%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM926+5 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:59:08 PM UTC 2026
% Result : Theorem 0.39s 1.62s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 395)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_29_le__number__of__eq__not__less,axiom,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X23,X17] :
( ord_less_eq(X1,number_number_of(X1,X23),number_number_of(X1,X17))
<=> ~ ord_less(X1,number_number_of(X1,X17),number_number_of(X1,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__number__of__eq__not__less) ).
fof(fact_52_add__nat__number__of,axiom,
! [X32,X13] :
( ( ord_less(int,X13,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X32) )
& ( ~ ord_less(int,X13,pls)
=> ( ( ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X13) )
& ( ~ ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,plus_plus(int,X13,X32)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__nat__number__of) ).
fof(fact_8_zadd__power3,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))),X7)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X6),power_power(int,X7,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X7,number_number_of(nat,bit1(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
fof(fact_7_zadd__power2,axiom,
! [X6,X7] : power_power(int,plus_plus(int,X6,X7),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X6,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X6),X7)),power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
fof(fact_9_power2__sum,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X8,X9] : power_power(X1,plus_plus(X1,X8,X9),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X1,plus_plus(X1,power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X9,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X8),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_power2__sum) ).
fof(fact_19__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/sandbox2/benchmark/theBenchmark.p',fact_19__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)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one(int)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,times_times(X1,X33,X34),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,X33,times_times(X1,X34,times_times(X1,X35,X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35,X36] : times_times(X1,times_times(X1,X33,X34),times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),times_times(X1,X34,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37,X38] : plus_plus(X1,plus_plus(X1,X6,X7),plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),plus_plus(X1,X7,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X12] : power_power(X1,X8,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X12)) = times_times(X1,power_power(X1,X8,X12),power_power(X1,X8,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : times_times(X1,power_power(X1,X8,X21),power_power(X1,X8,X22)) = power_power(X1,X8,plus_plus(nat,X21,X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_32_zadd__zless__mono,axiom,
! [X26,X15,X27,X11] :
( ord_less(int,X27,X11)
=> ( ord_less_eq(int,X26,X15)
=> ord_less(int,plus_plus(int,X27,X26),plus_plus(int,X11,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zadd__zless__mono) ).
fof(fact_34_zpower__zadd__distrib,axiom,
! [X8,X9,X15] : power_power(int,X8,plus_plus(nat,X9,X15)) = times_times(int,power_power(int,X8,X9),power_power(int,X8,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_zpower__zadd__distrib) ).
fof(fact_11_cube__square,axiom,
! [X6] : times_times(int,X6,power_power(int,X6,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X6,number_number_of(nat,bit1(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_cube__square) ).
fof(fact_51_zadd__left__mono,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ord_less_eq(int,plus_plus(int,X18,X19),plus_plus(int,X18,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__left__mono) ).
fof(fact_50_zadd__strict__right__mono,axiom,
! [X18,X19,X20] :
( ord_less(int,X19,X20)
=> ord_less(int,plus_plus(int,X19,X18),plus_plus(int,X20,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zadd__strict__right__mono) ).
fof(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,times_times(X1,X33,X35),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,plus_plus(X1,X6,X37),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X34,X35] : times_times(X1,times_times(X1,X33,X34),X35) = times_times(X1,X33,times_times(X1,X34,X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7,X37] : plus_plus(X1,plus_plus(X1,X6,X7),X37) = plus_plus(X1,X6,plus_plus(X1,X7,X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,times_times(X1,X33,X35),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,plus_plus(X1,X6,X37),X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X33,X35,X36] : times_times(X1,X33,times_times(X1,X35,X36)) = times_times(X1,X35,times_times(X1,X33,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37,X38] : plus_plus(X1,X6,plus_plus(X1,X37,X38)) = plus_plus(X1,X37,plus_plus(X1,X6,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8,X21,X22] : power_power(X1,power_power(X1,X8,X21),X22) = power_power(X1,X8,times_times(nat,X21,X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_28_zpower__zpower,axiom,
! [X8,X9,X15] : power_power(int,power_power(int,X8,X9),X15) = power_power(int,X8,times_times(nat,X9,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zpower__zpower) ).
fof(fact_84_zmult__assoc,axiom,
! [X39,X40,X41] : times_times(int,times_times(int,X39,X40),X41) = times_times(int,X39,times_times(int,X40,X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zmult__assoc) ).
fof(fact_87_zadd__assoc,axiom,
! [X39,X40,X41] : plus_plus(int,plus_plus(int,X39,X40),X41) = plus_plus(int,X39,plus_plus(int,X40,X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_zadd__assoc) ).
