%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM926+1 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 5 04:58:54 PM UTC 2026
% Result : Theorem 2.80s 3.61s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_134)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_38_le__number__of__eq__not__less,axiom,
! [X28,X18] :
( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
<=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_le__number__of__eq__not__less) ).
fof(fact_8_zadd__power3,axiom,
! [X3,X4] : power_power_int(plus_plus_int(X3,X4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(X3,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(X3,number_number_of_nat(bit0(bit1(pls))))),X4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),X3),power_power_int(X4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(X4,number_number_of_nat(bit1(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
fof(fact_111_number__of__is__id,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).
fof(fact_7_zadd__power2,axiom,
! [X3,X4] : power_power_int(plus_plus_int(X3,X4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X3),X4)),power_power_int(X4,number_number_of_nat(bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
fof(fact_10_power2__sum,axiom,
! [X5,X6] : power_power_int(plus_plus_int(X5,X6),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X5,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X6,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X5),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).
fof(fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
~ ! [X14] : plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ord_less_int(one_one_int,t)
=> ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one_int
=> ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_37_le__number__of__eq__not__less,axiom,
! [X28,X18] :
( ord_less_eq_nat(number_number_of_nat(X28),number_number_of_nat(X18))
<=> ~ ord_less_nat(number_number_of_nat(X18),number_number_of_nat(X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__number__of__eq__not__less) ).
fof(fact_62_add__nat__number__of,axiom,
! [X38,X39] :
( ( ord_less_int(X39,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(X38) )
& ( ~ ord_less_int(X39,pls)
=> ( ( ord_less_int(X38,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(X39) )
& ( ~ ord_less_int(X38,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(plus_plus_int(X39,X38)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add__nat__number__of) ).
fof(fact_11_power2__eq__square__number__of,axiom,
! [X7] : power_power_int(number_number_of_int(X7),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(X7),number_number_of_int(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__eq__square__number__of) ).
fof(fact_22_add__special_I2_J,axiom,
! [X12] : plus_plus_int(one_one_int,number_number_of_int(X12)) = number_number_of_int(plus_plus_int(bit1(pls),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__special_I2_J) ).
fof(fact_23_add__special_I3_J,axiom,
! [X13] : plus_plus_int(number_number_of_int(X13),one_one_int) = number_number_of_int(plus_plus_int(X13,bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__special_I3_J) ).
fof(fact_9_power2__sum,axiom,
! [X5,X6] : power_power_nat(plus_plus_nat(X5,X6),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X5,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(X6,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X5),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
fof(fact_6_qf1pt,axiom,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
fof(fact_5_t,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
fof(fact_3_t__l__p,axiom,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
fof(fact_4_p,axiom,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X10,X11] : power_power_nat(X10,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X11)) = times_times_nat(power_power_nat(X10,X11),power_power_nat(X10,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X10,X11] : power_power_int(X10,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X11)) = times_times_int(power_power_int(X10,X11),power_power_int(X10,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X44,X45,X46,X47] : times_times_nat(times_times_nat(X44,X45),times_times_nat(X46,X47)) = times_times_nat(X46,times_times_nat(times_times_nat(X44,X45),X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X44,X45,X46,X47] : times_times_int(times_times_int(X44,X45),times_times_int(X46,X47)) = times_times_int(X46,times_times_int(times_times_int(X44,X45),X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X48,X49,X50,X51] : times_times_nat(times_times_nat(X48,X49),times_times_nat(X50,X51)) = times_times_nat(X48,times_times_nat(X49,times_times_nat(X50,X51))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X48,X49,X50,X51] : times_times_int(times_times_int(X48,X49),times_times_int(X50,X51)) = times_times_int(X48,times_times_int(X49,times_times_int(X50,X51))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_13_cube__square,axiom,
! [X3] : times_times_int(X3,power_power_int(X3,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(X3,number_number_of_nat(bit1(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_cube__square) ).
fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X40,X41,X42,X43] : times_times_nat(times_times_nat(X40,X41),times_times_nat(X42,X43)) = times_times_nat(times_times_nat(X40,X42),times_times_nat(X41,X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X66,X67,X68,X69] : plus_plus_nat(plus_plus_nat(X66,X67),plus_plus_nat(X68,X69)) = plus_plus_nat(plus_plus_nat(X66,X68),plus_plus_nat(X67,X69)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X40,X41,X42,X43] : times_times_int(times_times_int(X40,X41),times_times_int(X42,X43)) = times_times_int(times_times_int(X40,X42),times_times_int(X41,X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X66,X67,X68,X69] : plus_plus_int(plus_plus_int(X66,X67),plus_plus_int(X68,X69)) = plus_plus_int(plus_plus_int(X66,X68),plus_plus_int(X67,X69)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_41_zadd__zless__mono,axiom,
! [X29,X16,X30,X15] :
( ord_less_int(X30,X15)
=> ( ord_less_eq_int(X29,X16)
=> ord_less_int(plus_plus_int(X30,X29),plus_plus_int(X15,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zadd__zless__mono) ).
fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X31,X32,X33] : times_times_nat(power_power_nat(X31,X32),power_power_nat(X31,X33)) = power_power_nat(X31,plus_plus_nat(X32,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X31,X32,X33] : times_times_int(power_power_int(X31,X32),power_power_int(X31,X33)) = power_power_int(X31,plus_plus_nat(X32,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_44_zpower__zadd__distrib,axiom,
! [X19,X20,X16] : power_power_int(X19,plus_plus_nat(X20,X16)) = times_times_int(power_power_int(X19,X20),power_power_int(X19,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zpower__zadd__distrib) ).
fof(fact_60_zadd__strict__right__mono,axiom,
! [X21,X22,X23] :
( ord_less_int(X22,X23)
=> ord_less_int(plus_plus_int(X22,X21),plus_plus_int(X23,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_zadd__strict__right__mono) ).
fof(fact_61_zadd__left__mono,axiom,
! [X21,X22,X23] :
( ord_less_eq_int(X22,X23)
=> ord_less_eq_int(plus_plus_int(X21,X22),plus_plus_int(X21,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_zadd__left__mono) ).
fof(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X52,X53,X54] : times_times_nat(times_times_nat(X52,X53),X54) = times_times_nat(times_times_nat(X52,X54),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X70,X71,X72] : plus_plus_nat(plus_plus_nat(X70,X71),X72) = plus_plus_nat(plus_plus_nat(X70,X72),X71),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X52,X53,X54] : times_times_int(times_times_int(X52,X53),X54) = times_times_int(times_times_int(X52,X54),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X70,X71,X72] : plus_plus_int(plus_plus_int(X70,X71),X72) = plus_plus_int(plus_plus_int(X70,X72),X71),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X55,X56,X57] : times_times_nat(times_times_nat(X55,X56),X57) = times_times_nat(X55,times_times_nat(X56,X57)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X24,X25,X26] : power_power_nat(power_power_nat(X24,X25),X26) = power_power_nat(X24,times_times_nat(X25,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X73,X74,X75] : plus_plus_nat(plus_plus_nat(X73,X74),X75) = plus_plus_nat(X73,plus_plus_nat(X74,X75)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_109_zmult__assoc,axiom,
! [X84,X85,X86] : times_times_int(times_times_int(X84,X85),X86) = times_times_int(X84,times_times_int(X85,X86)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_zmult__assoc) ).
fof(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X55,X56,X57] : times_times_int(times_times_int(X55,X56),X57) = times_times_int(X55,times_times_int(X56,X57)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_112_zadd__assoc,axiom,
! [X84,X85,X86] : plus_plus_int(plus_plus_int(X84,X85),X86) = plus_plus_int(X84,plus_plus_int(X85,X86)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_zadd__assoc) ).
fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X73,X74,X75] : plus_plus_int(plus_plus_int(X73,X74),X75) = plus_plus_int(X73,plus_plus_int(X74,X75)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_36_zpower__zpower,axiom,
! [X19,X20,X16] : power_power_int(power_power_int(X19,X20),X16) = power_power_int(X19,times_times_nat(X20,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zpower__zpower) ).
fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X24,X25,X26] : power_power_int(power_power_int(X24,X25),X26) = power_power_int(X24,times_times_nat(X25,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X58,X59,X60] : times_times_nat(X58,times_times_nat(X59,X60)) = times_times_nat(times_times_nat(X58,X59),X60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X76,X77,X78] : plus_plus_nat(X76,plus_plus_nat(X77,X78)) = plus_plus_nat(plus_plus_nat(X76,X77),X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X58,X59,X60] : times_times_int(X58,times_times_int(X59,X60)) = times_times_int(times_times_int(X58,X59),X60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X76,X77,X78] : plus_plus_int(X76,plus_plus_int(X77,X78)) = plus_plus_int(plus_plus_int(X76,X77),X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X61,X62,X63] : times_times_nat(X61,times_times_nat(X62,X63)) = times_times_nat(X62,times_times_nat(X61,X63)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X79,X80,X81] : plus_plus_nat(X79,plus_plus_nat(X80,X81)) = plus_plus_nat(X80,plus_plus_nat(X79,X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X61,X62,X63] : times_times_int(X61,times_times_int(X62,X63)) = times_times_int(X62,times_times_int(X61,X63)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_113_zadd__left__commute,axiom,
! [X19,X20,X16] : plus_plus_int(X19,plus_plus_int(X20,X16)) = plus_plus_int(X20,plus_plus_int(X19,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_zadd__left__commute) ).
fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X79,X80,X81] : plus_plus_int(X79,plus_plus_int(X80,X81)) = plus_plus_int(X80,plus_plus_int(X79,X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_12_power2__eq__square__number__of,axiom,
! [X7] : power_power_nat(number_number_of_nat(X7),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(X7),number_number_of_nat(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
fof(fact_72_add1__zle__eq,axiom,
! [X18,X17] :
( ord_less_eq_int(plus_plus_int(X18,one_one_int),X17)
<=> ord_less_int(X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add1__zle__eq) ).
fof(fact_73_zle__add1__eq__le,axiom,
! [X18,X17] :
( ord_less_int(X18,plus_plus_int(X17,one_one_int))
<=> ord_less_eq_int(X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zle__add1__eq__le) ).
