%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM926_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:27:30 PM UTC 2026
% Result : Theorem 35.86s 6.78s
% Output : CNFRefutation 35.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 20 prp; 0-3 aty)
% Number of functors : 109 ( 109 usr; 32 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cOMBB_1652995168ol_int: ( fun_int_bool * fun_bo1549164019l_bool ) > fun_in531499254l_bool ).
tff(pred_def_1,type,
hBOOL: bool > $o ).
tff(pred_def_2,type,
sP0: ( bool * ( int * bool ) ) > $o ).
tff(pred_def_3,type,
sP1: ( bool * ( bool * int ) ) > $o ).
tff(pred_def_4,type,
sP2: ( int * ( int * fun_int_bool ) ) > $o ).
tff(pred_def_5,type,
sP3: ( int * ( int * fun_int_bool ) ) > $o ).
tff(pred_def_6,type,
sP4: ( nat * ( fun_nat_bool * nat ) ) > $o ).
tff(func_def_7,type,
minus_minus_real: real > fun_real_real ).
tff(func_def_8,type,
one_one_int: int ).
tff(func_def_9,type,
one_one_nat: nat ).
tff(func_def_10,type,
one_one_real: real ).
tff(func_def_11,type,
plus_plus_int: int > fun_int_int ).
tff(func_def_12,type,
plus_plus_nat: nat > fun_nat_nat ).
tff(func_def_13,type,
plus_plus_real: real > fun_real_real ).
tff(func_def_14,type,
times_times_int: int > fun_int_int ).
tff(func_def_15,type,
times_times_nat: nat > fun_nat_nat ).
tff(func_def_16,type,
times_times_real: real > fun_real_real ).
tff(func_def_17,type,
zero_zero_int: int ).
tff(func_def_18,type,
zero_zero_nat: nat ).
tff(func_def_19,type,
zero_zero_real: real ).
tff(func_def_20,type,
multInv: ( int * int ) > int ).
tff(func_def_21,type,
d22set: int > fun_int_bool ).
tff(func_def_22,type,
zfact: int > int ).
tff(func_def_23,type,
zcong: ( int * int ) > fun_int_bool ).
tff(func_def_24,type,
zprime: fun_int_bool ).
tff(func_def_25,type,
bit0: int > int ).
tff(func_def_26,type,
bit1: int > int ).
tff(func_def_27,type,
min: int ).
tff(func_def_28,type,
pls: int ).
tff(func_def_29,type,
number_number_of_int: int > int ).
tff(func_def_30,type,
number_number_of_nat: int > nat ).
tff(func_def_31,type,
number267125858f_real: int > real ).
tff(func_def_32,type,
ord_less_int: fun_int_fun_int_bool ).
tff(func_def_33,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(func_def_34,type,
ord_less_real: fun_re413263731l_bool ).
tff(func_def_35,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(func_def_36,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(func_def_37,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(func_def_38,type,
power_power_int: int > fun_nat_int ).
tff(func_def_39,type,
power_power_nat: nat > fun_nat_nat ).
tff(func_def_40,type,
power_power_real: real > fun_nat_real ).
tff(func_def_41,type,
product_Pair_int_int: ( int * int ) > product_prod_int_int ).
tff(func_def_42,type,
legendre: ( int * int ) > int ).
tff(func_def_43,type,
quadRes: int > fun_int_bool ).
tff(func_def_44,type,
sr: int > fun_int_bool ).
tff(func_def_45,type,
standardRes: ( int * int ) > int ).
tff(func_def_46,type,
dvd_dvd_int: fun_int_fun_int_bool ).
tff(func_def_47,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(func_def_48,type,
dvd_dvd_real: fun_re413263731l_bool ).
tff(func_def_49,type,
collect_int: fun_int_bool > fun_int_bool ).
tff(func_def_50,type,
twoSqu820444569sum2sq: fun_int_bool ).
tff(func_def_51,type,
twoSqu949963151sum2sq: product_prod_int_int > int ).
tff(func_def_52,type,
inv: ( int * int ) > int ).
tff(func_def_53,type,
wset: ( int * int ) > fun_int_bool ).
tff(func_def_54,type,
fconj: fun_bo1549164019l_bool ).
tff(func_def_55,type,
hAPP_bool_bool: ( bool * fun_bool_bool ) > bool ).
tff(func_def_56,type,
hAPP_b589554111l_bool: ( bool * fun_bo1549164019l_bool ) > fun_bool_bool ).
tff(func_def_57,type,
hAPP_int_bool: ( int * fun_int_bool ) > bool ).
tff(func_def_58,type,
hAPP_int_int: ( int * fun_int_int ) > int ).
tff(func_def_59,type,
hAPP_i68813070l_bool: ( int * fun_in531499254l_bool ) > fun_bool_bool ).
tff(func_def_60,type,
hAPP_i1948725293t_bool: ( int * fun_int_fun_int_bool ) > fun_int_bool ).
tff(func_def_61,type,
hAPP_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(func_def_62,type,
hAPP_nat_int: ( nat * fun_nat_int ) > int ).