fof(fact_88_zadd__left__commute,axiom,
! [X8,X9,X15] : plus_plus(int,X8,plus_plus(int,X9,X15)) = plus_plus(int,X9,plus_plus(int,X8,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zadd__left__commute) ).
fof(fact_62_add1__zle__eq,axiom,
! [X17,X16] :
( ord_less_eq(int,plus_plus(int,X17,one_one(int)),X16)
<=> ord_less(int,X17,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add1__zle__eq) ).
fof(fact_63_zle__add1__eq__le,axiom,
! [X17,X16] :
( ord_less(int,X17,plus_plus(int,X16,one_one(int)))
<=> ord_less_eq(int,X17,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zle__add1__eq__le) ).
fof(fact_10_power2__eq__square__number__of,axiom,
! [X10] :
( ( monoid_mult(X10)
& number(X10) )
=> ! [X11] : power_power(X10,number_number_of(X10,X11),number_number_of(nat,bit0(bit1(pls)))) = times_times(X10,number_number_of(X10,X11),number_number_of(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__eq__square__number__of) ).
fof(fact_61_zless__imp__add1__zle,axiom,
! [X11,X15] :
( ord_less(int,X11,X15)
=> ord_less_eq(int,plus_plus(int,X11,one_one(int)),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_zless__imp__add1__zle) ).
fof(fact_31_le__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less_eq(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less_eq(int,X24,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_le__number__of) ).
fof(fact_30_less__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X24,X25] :
( ord_less(X1,number_number_of(X1,X24),number_number_of(X1,X25))
<=> ord_less(int,X24,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__number__of) ).
fof(fact_24_zle__trans,axiom,
! [X18,X19,X20] :
( ord_less_eq(int,X19,X20)
=> ( ord_less_eq(int,X20,X18)
=> ord_less_eq(int,X19,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zle__trans) ).
fof(fact_17_add__special_I3_J,axiom,
! [X1] :
( number_ring(X1)
=> ! [X13] : plus_plus(X1,number_number_of(X1,X13),one_one(X1)) = number_number_of(X1,plus_plus(int,X13,bit1(pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__special_I3_J) ).
fof(fact_16_add__special_I2_J,axiom,
! [X1] :
( number_ring(X1)
=> ! [X11] : plus_plus(X1,one_one(X1),number_number_of(X1,X11)) = number_number_of(X1,plus_plus(int,bit1(pls),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__special_I2_J) ).
fof(fact_49_less__eq__number__of__int__code,axiom,
! [X30,X31] :
( ord_less_eq(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less_eq(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__eq__number__of__int__code) ).
fof(fact_48_less__number__of__int__code,axiom,
! [X30,X31] :
( ord_less(int,number_number_of(int,X30),number_number_of(int,X31))
<=> ord_less(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__number__of__int__code) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_arg1,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,ti(X1,X2),X3)
<=> ord_less_eq(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_arg1) ).
fof(tsy_c_Orderings_Oord__class_Oless_arg1,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,ti(X1,X2),X3)
<=> ord_less(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_arg1) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_arg2,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less_eq(X1,X2,ti(X1,X3))
<=> ord_less_eq(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_arg2) ).
fof(tsy_c_Orderings_Oord__class_Oless_arg2,axiom,
! [X2,X3,X1] :
( ( number(X1)
& linorder(X1) )
=> ( ord_less(X1,X2,ti(X1,X3))
<=> ord_less(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_arg2) ).
fof(tsy_c_Power_Opower__class_Opower_res,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
fof(tsy_c_Groups_Otimes__class_Otimes_res,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_res) ).
fof(tsy_c_Groups_Oplus__class_Oplus_res,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_res) ).
fof(fact_25_zle__antisym,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
=> ( ord_less_eq(int,X11,X15)
=> X15 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zle__antisym) ).
fof(fact_14_power2__eq__square,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X6] : power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__eq__square) ).
fof(fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : times_times(X1,X8,X8) = power_power(X1,X8,number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_41_rel__simps_I34_J,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rel__simps_I34_J) ).
fof(fact_40_less__eq__int__code_I16_J,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_less__eq__int__code_I16_J) ).
fof(fact_97_rel__simps_I32_J,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_rel__simps_I32_J) ).
fof(fact_96_less__eq__int__code_I14_J,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_less__eq__int__code_I14_J) ).
fof(fact_47_rel__simps_I31_J,axiom,
! [X30,X31] :
( ord_less_eq(int,bit0(X30),bit0(X31))
<=> ord_less_eq(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I31_J) ).