fof(fact_71_zless__imp__add1__zle,axiom,
! [X15,X16] :
( ord_less_int(X15,X16)
=> ord_less_eq_int(plus_plus_int(X15,one_one_int),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zless__imp__add1__zle) ).
fof(fact_30_zle__trans,axiom,
! [X21,X22,X23] :
( ord_less_eq_int(X22,X23)
=> ( ord_less_eq_int(X23,X21)
=> ord_less_eq_int(X22,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zle__trans) ).
fof(fact_45_nat__mult__2,axiom,
! [X16] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),X16) = plus_plus_nat(X16,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__mult__2) ).
fof(fact_46_nat__mult__2__right,axiom,
! [X16] : times_times_nat(X16,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(X16,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat__mult__2__right) ).
fof(fact_19_power2__eq__square,axiom,
! [X9] : power_power_nat(X9,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_power2__eq__square) ).
fof(fact_18_power2__eq__square,axiom,
! [X9] : power_power_int(X9,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_power2__eq__square) ).
fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X8] : times_times_nat(X8,X8) = power_power_nat(X8,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X8] : times_times_int(X8,X8) = power_power_int(X8,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_54_rel__simps_I14_J,axiom,
! [X36,X37] :
( ord_less_int(bit0(X36),bit0(X37))
<=> ord_less_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I14_J) ).
fof(fact_53_less__int__code_I13_J,axiom,
! [X34,X35] :
( ord_less_int(bit0(X34),bit0(X35))
<=> ord_less_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_less__int__code_I13_J) ).
fof(fact_117_rel__simps_I16_J,axiom,
! [X36,X37] :
( ord_less_int(bit1(X36),bit0(X37))
<=> ord_less_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_rel__simps_I16_J) ).
fof(fact_116_less__int__code_I15_J,axiom,
! [X34,X35] :
( ord_less_int(bit1(X34),bit0(X35))
<=> ord_less_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_less__int__code_I15_J) ).
fof(fact_49_rel__simps_I17_J,axiom,
! [X36,X37] :
( ord_less_int(bit1(X36),bit1(X37))
<=> ord_less_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rel__simps_I17_J) ).
fof(fact_48_less__int__code_I16_J,axiom,
! [X34,X35] :
( ord_less_int(bit1(X34),bit1(X35))
<=> ord_less_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__int__code_I16_J) ).
fof(fact_68_rel__simps_I33_J,axiom,
! [X36,X37] :
( ord_less_eq_int(bit1(X36),bit0(X37))
<=> ord_less_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rel__simps_I33_J) ).
fof(fact_67_less__eq__int__code_I15_J,axiom,
! [X34,X35] :
( ord_less_eq_int(bit1(X34),bit0(X35))
<=> ord_less_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__eq__int__code_I15_J) ).
fof(fact_70_rel__simps_I15_J,axiom,
! [X36,X37] :
( ord_less_int(bit0(X36),bit1(X37))
<=> ord_less_eq_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I15_J) ).
fof(fact_69_less__int__code_I14_J,axiom,
! [X34,X35] :
( ord_less_int(bit0(X34),bit1(X35))
<=> ord_less_eq_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__int__code_I14_J) ).
fof(fact_57_rel__simps_I31_J,axiom,
! [X36,X37] :
( ord_less_eq_int(bit0(X36),bit0(X37))
<=> ord_less_eq_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I31_J) ).
fof(fact_56_less__eq__int__code_I13_J,axiom,
! [X34,X35] :
( ord_less_eq_int(bit0(X34),bit0(X35))
<=> ord_less_eq_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_less__eq__int__code_I13_J) ).
fof(fact_122_rel__simps_I32_J,axiom,
! [X36,X37] :
( ord_less_eq_int(bit0(X36),bit1(X37))
<=> ord_less_eq_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_rel__simps_I32_J) ).
fof(fact_121_less__eq__int__code_I14_J,axiom,
! [X34,X35] :
( ord_less_eq_int(bit0(X34),bit1(X35))
<=> ord_less_eq_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_less__eq__int__code_I14_J) ).
fof(fact_51_rel__simps_I34_J,axiom,
! [X36,X37] :
( ord_less_eq_int(bit1(X36),bit1(X37))
<=> ord_less_eq_int(X36,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I34_J) ).
fof(fact_50_less__eq__int__code_I16_J,axiom,
! [X34,X35] :
( ord_less_eq_int(bit1(X34),bit1(X35))
<=> ord_less_eq_int(X34,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__eq__int__code_I16_J) ).
fof(fact_31_zle__antisym,axiom,
! [X16,X15] :
( ord_less_eq_int(X16,X15)
=> ( ord_less_eq_int(X15,X16)
=> X16 = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_zle__antisym) ).
fof(fact_75_is__mult__sum2sq,axiom,
! [X20,X19] :
( twoSqu526106917sum2sq(X19)
=> ( twoSqu526106917sum2sq(X20)
=> twoSqu526106917sum2sq(times_times_int(X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_is__mult__sum2sq) ).
fof(fact_119_rel__simps_I4_J,axiom,
! [X36] :
( ord_less_int(pls,bit0(X36))
<=> ord_less_int(pls,X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rel__simps_I4_J) ).
fof(fact_66_rel__simps_I5_J,axiom,
! [X36] :
( ord_less_int(pls,bit1(X36))
<=> ord_less_eq_int(pls,X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I5_J) ).
fof(fact_120_rel__simps_I22_J,axiom,
! [X36] :
( ord_less_eq_int(pls,bit1(X36))
<=> ord_less_eq_int(pls,X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rel__simps_I22_J) ).
fof(fact_118_rel__simps_I10_J,axiom,
! [X36] :
( ord_less_int(bit0(X36),pls)
<=> ord_less_int(X36,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_rel__simps_I10_J) ).
fof(fact_115_rel__simps_I12_J,axiom,
! [X36] :
( ord_less_int(bit1(X36),pls)
<=> ord_less_int(X36,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_rel__simps_I12_J) ).
fof(fact_65_rel__simps_I29_J,axiom,
! [X36] :
( ord_less_eq_int(bit1(X36),pls)
<=> ord_less_int(X36,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_rel__simps_I29_J) ).
fof(fact_28_zless__le,axiom,
! [X17,X18] :
( ord_less_int(X17,X18)
<=> ( ord_less_eq_int(X17,X18)
& X17 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zless__le) ).
fof(fact_29_zless__linear,axiom,
! [X19,X20] :
( ord_less_int(X19,X20)
| X19 = X20
| ord_less_int(X20,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zless__linear) ).
fof(fact_27_zle__linear,axiom,
! [X16,X15] :
( ord_less_eq_int(X16,X15)
| ord_less_eq_int(X15,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zle__linear) ).
fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X64,X65] : times_times_nat(X64,X65) = times_times_nat(X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X82,X83] : plus_plus_nat(X82,X83) = plus_plus_nat(X83,X82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_110_zmult__commute,axiom,
! [X16,X15] : times_times_int(X16,X15) = times_times_int(X15,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_zmult__commute) ).
fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X64,X65] : times_times_int(X64,X65) = times_times_int(X65,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_114_zadd__commute,axiom,
! [X16,X15] : plus_plus_int(X16,X15) = plus_plus_int(X15,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zadd__commute) ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X82,X83] : plus_plus_int(X82,X83) = plus_plus_int(X83,X82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_24_one__add__one__is__two,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_one__add__one__is__two) ).
fof(fact_52_rel__simps_I2_J,axiom,
~ ord_less_int(pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I2_J) ).
fof(fact_74_zprime__2,axiom,
zprime(number_number_of_int(bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_zprime__2) ).
fof(fact_108_rel__simps_I48_J,axiom,
! [X36,X37] :
( bit0(X36) = bit0(X37)
<=> X36 = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_rel__simps_I48_J) ).
fof(fact_107_rel__simps_I51_J,axiom,
! [X36,X37] :
( bit1(X36) = bit1(X37)
<=> X36 = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_rel__simps_I51_J) ).
fof(fact_26_zle__refl,axiom,
! [X15] : ord_less_eq_int(X15,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_zle__refl) ).
fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X27] : power_power_nat(X27,one_one_nat) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X27] : power_power_int(X27,one_one_nat) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_14_one__power2,axiom,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_one__power2) ).
fof(fact_15_one__power2,axiom,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_one__power2) ).
fof(fact_47_nat__1__add__1,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__1__add__1) ).
fof(fact_55_rel__simps_I19_J,axiom,
ord_less_eq_int(pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I19_J) ).
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(fact_63_nat__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_nat__numeral__1__eq__1) ).
fof(fact_64_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Numeral1__eq1__nat) ).
fof(i_0_117,negated_conjecture,
~ ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_118,plain,
! [X28,X18] :
( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
<=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
inference(fof_simplification,[status(thm)],[fact_38_le__number__of__eq__not__less]) ).
fof(i_0_119,plain,
! [X337,X338] : power_power_int(plus_plus_int(X337,X338),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(X337,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(X337,number_number_of_nat(bit0(bit1(pls))))),X338)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),X337),power_power_int(X338,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(X338,number_number_of_nat(bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[fact_8_zadd__power3]) ).
fof(i_0_120,plain,
! [X552] : number_number_of_int(X552) = X552,
inference(variable_rename,[status(thm)],[fact_111_number__of__is__id]) ).
fof(i_0_121,plain,
! [X335,X336] : power_power_int(plus_plus_int(X335,X336),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X335,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X335),X336)),power_power_int(X336,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[fact_7_zadd__power2]) ).
fof(i_0_122,plain,
! [X341,X342] : power_power_int(plus_plus_int(X341,X342),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X341,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X342,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X341),X342)),
inference(variable_rename,[status(thm)],[fact_10_power2__sum]) ).
fof(i_0_123,negated_conjecture,
! [X573,X574] : plus_plus_int(power_power_int(X573,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X574,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_117])]) ).
fof(i_0_124,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_])])]) ).
fof(i_0_125,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).
fof(i_0_126,plain,
( t != one_one_int
| plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])]) ).
fof(i_0_127,plain,
! [X28,X18] :
( ord_less_eq_nat(number_number_of_nat(X28),number_number_of_nat(X18))
<=> ~ ord_less_nat(number_number_of_nat(X18),number_number_of_nat(X28)) ),
inference(fof_simplification,[status(thm)],[fact_37_le__number__of__eq__not__less]) ).