tff(func_def_63,type,
hAPP_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(func_def_64,type,
hAPP_nat_real: ( nat * fun_nat_real ) > real ).
tff(func_def_65,type,
hAPP_n1699378549t_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(func_def_66,type,
hAPP_real_bool: ( real * fun_real_bool ) > bool ).
tff(func_def_67,type,
hAPP_real_real: ( real * fun_real_real ) > real ).
tff(func_def_68,type,
hAPP_r1134773055l_bool: ( real * fun_re413263731l_bool ) > fun_real_bool ).
tff(func_def_69,type,
member_int: ( fun_int_bool * int ) > bool ).
tff(func_def_70,type,
m: int ).
tff(func_def_71,type,
s1: int ).
tff(func_def_72,type,
s: int ).
tff(func_def_73,type,
t: int ).
tff(func_def_74,type,
sK5: int ).
tff(func_def_75,type,
sK6: int ).
tff(func_def_76,type,
sK7: int ).
tff(func_def_77,type,
sK8: int ).
tff(func_def_78,type,
sK9: int ).
tff(func_def_79,type,
sK10: int ).
tff(func_def_80,type,
sK11: int ).
tff(func_def_81,type,
sK12: int > int ).
tff(func_def_82,type,
sK13: int ).
tff(func_def_83,type,
sK14: ( int * ( int * int ) ) > int ).
tff(func_def_84,type,
sK15: ( int * int ) > int ).
tff(func_def_85,type,
sK16: ( nat * real ) > real ).
tff(func_def_86,type,
sK17: ( nat * real ) > real ).
tff(func_def_87,type,
sK18: ( nat * nat ) > nat ).
tff(func_def_88,type,
sK19: ( nat * ( nat * fun_nat_bool ) ) > nat ).
tff(func_def_89,type,
sK20: ( nat * ( nat * fun_nat_bool ) ) > nat ).
tff(func_def_90,type,
sK21: ( fun_nat_bool * nat ) > nat ).
tff(func_def_91,type,
sK22: int > int ).
tff(func_def_92,type,
sK23: int > int ).
tff(func_def_93,type,
sK24: ( int * fun_int_bool ) > int ).
tff(func_def_94,type,
sK25: ( int * fun_int_bool ) > int ).
tff(func_def_95,type,
sK26: int > int ).
tff(func_def_96,type,
sK27: ( int * int ) > int ).
tff(func_def_97,type,
sK28: ( int * fun_int_bool ) > int ).
tff(func_def_98,type,
sK29: ( int * fun_int_bool ) > int ).
tff(func_def_99,type,
sK30: fun_int_bool > int ).
tff(func_def_100,type,
sK31: ( int * fun_int_bool ) > int ).
tff(func_def_101,type,
sK32: ( int * fun_int_bool ) > int ).
tff(func_def_102,type,
sK33: fun_nat_nat > nat ).
tff(func_def_103,type,
sK34: fun_nat_nat > nat ).
tff(func_def_104,type,
sK35: ( fun_nat_bool * nat ) > nat ).
tff(func_def_105,type,
sK36: ( nat * nat ) > nat ).
tff(func_def_106,type,
sK37: ( int * int ) > int ).
tff(func_def_107,type,
sK38: ( int * ( int * fun_int_bool ) ) > int ).
tff(func_def_108,type,
sK39: ( int * ( int * fun_int_bool ) ) > int ).
tff(func_def_109,type,
sK40: ( int * ( int * fun_int_bool ) ) > int ).
tff(func_def_110,type,
sK41: ( int * ( int * fun_int_bool ) ) > int ).
tff(func_def_111,type,
sK42: ( int * int ) > int ).
tff(func_def_112,type,
sK43: ( nat * nat ) > nat ).
tff(func_def_113,type,
sK44: ( nat * ( fun_nat_bool * nat ) ) > nat ).
tff(func_def_114,type,
sK45: ( nat * ( fun_nat_bool * nat ) ) > nat ).
tff(f1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f2,axiom,
( ( t = one_one_int )
=> ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_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) ).
tff(f3,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_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) ).
tff(f207,axiom,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Bit0__def) ).
tff(f254,axiom,
! [X0: int] : ( bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Bit1__def) ).
tff(f359,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_Pls__def) ).
tff(f571,axiom,
! [X0: int,X1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
=> ( ( X0 != X1 )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less) ).
tff(f1205,conjecture,
? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_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) ).
tff(f1206,negated_conjecture,
~ ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(negated_conjecture,[status(cth)],[f1205]) ).
tff(f1210,plain,
( ( one_one_int != t )
| ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f1211,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ? [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f1439,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ( X0 = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(ennf_transformation,[],[f571]) ).
tff(f1440,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ( X0 = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(flattening,[],[f1439]) ).
tff(f2083,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(ennf_transformation,[],[f1206]) ).
tff(f2093,plain,
( ( one_one_int != t )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f1210]) ).
tff(f2094,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f1211]) ).
tff(f2486,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[],[f1]) ).
