (2) cores
% 117.79/15.82  # Starting sh5l with 300s (1) cores
% 117.79/15.82  # SinE strategy is gf500_gu_R04_F100_L20000
% 117.79/15.82  # Search class: FGHSM-SMLM33-DFFFFFNN
% 117.79/15.82  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 117.79/15.82  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 117.79/15.82  # Preprocessing time       : 0.244 s
% 117.79/15.82  # Presaturation interreduction done
% 117.79/15.82  
% 117.79/15.82  # Proof found!
% 117.79/15.82  # SZS status Theorem
% 117.79/15.82  # SZS output start CNFRefutation
% See solution above
% 117.79/15.82  # Parsed axioms                        : 5738
% 117.79/15.82  # Removed by relevancy pruning/SinE    : 814
% 117.79/15.82  # Initial clauses                      : 7650
% 117.79/15.82  # Removed in clause preprocessing      : 208
% 117.79/15.82  # Initial clauses in saturation        : 7442
% 117.79/15.82  # Processed clauses                    : 25515
% 117.79/15.82  # ...of these trivial                  : 595
% 117.79/15.82  # ...subsumed                          : 14021
% 117.79/15.82  # ...remaining for further processing  : 10899
% 117.79/15.82  # Other redundant clauses eliminated   : 833
% 117.79/15.82  # Clauses deleted for lack of memory   : 0
% 117.79/15.82  # Backward-subsumed                    : 478
% 117.79/15.82  # Backward-rewritten                   : 297
% 117.79/15.82  # Generated clauses                    : 77993
% 117.79/15.82  # ...of the previous two non-redundant : 67143
% 117.79/15.82  # ...aggressively subsumed             : 0
% 117.79/15.82  # Contextual simplify-reflections      : 43
% 117.79/15.82  # Paramodulations                      : 77141
% 117.79/15.82  # Factorizations                       : 2
% 117.79/15.82  # NegExts                              : 0
% 117.79/15.82  # Equation resolutions                 : 871
% 117.79/15.82  # Disequality decompositions           : 0
% 117.79/15.82  # Total rewrite steps                  : 99505
% 117.79/15.82  # ...of those cached                   : 90713
% 117.79/15.82  # Propositional unsat checks           : 3
% 117.79/15.82  #    Propositional check models        : 2
% 117.79/15.82  #    Propositional check unsatisfiable : 0
% 117.79/15.82  #    Propositional clauses             : 0
% 117.79/15.82  #    Propositional clauses after purity: 0
% 117.79/15.82  #    Propositional unsat core size     : 0
% 117.79/15.82  #    Propositional preprocessing time  : 0.000
% 117.79/15.82  #    Propositional encoding time       : 0.280
% 117.79/15.82  #    Propositional solver time         : 0.092
% 117.79/15.82  #    Success case prop preproc time    : 0.000
% 117.79/15.82  #    Success case prop encoding time   : 0.000
% 117.79/15.82  #    Success case prop solver time     : 0.000
% 117.79/15.82  # Current number of processed clauses  : 3560
% 117.79/15.82  #    Positive orientable unit clauses  : 1499
% 117.79/15.82  #    Positive unorientable unit clauses: 45
% 117.79/15.82  #    Negative unit clauses             : 387
% 117.79/15.82  #    Non-unit-clauses                  : 1629
% 117.79/15.82  # Current number of unprocessed clauses: 54492
% 117.79/15.82  # ...number of literals in the above   : 122508
% 117.79/15.82  # Current number of archived formulas  : 0
% 117.79/15.82  # Current number of archived clauses   : 7038
% 117.79/15.82  # Clause-clause subsumption calls (NU) : 7535953
% 117.79/15.82  # Rec. Clause-clause subsumption calls : 1462323
% 117.79/15.82  # Non-unit clause-clause subsumptions  : 5754
% 117.79/15.82  # Unit Clause-clause subsumption calls : 23205
% 117.79/15.82  # Rewrite failures with RHS unbound    : 4
% 117.79/15.82  # BW rewrite match attempts            : 362374
% 117.79/15.82  # BW rewrite match successes           : 1143
% 117.79/15.82  # Condensation attempts                : 0
% 117.79/15.82  # Condensation successes               : 0
% 117.79/15.82  # Termbank termtop insertions          : 6882582
% 117.79/15.82  # Search garbage collected termcells   : 108294
% 117.79/15.82  
% 117.79/15.82  # -------------------------------------------------
% 117.79/15.82  # User time                : 14.762 s
% 117.79/15.82  # System time              : 0.205 s
% 117.79/15.82  # Total time               : 14.967 s
% 117.79/15.82  # Maximum resident set size: 40956 pages
% 117.79/15.82  
% 117.79/15.82  # -------------------------------------------------
% 117.79/15.82  # User time                : 15.011 s
% 117.79/15.82  # System time              : 0.215 s
% 117.79/15.82  # Total time               : 15.226 s
% 117.79/15.82  # Maximum resident set size: 9860 pages
% 117.79/15.82  % E---3.1 exiting
%------------------------------------------------------------------------------