fof(i_0_128,plain,
! [X38,X39] :
( ( ord_less_int(X39,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(X38) )
& ( ~ ord_less_int(X39,pls)
=> ( ( ord_less_int(X38,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(X39) )
& ( ~ ord_less_int(X38,pls)
=> plus_plus_nat(number_number_of_nat(X39),number_number_of_nat(X38)) = number_number_of_nat(plus_plus_int(X39,X38)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_62_add__nat__number__of]) ).
fof(i_0_129,plain,
! [X343] : power_power_int(number_number_of_int(X343),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(X343),number_number_of_int(X343)),
inference(variable_rename,[status(thm)],[fact_11_power2__eq__square__number__of]) ).
fof(i_0_130,plain,
! [X382,X383] :
( ( ~ ord_less_eq_int(number_number_of_int(X382),number_number_of_int(X383))
| ~ ord_less_int(number_number_of_int(X383),number_number_of_int(X382)) )
& ( ord_less_int(number_number_of_int(X383),number_number_of_int(X382))
| ord_less_eq_int(number_number_of_int(X382),number_number_of_int(X383)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_118])]) ).
fof(i_0_131,plain,
! [X354] : plus_plus_int(one_one_int,number_number_of_int(X354)) = number_number_of_int(plus_plus_int(bit1(pls),X354)),
inference(variable_rename,[status(thm)],[fact_22_add__special_I2_J]) ).
fof(i_0_132,plain,
! [X355] : plus_plus_int(number_number_of_int(X355),one_one_int) = number_number_of_int(plus_plus_int(X355,bit1(pls))),
inference(variable_rename,[status(thm)],[fact_23_add__special_I3_J]) ).
cnf(i_0_133,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),X2)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),X1),power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(X2,number_number_of_nat(bit1(bit1(pls))))),
inference(split_conjunct,[status(thm)],[i_0_119]) ).
cnf(i_0_134,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_120]) ).
fof(i_0_135,plain,
! [X339,X340] : power_power_nat(plus_plus_nat(X339,X340),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X339,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(X340,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X339),X340)),
inference(variable_rename,[status(thm)],[fact_9_power2__sum]) ).
cnf(i_0_136,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X1),X2)),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[i_0_121]) ).
cnf(i_0_137,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_122]) ).
cnf(i_0_138,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(split_conjunct,[status(thm)],[i_0_123]) ).
cnf(i_0_139,plain,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
inference(split_conjunct,[status(thm)],[fact_6_qf1pt]) ).
cnf(i_0_140,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),esk5_0),
inference(split_conjunct,[status(thm)],[i_0_124]) ).
cnf(i_0_141,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(split_conjunct,[status(thm)],[fact_5_t]) ).
cnf(i_0_142,plain,
( plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| ~ ord_less_int(one_one_int,t) ),
inference(split_conjunct,[status(thm)],[i_0_125]) ).
cnf(i_0_143,plain,
( plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| t != one_one_int ),
inference(split_conjunct,[status(thm)],[i_0_126]) ).
cnf(i_0_144,plain,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(split_conjunct,[status(thm)],[fact_3_t__l__p]) ).
cnf(i_0_145,plain,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(split_conjunct,[status(thm)],[fact_4_p]) ).
fof(i_0_146,plain,
! [X352,X353] : power_power_nat(X352,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X353)) = times_times_nat(power_power_nat(X352,X353),power_power_nat(X352,X353)),
inference(variable_rename,[status(thm)],[fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(i_0_147,plain,
! [X350,X351] : power_power_int(X350,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X351)) = times_times_int(power_power_int(X350,X351),power_power_int(X350,X351)),
inference(variable_rename,[status(thm)],[fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(i_0_148,plain,
! [X461,X462,X463,X464] : times_times_nat(times_times_nat(X461,X462),times_times_nat(X463,X464)) = times_times_nat(X463,times_times_nat(times_times_nat(X461,X462),X464)),
inference(variable_rename,[status(thm)],[fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(i_0_149,plain,
! [X457,X458,X459,X460] : times_times_int(times_times_int(X457,X458),times_times_int(X459,X460)) = times_times_int(X459,times_times_int(times_times_int(X457,X458),X460)),
inference(variable_rename,[status(thm)],[fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(i_0_150,plain,
! [X469,X470,X471,X472] : times_times_nat(times_times_nat(X469,X470),times_times_nat(X471,X472)) = times_times_nat(X469,times_times_nat(X470,times_times_nat(X471,X472))),
inference(variable_rename,[status(thm)],[fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(i_0_151,plain,
! [X465,X466,X467,X468] : times_times_int(times_times_int(X465,X466),times_times_int(X467,X468)) = times_times_int(X465,times_times_int(X466,times_times_int(X467,X468))),
inference(variable_rename,[status(thm)],[fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(i_0_152,plain,
! [X345] : times_times_int(X345,power_power_int(X345,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(X345,number_number_of_nat(bit1(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_13_cube__square]) ).
fof(i_0_153,plain,
! [X453,X454,X455,X456] : times_times_nat(times_times_nat(X453,X454),times_times_nat(X455,X456)) = times_times_nat(times_times_nat(X453,X455),times_times_nat(X454,X456)),
inference(variable_rename,[status(thm)],[fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(i_0_154,plain,
! [X505,X506,X507,X508] : plus_plus_nat(plus_plus_nat(X505,X506),plus_plus_nat(X507,X508)) = plus_plus_nat(plus_plus_nat(X505,X507),plus_plus_nat(X506,X508)),
inference(variable_rename,[status(thm)],[fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(i_0_155,plain,
! [X449,X450,X451,X452] : times_times_int(times_times_int(X449,X450),times_times_int(X451,X452)) = times_times_int(times_times_int(X449,X451),times_times_int(X450,X452)),
inference(variable_rename,[status(thm)],[fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(i_0_156,plain,
! [X501,X502,X503,X504] : plus_plus_int(plus_plus_int(X501,X502),plus_plus_int(X503,X504)) = plus_plus_int(plus_plus_int(X501,X503),plus_plus_int(X502,X504)),
inference(variable_rename,[status(thm)],[fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(i_0_157,plain,
! [X388,X389,X390,X391] :
( ~ ord_less_int(X390,X391)
| ~ ord_less_eq_int(X388,X389)
| ord_less_int(plus_plus_int(X390,X388),plus_plus_int(X391,X389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_zadd__zless__mono])]) ).
fof(i_0_158,plain,
! [X395,X396,X397] : times_times_nat(power_power_nat(X395,X396),power_power_nat(X395,X397)) = power_power_nat(X395,plus_plus_nat(X396,X397)),
inference(variable_rename,[status(thm)],[fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(i_0_159,plain,
! [X392,X393,X394] : times_times_int(power_power_int(X392,X393),power_power_int(X392,X394)) = power_power_int(X392,plus_plus_nat(X393,X394)),
inference(variable_rename,[status(thm)],[fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(i_0_160,plain,
! [X398,X399,X400] : power_power_int(X398,plus_plus_nat(X399,X400)) = times_times_int(power_power_int(X398,X399),power_power_int(X398,X400)),
inference(variable_rename,[status(thm)],[fact_44_zpower__zadd__distrib]) ).
fof(i_0_161,plain,
! [X423,X424,X425] :
( ~ ord_less_int(X424,X425)
| ord_less_int(plus_plus_int(X424,X423),plus_plus_int(X425,X423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_zadd__strict__right__mono])]) ).
fof(i_0_162,plain,
! [X426,X427,X428] :
( ~ ord_less_eq_int(X427,X428)
| ord_less_eq_int(plus_plus_int(X426,X427),plus_plus_int(X426,X428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_zadd__left__mono])]) ).
fof(i_0_163,plain,
! [X380,X381] :
( ( ~ ord_less_eq_nat(number_number_of_nat(X380),number_number_of_nat(X381))
| ~ ord_less_nat(number_number_of_nat(X381),number_number_of_nat(X380)) )
& ( ord_less_nat(number_number_of_nat(X381),number_number_of_nat(X380))
| ord_less_eq_nat(number_number_of_nat(X380),number_number_of_nat(X381)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_127])]) ).
fof(i_0_164,plain,
! [X429,X430] :
( ( ~ ord_less_int(X430,pls)
| plus_plus_nat(number_number_of_nat(X430),number_number_of_nat(X429)) = number_number_of_nat(X429) )
& ( ~ ord_less_int(X429,pls)
| plus_plus_nat(number_number_of_nat(X430),number_number_of_nat(X429)) = number_number_of_nat(X430)
| ord_less_int(X430,pls) )
& ( ord_less_int(X429,pls)
| plus_plus_nat(number_number_of_nat(X430),number_number_of_nat(X429)) = number_number_of_nat(plus_plus_int(X430,X429))
| ord_less_int(X430,pls) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_128])])]) ).
fof(i_0_165,plain,
! [X476,X477,X478] : times_times_nat(times_times_nat(X476,X477),X478) = times_times_nat(times_times_nat(X476,X478),X477),
inference(variable_rename,[status(thm)],[fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(i_0_166,plain,
! [X512,X513,X514] : plus_plus_nat(plus_plus_nat(X512,X513),X514) = plus_plus_nat(plus_plus_nat(X512,X514),X513),
inference(variable_rename,[status(thm)],[fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(i_0_167,plain,
! [X473,X474,X475] : times_times_int(times_times_int(X473,X474),X475) = times_times_int(times_times_int(X473,X475),X474),
inference(variable_rename,[status(thm)],[fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(i_0_168,plain,
! [X509,X510,X511] : plus_plus_int(plus_plus_int(X509,X510),X511) = plus_plus_int(plus_plus_int(X509,X511),X510),
inference(variable_rename,[status(thm)],[fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(i_0_169,plain,
! [X482,X483,X484] : times_times_nat(times_times_nat(X482,X483),X484) = times_times_nat(X482,times_times_nat(X483,X484)),
inference(variable_rename,[status(thm)],[fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(i_0_170,plain,
! [X372,X373,X374] : power_power_nat(power_power_nat(X372,X373),X374) = power_power_nat(X372,times_times_nat(X373,X374)),
inference(variable_rename,[status(thm)],[fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(i_0_171,plain,
! [X518,X519,X520] : plus_plus_nat(plus_plus_nat(X518,X519),X520) = plus_plus_nat(X518,plus_plus_nat(X519,X520)),
inference(variable_rename,[status(thm)],[fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(i_0_172,plain,
! [X547,X548,X549] : times_times_int(times_times_int(X547,X548),X549) = times_times_int(X547,times_times_int(X548,X549)),
inference(variable_rename,[status(thm)],[fact_109_zmult__assoc]) ).