tff(f2487,plain,
( ( one_one_int != t )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f2093]) ).
tff(f2488,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f2094]) ).
tff(f2763,plain,
! [X0: int] : ( bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0) ),
inference(cnf_transformation,[],[f207]) ).
tff(f2810,plain,
! [X0: int] : ( bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f2939,plain,
pls = zero_zero_int,
inference(cnf_transformation,[],[f359]) ).
tff(f3244,plain,
! [X0: int,X1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| ( X0 = X1 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f1440]) ).
tff(f4174,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(cnf_transformation,[],[f2083]) ).
tff(f4175,plain,
( ( one_one_int != t )
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f2487,f2763,f2763,f2810,f2939,f2763,f2810,f2939,f2763,f2810,f2939]) ).
tff(f4176,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) = hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) ) ),
inference(definition_unfolding,[],[f2488,f2763,f2763,f2810,f2939,f2763,f2810,f2939,f2763,f2810,f2939]) ).
tff(f4572,plain,
! [X0: int,X1: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) != hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) ),
inference(definition_unfolding,[],[f4174,f2763,f2810,f2939,f2763,f2810,f2939,f2763,f2763,f2810,f2939]) ).
tcf(c_49,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[],[f2486]) ).
tcf(c_50,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f4175]) ).
tcf(c_51,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(cnf_transformation,[],[f4176]) ).
tcf(c_784,plain,
! [X0_int: int,X1_int: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0_int),X1_int))
| ( X0_int = X1_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0_int),X1_int)) ),
inference(cnf_transformation,[],[f3244]) ).
tcf(c_1664,negated_conjecture,
! [X0_int: int,X1_int: int] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X0_int),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(X1_int),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int),
inference(cnf_transformation,[],[f4572]) ).
tcf(c_2632,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK5),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK6),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) )
| ( one_one_int != t ) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_2634,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK7),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),hAPP_nat_int(power_power_int(sK8),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),m)),one_one_int) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_6013,plain,
one_one_int != t,
inference(backward_subsumption_resolution,[status(thm)],[c_2632,c_1664]) ).
tcf(c_6014,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(backward_subsumption_resolution,[status(thm)],[c_2634,c_1664]) ).
tcf(c_58815,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ( one_one_int = t )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
inference(instantiation,[status(thm)],[c_784]) ).
tcf(c_58816,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58815,c_6013,c_6014,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 05:49:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 35.86/6.78 % SZS status Started for theBenchmark.p
% 35.86/6.78 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.86/6.78 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.86/6.78 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 0.33 --show_fool true" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_4il48l5f/7vq_bus_ 2>> /export/starexec/sandbox2/tmp/iprover_out_4il48l5f/7vq_bus__error
% 35.86/6.78 % SZS status Theorem for theBenchmark.p
% 35.86/6.78
% 35.86/6.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.86/6.78
% 35.86/6.78 % ------ iProver source info
% 35.86/6.78
% 35.86/6.78 % git: date: 2026-07-19 20:42:38 +0200
% 35.86/6.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.86/6.78 % git: non_committed_changes: false
% 35.86/6.78
% 35.86/6.78 % ------ Parsing...
% 35.86/6.78 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 35.86/6.78 %
% 35.86/6.78
% 35.86/6.78 % ------ Preprocessing... sup_sim: 367 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 35.86/6.78
% 35.86/6.78 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 35.86/6.78 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 35.86/6.78 %
% 35.86/6.78
% 35.86/6.78 % ------ Preprocessing...
% 35.86/6.78 % ------ Proving...
% 35.86/6.78 % ------ Problem Properties
% 35.86/6.78
% 35.86/6.78 %
% 35.86/6.78 % clauses 1016
% 35.86/6.78 % conjectures 0
% 35.86/6.78 % EPR 6
% 35.86/6.78 % Horn 849
% 35.86/6.78 % unary 277
% 35.86/6.78 % binary 364
% 35.86/6.78 % lits 2289
% 35.86/6.78 % lits eq 516
% 35.86/6.78 % fd_pure 0
% 35.86/6.78 % fd_pseudo 0
% 35.86/6.78 % fd_cond 83
% 35.86/6.78 % fd_pseudo_cond 47
% 35.86/6.78 % AC symbols 0
% 35.86/6.78
% 35.86/6.78 % ------ Schedule dynamic 5 is on
% 35.86/6.78
% 35.86/6.78 % ------ no conjectures: strip conj schedule
% 35.86/6.78
% 35.86/6.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 35.86/6.78
% 35.86/6.78
% 35.86/6.78 % ------
% 35.86/6.78 % Current options:
% 35.86/6.78 % ------
% 35.86/6.78
% 35.86/6.78
% 35.86/6.78 %
% 35.86/6.78
% 35.86/6.78 % ------ Proving...
% 35.86/6.78 %
% 35.86/6.78
% 35.86/6.78 % SZS status Theorem for theBenchmark.p
% 35.86/6.78
% 35.86/6.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.86/6.78
% 35.86/6.78
%------------------------------------------------------------------------------