fof(fact_46_less__eq__int__code_I13_J,axiom,
! [X28,X29] :
( ord_less_eq(int,bit0(X28),bit0(X29))
<=> ord_less_eq(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__eq__int__code_I13_J) ).
fof(fact_60_rel__simps_I15_J,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit1(X31))
<=> ord_less_eq(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rel__simps_I15_J) ).
fof(fact_59_less__int__code_I14_J,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit1(X29))
<=> ord_less_eq(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__int__code_I14_J) ).
fof(fact_58_rel__simps_I33_J,axiom,
! [X30,X31] :
( ord_less_eq(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I33_J) ).
fof(fact_57_less__eq__int__code_I15_J,axiom,
! [X28,X29] :
( ord_less_eq(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__eq__int__code_I15_J) ).
fof(fact_39_rel__simps_I17_J,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit1(X31))
<=> ord_less(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_rel__simps_I17_J) ).
fof(fact_38_less__int__code_I16_J,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit1(X29))
<=> ord_less(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__int__code_I16_J) ).
fof(fact_92_rel__simps_I16_J,axiom,
! [X30,X31] :
( ord_less(int,bit1(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rel__simps_I16_J) ).
fof(fact_91_less__int__code_I15_J,axiom,
! [X28,X29] :
( ord_less(int,bit1(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__int__code_I15_J) ).
fof(fact_44_rel__simps_I14_J,axiom,
! [X30,X31] :
( ord_less(int,bit0(X30),bit0(X31))
<=> ord_less(int,X30,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_rel__simps_I14_J) ).
fof(fact_43_less__int__code_I13_J,axiom,
! [X28,X29] :
( ord_less(int,bit0(X28),bit0(X29))
<=> ord_less(int,X28,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_less__int__code_I13_J) ).
fof(fact_35_nat__mult__2,axiom,
! [X15] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X15) = plus_plus(nat,X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_nat__mult__2) ).
fof(fact_36_nat__mult__2__right,axiom,
! [X15] : times_times(nat,X15,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_nat__mult__2__right) ).
fof(fact_95_rel__simps_I22_J,axiom,
! [X30] :
( ord_less_eq(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I22_J) ).
fof(fact_56_rel__simps_I5_J,axiom,
! [X30] :
( ord_less(int,pls,bit1(X30))
<=> ord_less_eq(int,pls,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rel__simps_I5_J) ).
fof(fact_94_rel__simps_I4_J,axiom,
! [X30] :
( ord_less(int,pls,bit0(X30))
<=> ord_less(int,pls,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I4_J) ).
fof(fact_55_rel__simps_I29_J,axiom,
! [X30] :
( ord_less_eq(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I29_J) ).
fof(fact_90_rel__simps_I12_J,axiom,
! [X30] :
( ord_less(int,bit1(X30),pls)
<=> ord_less(int,X30,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_rel__simps_I12_J) ).
fof(fact_93_rel__simps_I10_J,axiom,
! [X30] :
( ord_less(int,bit0(X30),pls)
<=> ord_less(int,X30,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rel__simps_I10_J) ).
fof(tsy_c_Power_Opower__class_Opower_arg1,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
fof(tsy_c_Groups_Otimes__class_Otimes_arg1,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_arg1) ).
fof(tsy_c_Groups_Oplus__class_Oplus_arg1,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_arg1) ).
fof(tsy_c_Groups_Otimes__class_Otimes_arg2,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_arg2) ).
fof(tsy_c_Groups_Oplus__class_Oplus_arg2,axiom,
! [X2,X3,X1] :
( comm_semiring_1(X1)
=> plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_arg2) ).
fof(fact_22_zless__le,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( ord_less_eq(int,X16,X17)
& X16 != X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(tsy_c_Power_Opower__class_Opower_arg2,axiom,
! [X2,X3,X1] :
( monoid_mult(X1)
=> power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg2) ).
fof(fact_65_is__mult__sum2sq,axiom,
! [X9,X8] :
( twoSqu33214720sum2sq(X8)
=> ( twoSqu33214720sum2sq(X9)
=> twoSqu33214720sum2sq(times_times(int,X8,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_is__mult__sum2sq) ).
fof(fact_12_one__power2,axiom,
! [X1] :
( semiring_1(X1)
=> power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
fof(fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X7] : times_times(X1,X6,X7) = times_times(X1,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X6,X37] : plus_plus(X1,X6,X37) = plus_plus(X1,X37,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_23_zless__linear,axiom,
! [X8,X9] :
( ord_less(int,X8,X9)
| X8 = X9
| ord_less(int,X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zless__linear) ).