fof(i_0_173,plain,
! [X479,X480,X481] : times_times_int(times_times_int(X479,X480),X481) = times_times_int(X479,times_times_int(X480,X481)),
inference(variable_rename,[status(thm)],[fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(i_0_174,plain,
! [X553,X554,X555] : plus_plus_int(plus_plus_int(X553,X554),X555) = plus_plus_int(X553,plus_plus_int(X554,X555)),
inference(variable_rename,[status(thm)],[fact_112_zadd__assoc]) ).
fof(i_0_175,plain,
! [X515,X516,X517] : plus_plus_int(plus_plus_int(X515,X516),X517) = plus_plus_int(X515,plus_plus_int(X516,X517)),
inference(variable_rename,[status(thm)],[fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(i_0_176,plain,
! [X377,X378,X379] : power_power_int(power_power_int(X377,X378),X379) = power_power_int(X377,times_times_nat(X378,X379)),
inference(variable_rename,[status(thm)],[fact_36_zpower__zpower]) ).
fof(i_0_177,plain,
! [X369,X370,X371] : power_power_int(power_power_int(X369,X370),X371) = power_power_int(X369,times_times_nat(X370,X371)),
inference(variable_rename,[status(thm)],[fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(i_0_178,plain,
! [X488,X489,X490] : times_times_nat(X488,times_times_nat(X489,X490)) = times_times_nat(times_times_nat(X488,X489),X490),
inference(variable_rename,[status(thm)],[fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(i_0_179,plain,
! [X524,X525,X526] : plus_plus_nat(X524,plus_plus_nat(X525,X526)) = plus_plus_nat(plus_plus_nat(X524,X525),X526),
inference(variable_rename,[status(thm)],[fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(i_0_180,plain,
! [X485,X486,X487] : times_times_int(X485,times_times_int(X486,X487)) = times_times_int(times_times_int(X485,X486),X487),
inference(variable_rename,[status(thm)],[fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(i_0_181,plain,
! [X521,X522,X523] : plus_plus_int(X521,plus_plus_int(X522,X523)) = plus_plus_int(plus_plus_int(X521,X522),X523),
inference(variable_rename,[status(thm)],[fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(i_0_182,plain,
! [X494,X495,X496] : times_times_nat(X494,times_times_nat(X495,X496)) = times_times_nat(X495,times_times_nat(X494,X496)),
inference(variable_rename,[status(thm)],[fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(i_0_183,plain,
! [X530,X531,X532] : plus_plus_nat(X530,plus_plus_nat(X531,X532)) = plus_plus_nat(X531,plus_plus_nat(X530,X532)),
inference(variable_rename,[status(thm)],[fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(i_0_184,plain,
! [X491,X492,X493] : times_times_int(X491,times_times_int(X492,X493)) = times_times_int(X492,times_times_int(X491,X493)),
inference(variable_rename,[status(thm)],[fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(i_0_185,plain,
! [X556,X557,X558] : plus_plus_int(X556,plus_plus_int(X557,X558)) = plus_plus_int(X557,plus_plus_int(X556,X558)),
inference(variable_rename,[status(thm)],[fact_113_zadd__left__commute]) ).
fof(i_0_186,plain,
! [X527,X528,X529] : plus_plus_int(X527,plus_plus_int(X528,X529)) = plus_plus_int(X528,plus_plus_int(X527,X529)),
inference(variable_rename,[status(thm)],[fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(i_0_187,plain,
! [X344] : power_power_nat(number_number_of_nat(X344),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(X344),number_number_of_nat(X344)),
inference(variable_rename,[status(thm)],[fact_12_power2__eq__square__number__of]) ).
fof(i_0_188,plain,
! [X443,X444] :
( ( ~ ord_less_eq_int(plus_plus_int(X443,one_one_int),X444)
| ord_less_int(X443,X444) )
& ( ~ ord_less_int(X443,X444)
| ord_less_eq_int(plus_plus_int(X443,one_one_int),X444) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_add1__zle__eq])]) ).
fof(i_0_189,plain,
! [X445,X446] :
( ( ~ ord_less_int(X445,plus_plus_int(X446,one_one_int))
| ord_less_eq_int(X445,X446) )
& ( ~ ord_less_eq_int(X445,X446)
| ord_less_int(X445,plus_plus_int(X446,one_one_int)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_zle__add1__eq__le])]) ).
fof(i_0_190,plain,
! [X441,X442] :
( ~ ord_less_int(X441,X442)
| ord_less_eq_int(plus_plus_int(X441,one_one_int),X442) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_zless__imp__add1__zle])]) ).
fof(i_0_191,plain,
! [X364,X365,X366] :
( ~ ord_less_eq_int(X365,X366)
| ~ ord_less_eq_int(X366,X364)
| ord_less_eq_int(X365,X364) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_zle__trans])]) ).
fof(i_0_192,plain,
! [X401] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),X401) = plus_plus_nat(X401,X401),
inference(variable_rename,[status(thm)],[fact_45_nat__mult__2]) ).
fof(i_0_193,plain,
! [X402] : times_times_nat(X402,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(X402,X402),
inference(variable_rename,[status(thm)],[fact_46_nat__mult__2__right]) ).
fof(i_0_194,plain,
! [X349] : power_power_nat(X349,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(X349,X349),
inference(variable_rename,[status(thm)],[fact_19_power2__eq__square]) ).
fof(i_0_195,plain,
! [X348] : power_power_int(X348,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X348,X348),
inference(variable_rename,[status(thm)],[fact_18_power2__eq__square]) ).
cnf(i_0_196,plain,
power_power_int(number_number_of_int(X1),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(X1),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[i_0_129]) ).
fof(i_0_197,plain,
! [X347] : times_times_nat(X347,X347) = power_power_nat(X347,number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(i_0_198,plain,
! [X346] : times_times_int(X346,X346) = power_power_int(X346,number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(i_0_199,plain,
! [X413,X414] :
( ( ~ ord_less_int(bit0(X413),bit0(X414))
| ord_less_int(X413,X414) )
& ( ~ ord_less_int(X413,X414)
| ord_less_int(bit0(X413),bit0(X414)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_rel__simps_I14_J])]) ).
fof(i_0_200,plain,
! [X411,X412] :
( ( ~ ord_less_int(bit0(X411),bit0(X412))
| ord_less_int(X411,X412) )
& ( ~ ord_less_int(X411,X412)
| ord_less_int(bit0(X411),bit0(X412)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_53_less__int__code_I13_J])]) ).
fof(i_0_201,plain,
! [X564,X565] :
( ( ~ ord_less_int(bit1(X564),bit0(X565))
| ord_less_int(X564,X565) )
& ( ~ ord_less_int(X564,X565)
| ord_less_int(bit1(X564),bit0(X565)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_rel__simps_I16_J])]) ).
fof(i_0_202,plain,
! [X562,X563] :
( ( ~ ord_less_int(bit1(X562),bit0(X563))
| ord_less_int(X562,X563) )
& ( ~ ord_less_int(X562,X563)
| ord_less_int(bit1(X562),bit0(X563)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_less__int__code_I15_J])]) ).
fof(i_0_203,plain,
! [X405,X406] :
( ( ~ ord_less_int(bit1(X405),bit1(X406))
| ord_less_int(X405,X406) )
& ( ~ ord_less_int(X405,X406)
| ord_less_int(bit1(X405),bit1(X406)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_rel__simps_I17_J])]) ).
fof(i_0_204,plain,
! [X403,X404] :
( ( ~ ord_less_int(bit1(X403),bit1(X404))
| ord_less_int(X403,X404) )
& ( ~ ord_less_int(X403,X404)
| ord_less_int(bit1(X403),bit1(X404)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_less__int__code_I16_J])]) ).
fof(i_0_205,plain,
! [X435,X436] :
( ( ~ ord_less_eq_int(bit1(X435),bit0(X436))
| ord_less_int(X435,X436) )
& ( ~ ord_less_int(X435,X436)
| ord_less_eq_int(bit1(X435),bit0(X436)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_rel__simps_I33_J])]) ).
fof(i_0_206,plain,
! [X433,X434] :
( ( ~ ord_less_eq_int(bit1(X433),bit0(X434))
| ord_less_int(X433,X434) )
& ( ~ ord_less_int(X433,X434)
| ord_less_eq_int(bit1(X433),bit0(X434)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_less__eq__int__code_I15_J])]) ).
fof(i_0_207,plain,
! [X439,X440] :
( ( ~ ord_less_int(bit0(X439),bit1(X440))
| ord_less_eq_int(X439,X440) )
& ( ~ ord_less_eq_int(X439,X440)
| ord_less_int(bit0(X439),bit1(X440)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_rel__simps_I15_J])]) ).
fof(i_0_208,plain,
! [X437,X438] :
( ( ~ ord_less_int(bit0(X437),bit1(X438))
| ord_less_eq_int(X437,X438) )
& ( ~ ord_less_eq_int(X437,X438)
| ord_less_int(bit0(X437),bit1(X438)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_less__int__code_I14_J])]) ).
fof(i_0_209,plain,
! [X417,X418] :
( ( ~ ord_less_eq_int(bit0(X417),bit0(X418))
| ord_less_eq_int(X417,X418) )
& ( ~ ord_less_eq_int(X417,X418)
| ord_less_eq_int(bit0(X417),bit0(X418)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_rel__simps_I31_J])]) ).
fof(i_0_210,plain,
! [X415,X416] :
( ( ~ ord_less_eq_int(bit0(X415),bit0(X416))
| ord_less_eq_int(X415,X416) )
& ( ~ ord_less_eq_int(X415,X416)
| ord_less_eq_int(bit0(X415),bit0(X416)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_less__eq__int__code_I13_J])]) ).
fof(i_0_211,plain,
! [X571,X572] :
( ( ~ ord_less_eq_int(bit0(X571),bit1(X572))
| ord_less_eq_int(X571,X572) )
& ( ~ ord_less_eq_int(X571,X572)
| ord_less_eq_int(bit0(X571),bit1(X572)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_122_rel__simps_I32_J])]) ).
fof(i_0_212,plain,
! [X569,X570] :
( ( ~ ord_less_eq_int(bit0(X569),bit1(X570))
| ord_less_eq_int(X569,X570) )
& ( ~ ord_less_eq_int(X569,X570)
| ord_less_eq_int(bit0(X569),bit1(X570)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_121_less__eq__int__code_I14_J])]) ).
fof(i_0_213,plain,
! [X409,X410] :
( ( ~ ord_less_eq_int(bit1(X409),bit1(X410))
| ord_less_eq_int(X409,X410) )
& ( ~ ord_less_eq_int(X409,X410)
| ord_less_eq_int(bit1(X409),bit1(X410)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_rel__simps_I34_J])]) ).
fof(i_0_214,plain,
! [X407,X408] :
( ( ~ ord_less_eq_int(bit1(X407),bit1(X408))
| ord_less_eq_int(X407,X408) )
& ( ~ ord_less_eq_int(X407,X408)
| ord_less_eq_int(bit1(X407),bit1(X408)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_less__eq__int__code_I16_J])]) ).
fof(i_0_215,plain,
! [X367,X368] :
( ~ ord_less_eq_int(X367,X368)
| ~ ord_less_eq_int(X368,X367)
| X367 = X368 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_zle__antisym])]) ).
cnf(i_0_216,plain,
( ~ ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2))
| ~ ord_less_int(number_number_of_int(X2),number_number_of_int(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_130]) ).
fof(i_0_217,plain,
! [X447,X448] :
( ~ twoSqu526106917sum2sq(X448)
| ~ twoSqu526106917sum2sq(X447)
| twoSqu526106917sum2sq(times_times_int(X448,X447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_is__mult__sum2sq])]) ).
fof(i_0_218,plain,
! [X567] :
( ( ~ ord_less_int(pls,bit0(X567))
| ord_less_int(pls,X567) )
& ( ~ ord_less_int(pls,X567)
| ord_less_int(pls,bit0(X567)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_rel__simps_I4_J])]) ).
fof(i_0_219,plain,
! [X432] :
( ( ~ ord_less_int(pls,bit1(X432))
| ord_less_eq_int(pls,X432) )
& ( ~ ord_less_eq_int(pls,X432)
| ord_less_int(pls,bit1(X432)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_rel__simps_I5_J])]) ).
fof(i_0_220,plain,
! [X568] :
( ( ~ ord_less_eq_int(pls,bit1(X568))
| ord_less_eq_int(pls,X568) )
& ( ~ ord_less_eq_int(pls,X568)
| ord_less_eq_int(pls,bit1(X568)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_120_rel__simps_I22_J])]) ).
fof(i_0_221,plain,
! [X566] :
( ( ~ ord_less_int(bit0(X566),pls)
| ord_less_int(X566,pls) )
& ( ~ ord_less_int(X566,pls)
| ord_less_int(bit0(X566),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_rel__simps_I10_J])]) ).
fof(i_0_222,plain,
! [X561] :
( ( ~ ord_less_int(bit1(X561),pls)
| ord_less_int(X561,pls) )
& ( ~ ord_less_int(X561,pls)
| ord_less_int(bit1(X561),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_115_rel__simps_I12_J])]) ).
fof(i_0_223,plain,
! [X431] :
( ( ~ ord_less_eq_int(bit1(X431),pls)
| ord_less_int(X431,pls) )
& ( ~ ord_less_int(X431,pls)
| ord_less_eq_int(bit1(X431),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_rel__simps_I29_J])]) ).
fof(i_0_224,plain,
! [X360,X361] :
( ( ord_less_eq_int(X360,X361)
| ~ ord_less_int(X360,X361) )
& ( X360 != X361
| ~ ord_less_int(X360,X361) )
& ( ~ ord_less_eq_int(X360,X361)
| X360 = X361
| ord_less_int(X360,X361) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_zless__le])])]) ).
fof(i_0_225,plain,
! [X362,X363] :
( ord_less_int(X362,X363)
| X362 = X363
| ord_less_int(X363,X362) ),
inference(variable_rename,[status(thm)],[fact_29_zless__linear]) ).
cnf(i_0_226,plain,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(bit1(pls),X1)),
inference(split_conjunct,[status(thm)],[i_0_131]) ).
cnf(i_0_227,plain,
plus_plus_int(number_number_of_int(X1),one_one_int) = number_number_of_int(plus_plus_int(X1,bit1(pls))),
inference(split_conjunct,[status(thm)],[i_0_132]) ).
cnf(i_0_228,plain,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_eq_int(number_number_of_int(X2),number_number_of_int(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_130]) ).
fof(i_0_229,plain,
! [X358,X359] :
( ord_less_eq_int(X358,X359)
| ord_less_eq_int(X359,X358) ),
inference(variable_rename,[status(thm)],[fact_27_zle__linear]) ).
fof(i_0_230,plain,
! [X499,X500] : times_times_nat(X499,X500) = times_times_nat(X500,X499),
inference(variable_rename,[status(thm)],[fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(i_0_231,plain,
! [X535,X536] : plus_plus_nat(X535,X536) = plus_plus_nat(X536,X535),
inference(variable_rename,[status(thm)],[fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(i_0_232,plain,
! [X550,X551] : times_times_int(X550,X551) = times_times_int(X551,X550),
inference(variable_rename,[status(thm)],[fact_110_zmult__commute]) ).
fof(i_0_233,plain,
! [X497,X498] : times_times_int(X497,X498) = times_times_int(X498,X497),
inference(variable_rename,[status(thm)],[fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(i_0_234,plain,
! [X559,X560] : plus_plus_int(X559,X560) = plus_plus_int(X560,X559),
inference(variable_rename,[status(thm)],[fact_114_zadd__commute]) ).
fof(i_0_235,plain,
! [X533,X534] : plus_plus_int(X533,X534) = plus_plus_int(X534,X533),
inference(variable_rename,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
cnf(i_0_236,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_24_one__add__one__is__two]) ).
fof(i_0_237,plain,
~ ord_less_int(pls,pls),
inference(fof_simplification,[status(thm)],[fact_52_rel__simps_I2_J]) ).
cnf(i_0_238,plain,
zprime(number_number_of_int(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[fact_74_zprime__2]) ).
fof(i_0_239,plain,
! [X545,X546] :
( ( bit0(X545) != bit0(X546)
| X545 = X546 )
& ( X545 != X546
| bit0(X545) = bit0(X546) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_108_rel__simps_I48_J])]) ).
fof(i_0_240,plain,
! [X543,X544] :
( ( bit1(X543) != bit1(X544)
| X543 = X544 )
& ( X543 != X544
| bit1(X543) = bit1(X544) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_107_rel__simps_I51_J])]) ).
fof(i_0_241,plain,
! [X357] : ord_less_eq_int(X357,X357),
inference(variable_rename,[status(thm)],[fact_26_zle__refl]) ).
fof(i_0_242,plain,
! [X376] : power_power_nat(X376,one_one_nat) = X376,
inference(variable_rename,[status(thm)],[fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(i_0_243,plain,
! [X375] : power_power_int(X375,one_one_nat) = X375,
inference(variable_rename,[status(thm)],[fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
cnf(i_0_244,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(bit1(bit1(pls)),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),X2)),times_times_int(times_times_int(bit1(bit1(pls)),X1),power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(X2,number_number_of_nat(bit1(bit1(pls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_133,c_0_134]),c_0_134]),
[final] ).
cnf(i_0_245,plain,
power_power_nat(plus_plus_nat(X1,X2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(X2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_246,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(bit0(bit1(pls)),X1),X2)),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),
inference(rw,[status(thm)],[i_0_136,c_0_134]),
[final] ).
cnf(i_0_247,plain,
power_power_int(plus_plus_int(X1,X2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(bit0(bit1(pls)),X1),X2)),
inference(rw,[status(thm)],[i_0_137,c_0_134]),
[final] ).
cnf(i_0_248,negated_conjecture,
plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),
inference(rw,[status(thm)],[i_0_138,c_0_134]),
[final] ).
cnf(i_0_249,plain,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),t)),
inference(rw,[status(thm)],[i_0_139,c_0_134]),
[final] ).
cnf(i_0_250,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),esk5_0),
inference(rw,[status(thm)],[i_0_140,c_0_134]),
[final] ).
cnf(i_0_251,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),t),
inference(rw,[status(thm)],[i_0_141,c_0_134]),
[final] ).
cnf(i_0_252,plain,
( plus_plus_int(power_power_int(esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk4_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)
| ~ ord_less_int(one_one_int,t) ),
inference(rw,[status(thm)],[i_0_142,c_0_134]),
[final] ).
cnf(i_0_253,plain,
( plus_plus_int(power_power_int(esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(esk2_0,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)
| t != one_one_int ),
inference(rw,[status(thm)],[i_0_143,c_0_134]),
[final] ).
cnf(i_0_254,plain,
ord_less_int(t,plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)),
inference(rw,[status(thm)],[i_0_144,c_0_134]),
[final] ).
cnf(i_0_255,plain,
zprime(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)),
inference(rw,[status(thm)],[i_0_145,c_0_134]),
[final] ).
cnf(i_0_256,plain,
power_power_nat(X1,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X2)) = times_times_nat(power_power_nat(X1,X2),power_power_nat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_257,plain,
power_power_int(X1,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X2)) = times_times_int(power_power_int(X1,X2),power_power_int(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_258,plain,
times_times_nat(times_times_nat(X1,X2),times_times_nat(X3,X4)) = times_times_nat(X3,times_times_nat(times_times_nat(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_259,plain,
times_times_int(times_times_int(X1,X2),times_times_int(X3,X4)) = times_times_int(X3,times_times_int(times_times_int(X1,X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_260,plain,
times_times_nat(times_times_nat(X1,X2),times_times_nat(X3,X4)) = times_times_nat(X1,times_times_nat(X2,times_times_nat(X3,X4))),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_261,plain,
times_times_int(times_times_int(X1,X2),times_times_int(X3,X4)) = times_times_int(X1,times_times_int(X2,times_times_int(X3,X4))),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_262,plain,
times_times_int(X1,power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(X1,number_number_of_nat(bit1(bit1(pls)))),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_263,plain,
times_times_nat(times_times_nat(X1,X2),times_times_nat(X3,X4)) = times_times_nat(times_times_nat(X1,X3),times_times_nat(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_264,plain,
plus_plus_nat(plus_plus_nat(X1,X2),plus_plus_nat(X3,X4)) = plus_plus_nat(plus_plus_nat(X1,X3),plus_plus_nat(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_265,plain,
times_times_int(times_times_int(X1,X2),times_times_int(X3,X4)) = times_times_int(times_times_int(X1,X3),times_times_int(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_266,plain,
plus_plus_int(plus_plus_int(X1,X2),plus_plus_int(X3,X4)) = plus_plus_int(plus_plus_int(X1,X3),plus_plus_int(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_267,plain,
( ord_less_int(plus_plus_int(X1,X3),plus_plus_int(X2,X4))
| ~ ord_less_int(X1,X2)
| ~ ord_less_eq_int(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_268,plain,
times_times_nat(power_power_nat(X1,X2),power_power_nat(X1,X3)) = power_power_nat(X1,plus_plus_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_269,plain,
times_times_int(power_power_int(X1,X2),power_power_int(X1,X3)) = power_power_int(X1,plus_plus_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_270,plain,
power_power_int(X1,plus_plus_nat(X2,X3)) = times_times_int(power_power_int(X1,X2),power_power_int(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_271,plain,
( ord_less_int(plus_plus_int(X1,X3),plus_plus_int(X2,X3))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_272,plain,
( ord_less_eq_int(plus_plus_int(X3,X1),plus_plus_int(X3,X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_273,plain,
( ~ ord_less_eq_nat(number_number_of_nat(X1),number_number_of_nat(X2))
| ~ ord_less_nat(number_number_of_nat(X2),number_number_of_nat(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_274,plain,
( ord_less_int(X1,pls)
| plus_plus_nat(number_number_of_nat(X2),number_number_of_nat(X1)) = number_number_of_nat(plus_plus_int(X2,X1))
| ord_less_int(X2,pls) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_275,plain,
times_times_nat(times_times_nat(X1,X2),X3) = times_times_nat(times_times_nat(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_276,plain,
plus_plus_nat(plus_plus_nat(X1,X2),X3) = plus_plus_nat(plus_plus_nat(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_277,plain,
times_times_int(times_times_int(X1,X2),X3) = times_times_int(times_times_int(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_278,plain,
plus_plus_int(plus_plus_int(X1,X2),X3) = plus_plus_int(plus_plus_int(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_279,plain,
times_times_nat(times_times_nat(X1,X2),X3) = times_times_nat(X1,times_times_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_280,plain,
power_power_nat(power_power_nat(X1,X2),X3) = power_power_nat(X1,times_times_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_170]),
[final] ).
cnf(i_0_281,plain,
plus_plus_nat(plus_plus_nat(X1,X2),X3) = plus_plus_nat(X1,plus_plus_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_282,plain,
times_times_int(times_times_int(X1,X2),X3) = times_times_int(X1,times_times_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_283,plain,
times_times_int(times_times_int(X1,X2),X3) = times_times_int(X1,times_times_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_173]),
[final] ).
cnf(i_0_284,plain,
plus_plus_int(plus_plus_int(X1,X2),X3) = plus_plus_int(X1,plus_plus_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_285,plain,
plus_plus_int(plus_plus_int(X1,X2),X3) = plus_plus_int(X1,plus_plus_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_175]),
[final] ).
cnf(i_0_286,plain,
power_power_int(power_power_int(X1,X2),X3) = power_power_int(X1,times_times_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_287,plain,
power_power_int(power_power_int(X1,X2),X3) = power_power_int(X1,times_times_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_288,plain,
times_times_nat(X1,times_times_nat(X2,X3)) = times_times_nat(times_times_nat(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_289,plain,
plus_plus_nat(X1,plus_plus_nat(X2,X3)) = plus_plus_nat(plus_plus_nat(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_290,plain,
times_times_int(X1,times_times_int(X2,X3)) = times_times_int(times_times_int(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_291,plain,
plus_plus_int(X1,plus_plus_int(X2,X3)) = plus_plus_int(plus_plus_int(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_292,plain,
times_times_nat(X1,times_times_nat(X2,X3)) = times_times_nat(X2,times_times_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_293,plain,
plus_plus_nat(X1,plus_plus_nat(X2,X3)) = plus_plus_nat(X2,plus_plus_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_294,plain,
times_times_int(X1,times_times_int(X2,X3)) = times_times_int(X2,times_times_int(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_295,plain,
plus_plus_int(X1,plus_plus_int(X2,X3)) = plus_plus_int(X2,plus_plus_int(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_296,plain,
plus_plus_int(X1,plus_plus_int(X2,X3)) = plus_plus_int(X2,plus_plus_int(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_297,plain,
power_power_nat(number_number_of_nat(X1),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(X1),number_number_of_nat(X1)),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_298,plain,
( ord_less_int(X1,X2)
| ~ ord_less_eq_int(plus_plus_int(X1,one_one_int),X2) ),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_299,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_int(X1,plus_plus_int(X2,one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_300,plain,
( plus_plus_nat(number_number_of_nat(X2),number_number_of_nat(X1)) = number_number_of_nat(X2)
| ord_less_int(X2,pls)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_301,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_302,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_303,plain,
( ord_less_int(X1,plus_plus_int(X2,one_one_int))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_304,plain,
( ord_less_eq_int(X1,X3)
| ~ ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_191]),
[final] ).
cnf(i_0_305,plain,
times_times_nat(number_number_of_nat(bit0(bit1(pls))),X1) = plus_plus_nat(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_192]),
[final] ).
cnf(i_0_306,plain,
times_times_nat(X1,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_307,plain,
power_power_nat(X1,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_194]),
[final] ).
cnf(i_0_308,plain,
power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_309,plain,
power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_196,c_0_134]),c_0_134]),c_0_134]),
[final] ).
cnf(i_0_310,plain,
times_times_nat(X1,X1) = power_power_nat(X1,number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[i_0_197]),
[final] ).
cnf(i_0_311,plain,
times_times_int(X1,X1) = power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_312,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_313,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_314,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_315,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_316,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_317,plain,
( ord_less_int(X1,X2)
| ~ ord_less_int(bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_318,plain,
( ord_less_int(X1,X2)
| ~ ord_less_eq_int(bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_319,plain,
( ord_less_int(X1,X2)
| ~ ord_less_eq_int(bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_206]),
[final] ).
cnf(i_0_320,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_int(bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_321,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_int(bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_322,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_323,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_324,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_325,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_326,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_327,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_328,plain,
( ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2))
| ord_less_eq_nat(number_number_of_nat(X2),number_number_of_nat(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_329,plain,
( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X2)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_330,plain,
( ord_less_int(bit0(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_331,plain,
( ord_less_int(bit0(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_332,plain,
( ord_less_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_333,plain,
( ord_less_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_334,plain,
( ord_less_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_335,plain,
( ord_less_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_336,plain,
( ord_less_int(bit1(X1),bit1(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_337,plain,
( ord_less_int(bit1(X1),bit1(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_338,plain,
( ord_less_eq_int(bit0(X1),bit0(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_339,plain,
( ord_less_eq_int(bit0(X1),bit0(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_340,plain,
( ord_less_eq_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_341,plain,
( ord_less_eq_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_342,plain,
( ord_less_eq_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_343,plain,
( ord_less_eq_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_206]),
[final] ).
cnf(i_0_344,plain,
( ord_less_eq_int(bit1(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_345,plain,
( ord_less_eq_int(bit1(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_346,plain,
( X1 = X2
| ~ ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_215]),
[final] ).
cnf(i_0_347,plain,
( ~ ord_less_eq_int(X1,X2)
| ~ ord_less_int(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_216,c_0_134]),c_0_134]),c_0_134]),c_0_134]),
[final] ).
cnf(i_0_348,plain,
( twoSqu526106917sum2sq(times_times_int(X1,X2))
| ~ twoSqu526106917sum2sq(X1)
| ~ twoSqu526106917sum2sq(X2) ),
inference(split_conjunct,[status(thm)],[i_0_217]),
[final] ).
cnf(i_0_349,plain,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(split_conjunct,[status(thm)],[fact_14_one__power2]),
[final] ).
cnf(i_0_350,plain,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(split_conjunct,[status(thm)],[fact_15_one__power2]),
[final] ).
cnf(i_0_351,plain,
( ord_less_int(pls,X1)
| ~ ord_less_int(pls,bit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_352,plain,
( ord_less_eq_int(pls,X1)
| ~ ord_less_int(pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_353,plain,
( ord_less_eq_int(pls,X1)
| ~ ord_less_eq_int(pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_354,plain,
( ord_less_int(X1,pls)
| ~ ord_less_int(bit0(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_355,plain,
( ord_less_int(X1,pls)
| ~ ord_less_int(bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_222]),
[final] ).
cnf(i_0_356,plain,
( ord_less_int(X1,pls)
| ~ ord_less_eq_int(bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_357,plain,
( X1 = X2
| ord_less_int(X1,X2)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_358,plain,
( ord_less_int(bit0(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_359,plain,
( ord_less_int(bit1(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_222]),
[final] ).
cnf(i_0_360,plain,
( ord_less_eq_int(bit1(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_361,plain,
( ord_less_int(pls,bit0(X1))
| ~ ord_less_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_362,plain,
( ord_less_int(pls,bit1(X1))
| ~ ord_less_eq_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_363,plain,
( ord_less_eq_int(pls,bit1(X1))
| ~ ord_less_eq_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_364,plain,
( ord_less_eq_int(X1,X2)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_365,plain,
( ord_less_int(X1,X2)
| X1 = X2
| ord_less_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_366,plain,
plus_plus_int(one_one_int,X1) = plus_plus_int(bit1(pls),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_226,c_0_134]),c_0_134]),
[final] ).
cnf(i_0_367,plain,
plus_plus_int(X1,one_one_int) = plus_plus_int(X1,bit1(pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_227,c_0_134]),c_0_134]),
[final] ).
cnf(i_0_368,plain,
( ord_less_eq_int(X2,X1)
| ord_less_int(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_228,c_0_134]),c_0_134]),c_0_134]),c_0_134]),
[final] ).
cnf(i_0_369,plain,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_229]),
[final] ).
cnf(i_0_370,plain,
times_times_nat(X1,X2) = times_times_nat(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_371,plain,
plus_plus_nat(X1,X2) = plus_plus_nat(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_231]),
[final] ).
cnf(i_0_372,plain,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_232]),
[final] ).
cnf(i_0_373,plain,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_374,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_375,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_376,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_47_nat__1__add__1]),
[final] ).
cnf(i_0_377,plain,
( X1 != X2
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_378,plain,
plus_plus_int(one_one_int,one_one_int) = bit0(bit1(pls)),
inference(rw,[status(thm)],[i_0_236,c_0_134]),
[final] ).
cnf(i_0_379,plain,
~ ord_less_int(pls,pls),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_380,plain,
zprime(bit0(bit1(pls))),
inference(rw,[status(thm)],[i_0_238,c_0_134]),
[final] ).
cnf(i_0_381,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_239]),
[final] ).
cnf(i_0_382,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_240]),
[final] ).
cnf(i_0_383,plain,
ord_less_eq_int(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_241]),
[final] ).
cnf(i_0_384,plain,
power_power_nat(X1,one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_242]),
[final] ).
cnf(i_0_385,plain,
power_power_int(X1,one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_243]),
[final] ).
cnf(i_0_386,plain,
ord_less_eq_int(pls,pls),
inference(split_conjunct,[status(thm)],[fact_55_rel__simps_I19_J]),
[final] ).
cnf(i_0_387,plain,
ord_less_eq_int(one_one_int,t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]),
[final] ).
cnf(i_0_388,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(split_conjunct,[status(thm)],[fact_63_nat__numeral__1__eq__1]),
[final] ).
cnf(i_0_389,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_64_Numeral1__eq1__nat]),
[final] ).
cnf(i_0_390,axiom,
X1 = X1 ).
cnf(i_0_391,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_392,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_393,axiom,
( X1 != X2
| power_power_int(X1,X3) = power_power_int(X2,X3) ) ).
cnf(i_0_394,axiom,
( X1 != X2
| power_power_int(X3,X1) = power_power_int(X3,X2) ) ).
cnf(i_0_395,axiom,
( X1 != X2
| plus_plus_int(X1,X3) = plus_plus_int(X2,X3) ) ).
cnf(i_0_396,axiom,
( X1 != X2
| plus_plus_int(X3,X1) = plus_plus_int(X3,X2) ) ).
cnf(i_0_397,axiom,
( X1 != X2
| number_number_of_nat(X1) = number_number_of_nat(X2) ) ).
cnf(i_0_398,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ) ).
cnf(i_0_399,axiom,
( X1 != X2
| times_times_int(X1,X3) = times_times_int(X2,X3) ) ).
cnf(i_0_400,axiom,
( X1 != X2
| times_times_int(X3,X1) = times_times_int(X3,X2) ) ).
cnf(i_0_401,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ) ).
cnf(i_0_402,axiom,
( X1 != X2
| power_power_nat(X1,X3) = power_power_nat(X2,X3) ) ).
cnf(i_0_403,axiom,
( X1 != X2
| power_power_nat(X3,X1) = power_power_nat(X3,X2) ) ).
cnf(i_0_404,axiom,
( X1 != X2
| plus_plus_nat(X1,X3) = plus_plus_nat(X2,X3) ) ).
cnf(i_0_405,axiom,
( X1 != X2
| plus_plus_nat(X3,X1) = plus_plus_nat(X3,X2) ) ).
cnf(i_0_406,axiom,
( X1 != X2
| times_times_nat(X1,X3) = times_times_nat(X2,X3) ) ).
cnf(i_0_407,axiom,
( X1 != X2
| times_times_nat(X3,X1) = times_times_nat(X3,X2) ) ).
cnf(i_0_408,axiom,
( X1 != X2
| ~ twoSqu526106917sum2sq(X1)
| twoSqu526106917sum2sq(X2) ) ).
cnf(i_0_409,axiom,
( X1 != X2
| ~ ord_less_int(X1,X3)
| ord_less_int(X2,X3) ) ).
cnf(i_0_410,axiom,
( X1 != X2
| ~ ord_less_int(X3,X1)
| ord_less_int(X3,X2) ) ).
cnf(i_0_411,axiom,
( X1 != X2
| ~ zprime(X1)
| zprime(X2) ) ).
cnf(i_0_412,axiom,
( X1 != X2
| ~ ord_less_eq_int(X1,X3)
| ord_less_eq_int(X2,X3) ) ).
cnf(i_0_413,axiom,
( X1 != X2
| ~ ord_less_eq_int(X3,X1)
| ord_less_eq_int(X3,X2) ) ).
cnf(i_0_414,axiom,
( X1 != X2
| ~ ord_less_eq_nat(X1,X3)
| ord_less_eq_nat(X2,X3) ) ).
cnf(i_0_415,axiom,
( X1 != X2
| ~ ord_less_eq_nat(X3,X1)
| ord_less_eq_nat(X3,X2) ) ).
cnf(i_0_416,axiom,
( X1 != X2
| ~ ord_less_nat(X1,X3)
| ord_less_nat(X2,X3) ) ).
cnf(i_0_417,axiom,
( X1 != X2
| ~ ord_less_nat(X3,X1)
| ord_less_nat(X3,X2) ) ).
cnf(i_0_390_001,axiom,
X1 = X1 ).
cnf(i_0_391_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_392_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_393_004,axiom,
( X1 != X2
| power_power_int(X1,X3) = power_power_int(X2,X3) ) ).
cnf(i_0_394_005,axiom,
( X1 != X2
| power_power_int(X3,X1) = power_power_int(X3,X2) ) ).
cnf(i_0_395_006,axiom,
( X1 != X2
| plus_plus_int(X1,X3) = plus_plus_int(X2,X3) ) ).
cnf(i_0_396_007,axiom,
( X1 != X2
| plus_plus_int(X3,X1) = plus_plus_int(X3,X2) ) ).
cnf(i_0_397_008,axiom,
( X1 != X2
| number_number_of_nat(X1) = number_number_of_nat(X2) ) ).
cnf(i_0_398_009,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ) ).
cnf(i_0_399_010,axiom,
( X1 != X2
| times_times_int(X1,X3) = times_times_int(X2,X3) ) ).
cnf(i_0_400_011,axiom,
( X1 != X2
| times_times_int(X3,X1) = times_times_int(X3,X2) ) ).
cnf(i_0_401_012,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ) ).
cnf(i_0_402_013,axiom,
( X1 != X2
| power_power_nat(X1,X3) = power_power_nat(X2,X3) ) ).
cnf(i_0_403_014,axiom,
( X1 != X2
| power_power_nat(X3,X1) = power_power_nat(X3,X2) ) ).
cnf(i_0_404_015,axiom,
( X1 != X2
| plus_plus_nat(X1,X3) = plus_plus_nat(X2,X3) ) ).
cnf(i_0_405_016,axiom,
( X1 != X2
| plus_plus_nat(X3,X1) = plus_plus_nat(X3,X2) ) ).
cnf(i_0_406_017,axiom,
( X1 != X2
| times_times_nat(X1,X3) = times_times_nat(X2,X3) ) ).
cnf(i_0_407_018,axiom,
( X1 != X2
| times_times_nat(X3,X1) = times_times_nat(X3,X2) ) ).
cnf(i_0_408_019,axiom,
( X1 != X2
| ~ twoSqu526106917sum2sq(X1)
| twoSqu526106917sum2sq(X2) ) ).
cnf(i_0_409_020,axiom,
( X1 != X2
| ~ ord_less_int(X1,X3)
| ord_less_int(X2,X3) ) ).
cnf(i_0_410_021,axiom,
( X1 != X2
| ~ ord_less_int(X3,X1)
| ord_less_int(X3,X2) ) ).
cnf(i_0_411_022,axiom,
( X1 != X2
| ~ zprime(X1)
| zprime(X2) ) ).
cnf(i_0_412_023,axiom,
( X1 != X2
| ~ ord_less_eq_int(X1,X3)
| ord_less_eq_int(X2,X3) ) ).
cnf(i_0_413_024,axiom,
( X1 != X2
| ~ ord_less_eq_int(X3,X1)
| ord_less_eq_int(X3,X2) ) ).
cnf(i_0_414_025,axiom,
( X1 != X2
| ~ ord_less_eq_nat(X1,X3)
| ord_less_eq_nat(X2,X3) ) ).
cnf(i_0_415_026,axiom,
( X1 != X2
| ~ ord_less_eq_nat(X3,X1)
| ord_less_eq_nat(X3,X2) ) ).
cnf(i_0_416_027,axiom,
( X1 != X2
| ~ ord_less_nat(X1,X3)
| ord_less_nat(X2,X3) ) ).
cnf(i_0_417_028,axiom,
( X1 != X2
| ~ ord_less_nat(X3,X1)
| ord_less_nat(X3,X2) ) ).
cnf(i_0_418,plain,
~ ord_less_int(X1,X1),
inference(equality_inference,[],[377]) ).
cnf(i_0_419,plain,
X1 = X1,
inference(equality_inference,[],[381]) ).
cnf(i_0_420,plain,
X1 = X1,
inference(equality_inference,[],[382]) ).
cnf(i_0_421,plain,
~ ord_less_int(one_one_int,t),
inference(scs_inference,[],[i_0_248,i_0_252]) ).
cnf(i_0_422,plain,
t != one_one_int,
inference(scs_inference,[],[i_0_248,i_0_253]) ).
cnf(i_0_423,plain,
t != plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),
inference(scs_inference,[],[i_0_254,i_0_377]) ).
cnf(i_0_424,plain,
( ~ ord_less_int(X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_377]) ).
cnf(i_0_425,plain,
X1 = power_power_nat(X1,one_one_nat),
inference(scs_inference,[],[i_0_384,i_0_254,i_0_377,i_0_391]) ).
cnf(i_0_426,plain,
ord_less_int(X1,plus_plus_int(X1,one_one_int)),
inference(scs_inference,[],[i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298]) ).
cnf(i_0_427,plain,
ord_less_eq_int(X1,X1),
inference(rename_variables,[],[i_0_383]) ).
cnf(i_0_428,plain,
( ~ ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_298]) ).
cnf(i_0_429,plain,
ord_less_eq_int(t,times_times_int(bit0(bit0(bit1(pls))),m)),
inference(scs_inference,[],[i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299]) ).
cnf(i_0_430,plain,
( ~ ord_less_int(X1,plus_plus_int(X2,one_one_int))
| ord_less_eq_int(X1,X2) ),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_431,plain,
~ ord_less_eq_int(plus_plus_int(X1,one_one_int),X1),
inference(scs_inference,[],[i_0_418,i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303]) ).
cnf(i_0_432,plain,
~ ord_less_int(X1,X1),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_433,plain,
( ord_less_int(X1,plus_plus_int(X2,one_one_int))
| ~ ord_less_eq_int(X1,X2) ),
inference(rename_variables,[],[i_0_303]) ).
cnf(i_0_434,plain,
~ ord_less_eq_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),t),
inference(scs_inference,[],[i_0_418,i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347]) ).
cnf(i_0_435,plain,
( ~ ord_less_int(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_436,plain,
ord_less_eq_int(t,plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)),
inference(scs_inference,[],[i_0_418,i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364]) ).
cnf(i_0_437,plain,
( ~ ord_less_int(X1,X2)
| ord_less_eq_int(X1,X2) ),
inference(rename_variables,[],[i_0_364]) ).
cnf(i_0_438,plain,
ord_less_eq_int(X1,plus_plus_int(X1,one_one_int)),
inference(scs_inference,[],[i_0_418,i_0_383,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369]) ).
cnf(i_0_439,plain,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_369]) ).
cnf(i_0_440,plain,
plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(one_one_int,times_times_int(bit0(bit0(bit1(pls))),m)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_383,i_0_375,i_0_384,i_0_254,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392]) ).
cnf(i_0_441,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(rename_variables,[],[i_0_375]) ).
cnf(i_0_442,plain,
twoSqu526106917sum2sq(times_times_int(t,plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int))),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_383,i_0_373,i_0_375,i_0_384,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408]) ).
cnf(i_0_443,plain,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(rename_variables,[],[i_0_373]) ).
cnf(i_0_444,plain,
~ ord_less_int(times_times_nat(X1,X2),times_times_nat(X2,X1)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_384,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409]) ).
cnf(i_0_445,plain,
~ ord_less_int(X1,X1),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_446,plain,
zprime(power_power_nat(bit0(bit1(pls)),one_one_nat)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_384,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411]) ).
cnf(i_0_447,plain,
~ ord_less_eq_int(plus_plus_int(one_one_int,X1),X1),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412]) ).
cnf(i_0_448,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(rename_variables,[],[i_0_375]) ).
cnf(i_0_449,plain,
~ ord_less_eq_int(plus_plus_int(times_times_nat(X1,X2),one_one_int),times_times_nat(X2,X1)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413]) ).
cnf(i_0_450,plain,
~ ord_less_eq_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),one_one_int),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304]) ).
cnf(i_0_451,plain,
( ~ ord_less_eq_int(X1,X2)
| ord_less_eq_int(X3,X2)
| ~ ord_less_eq_int(X3,X1) ),
inference(rename_variables,[],[i_0_304]) ).
cnf(i_0_452,plain,
~ ord_less_int(times_times_int(bit0(bit0(bit1(pls))),m),t),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302]) ).
cnf(i_0_453,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ~ ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_302]) ).
cnf(i_0_454,plain,
ord_less_eq_int(times_times_nat(X1,X2),times_times_nat(X2,X1)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302,i_0_368]) ).
cnf(i_0_455,plain,
( ord_less_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_456,plain,
( ~ ord_less_eq_int(t,one_one_int)
| one_one_int = t ),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302,i_0_368,i_0_346]) ).
cnf(i_0_457,plain,
( ~ ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_346]) ).
cnf(i_0_458,plain,
~ ord_less_int(times_times_int(bit0(bit0(bit1(pls))),m),power_power_int(t,one_one_nat)),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_385,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302,i_0_368,i_0_346,i_0_410]) ).
cnf(i_0_459,plain,
power_power_int(X1,one_one_nat) = X1,
inference(rename_variables,[],[i_0_385]) ).
cnf(i_0_460,plain,
( ~ ord_less_eq_int(times_times_int(bit0(bit0(bit1(pls))),m),t)
| times_times_int(bit0(bit0(bit1(pls))),m) = t ),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_385,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302,i_0_368,i_0_346,i_0_410,i_0_357]) ).
cnf(i_0_461,plain,
( ord_less_int(X1,X2)
| ~ ord_less_eq_int(X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_357]) ).
cnf(i_0_462,plain,
( ord_less_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))))
| ord_less_int(plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int)) ),
inference(scs_inference,[],[i_0_248,i_0_418,i_0_432,i_0_383,i_0_370,i_0_373,i_0_375,i_0_441,i_0_384,i_0_385,i_0_387,i_0_380,i_0_254,i_0_249,i_0_377,i_0_391,i_0_298,i_0_299,i_0_303,i_0_347,i_0_364,i_0_369,i_0_392,i_0_408,i_0_409,i_0_411,i_0_412,i_0_413,i_0_304,i_0_302,i_0_368,i_0_346,i_0_410,i_0_357,i_0_365]) ).
cnf(i_0_463,plain,
( X1 = X2
| ord_less_int(X2,X1)
| ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_365]) ).
cnf(i_0_464,plain,
X1 != plus_plus_int(X1,one_one_int),
inference(scs_inference,[],[i_0_426,i_0_377]) ).
cnf(i_0_465,plain,
( ~ ord_less_int(X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_377]) ).
cnf(i_0_466,plain,
ord_less_int(X1,plus_plus_int(plus_plus_int(X1,one_one_int),one_one_int)),
inference(scs_inference,[],[i_0_426,i_0_438,i_0_377,i_0_298]) ).
cnf(i_0_467,plain,
ord_less_eq_int(X1,plus_plus_int(X1,one_one_int)),
inference(rename_variables,[],[i_0_438]) ).
cnf(i_0_468,plain,
( ~ ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_298]) ).
cnf(i_0_469,plain,
~ ord_less_eq_int(plus_plus_int(plus_plus_int(X1,one_one_int),one_one_int),X1),
inference(scs_inference,[],[i_0_426,i_0_438,i_0_377,i_0_298,i_0_347]) ).
cnf(i_0_470,plain,
( ~ ord_less_int(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_471,plain,
ord_less_eq_int(X1,plus_plus_int(plus_plus_int(X1,one_one_int),one_one_int)),
inference(scs_inference,[],[i_0_426,i_0_438,i_0_377,i_0_298,i_0_347,i_0_364]) ).
cnf(i_0_472,plain,
( ~ ord_less_int(X1,X2)
| ord_less_eq_int(X1,X2) ),
inference(rename_variables,[],[i_0_364]) ).
cnf(i_0_473,plain,
ord_less_eq_int(X1,plus_plus_int(one_one_int,X1)),
inference(scs_inference,[],[i_0_447,i_0_426,i_0_438,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369]) ).
cnf(i_0_474,plain,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_369]) ).
cnf(i_0_475,plain,
~ ord_less_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),
inference(scs_inference,[],[i_0_447,i_0_426,i_0_438,i_0_450,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302]) ).
cnf(i_0_476,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ~ ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_302]) ).
cnf(i_0_477,plain,
ord_less_eq_int(t,one_one_int),
inference(scs_inference,[],[i_0_421,i_0_447,i_0_426,i_0_438,i_0_450,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302,i_0_368]) ).
cnf(i_0_478,plain,
( ord_less_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_479,plain,
power_power_nat(X1,plus_plus_nat(X2,X3)) = times_times_nat(power_power_nat(X1,X2),power_power_nat(X1,X3)),
inference(scs_inference,[],[i_0_421,i_0_447,i_0_426,i_0_438,i_0_450,i_0_268,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302,i_0_368,i_0_391]) ).
cnf(i_0_480,plain,
one_one_int = t,
inference(scs_inference,[],[i_0_421,i_0_447,i_0_426,i_0_438,i_0_450,i_0_268,i_0_387,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302,i_0_368,i_0_391,i_0_357]) ).
cnf(i_0_481,plain,
( ord_less_int(X1,X2)
| ~ ord_less_eq_int(X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_357]) ).
cnf(i_0_482,plain,
ord_less_int(t,one_one_int),
inference(scs_inference,[],[i_0_421,i_0_422,i_0_447,i_0_426,i_0_438,i_0_450,i_0_268,i_0_387,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302,i_0_368,i_0_391,i_0_357,i_0_365]) ).
cnf(i_0_483,plain,
( X1 = X2
| ord_less_int(X2,X1)
| ord_less_int(X1,X2) ),
inference(rename_variables,[],[i_0_365]) ).
cnf(i_0_484,plain,
$false,
inference(scs_inference,[],[i_0_421,i_0_422,i_0_447,i_0_426,i_0_438,i_0_450,i_0_268,i_0_387,i_0_377,i_0_298,i_0_347,i_0_364,i_0_369,i_0_302,i_0_368,i_0_391,i_0_357,i_0_365,i_0_346]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+1 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:19:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.80/3.61 % Version : CSE_E---1.7
% 2.80/3.61 % Problem : theBenchmark.p
% 2.80/3.61 % SZS status Theorem for theBenchmark.p
% 2.80/3.61 % SZS output start CNFRefutation
% See solution above
% 2.99/3.84 % Total time : 3.270s
%------------------------------------------------------------------------------