fof(fact_21_zle__linear,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
| ord_less_eq(int,X11,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zle__linear) ).
fof(fact_85_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
fof(fact_89_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
fof(fact_18_one__add__one__is__two,axiom,
! [X1] :
( number_ring(X1)
=> plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__add__one__is__two) ).
fof(fact_42_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I2_J) ).
fof(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X8] : power_power(X1,X8,one_one(nat)) = ti(X1,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(tsy_c_Int_Onumber__class_Onumber__of_res,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(fact_80_eq__number__of,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X24,X25] :
( number_number_of(X1,X24) = number_number_of(X1,X25)
<=> X24 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_eq__number__of) ).
fof(tsy_c_Int_Onumber__class_Onumber__of_arg1,axiom,
! [X2,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
fof(help_ti_idem,axiom,
! [X42,X43] : ti(X42,ti(X42,X43)) = ti(X42,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
fof(fact_20_zle__refl,axiom,
! [X11] : ord_less_eq(int,X11,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zle__refl) ).
fof(tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1,axiom,
! [X2] :
( twoSqu33214720sum2sq(ti(int,X2))
<=> twoSqu33214720sum2sq(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) ).
fof(tsy_c_IntPrimes_Ozprime_arg1,axiom,
! [X2] :
( zprime(ti(int,X2))
<=> zprime(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
! [X1] :
( semiring_1(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
fof(tsy_c_Int_OBit1_arg1,hypothesis,
! [X2] : bit1(ti(int,X2)) = bit1(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
fof(tsy_c_Int_OBit0_arg1,hypothesis,
! [X2] : bit0(ti(int,X2)) = bit0(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(tsy_c_Int_OBit1_res,hypothesis,
! [X2] : ti(int,bit1(X2)) = bit1(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(tsy_c_Int_OBit0_res,hypothesis,
! [X2] : ti(int,bit0(X2)) = bit0(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
fof(fact_82_rel__simps_I51_J,axiom,
! [X30,X31] :
( bit1(X30) = bit1(X31)
<=> X30 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_rel__simps_I51_J) ).
fof(fact_83_rel__simps_I48_J,axiom,
! [X30,X31] :
( bit0(X30) = bit0(X31)
<=> X30 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I48_J) ).
fof(fact_86_number__of__is__id,axiom,
! [X18] : number_number_of(int,X18) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
fof(fact_6_qf1pt,axiom,
twoSqu33214720sum2sq(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_4_p) ).
fof(fact_37_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_nat__1__add__1) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(fact_64_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_zprime__2) ).
fof(fact_45_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rel__simps_I19_J) ).
fof(fact_53_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_nat__numeral__1__eq__1) ).
fof(fact_54_Numeral1__eq1__nat,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Numeral1__eq1__nat) ).
fof(tsy_v_t_____res,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
fof(tsy_v_s_____res,axiom,
ti(int,s) = s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_s_____res) ).
fof(tsy_v_m_res,hypothesis,
ti(int,m) = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m_res) ).
fof(tsy_c_Int_OPls_res,hypothesis,
ti(int,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
fof(arity_Int_Oint___Int_Oring__char__0,axiom,
ring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(arity_Nat_Onat___Int_Onumber__semiring,axiom,
number_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(arity_Int_Oint___Int_Onumber__semiring,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(arity_Nat_Onat___Int_Onumber,axiom,
number(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
fof(arity_Int_Oint___Int_Onumber,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
fof(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
monoid_mult(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(arity_Int_Oint___Groups_Omonoid__mult,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(arity_Int_Oint___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
fof(arity_Nat_Onat___Rings_Osemiring__1,axiom,
semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(arity_Int_Oint___Rings_Osemiring__1,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
fof(i_0_141,negated_conjecture,
~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_142,plain,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X23,X17] :
( ord_less_eq(X1,number_number_of(X1,X23),number_number_of(X1,X17))
<=> ~ ord_less(X1,number_number_of(X1,X17),number_number_of(X1,X23)) ) ),
inference(fof_simplification,[status(thm)],[fact_29_le__number__of__eq__not__less]) ).
fof(i_0_143,plain,
! [X32,X13] :
( ( ord_less(int,X13,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X32) )
& ( ~ ord_less(int,X13,pls)
=> ( ( ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,X13) )
& ( ~ ord_less(int,X32,pls)
=> plus_plus(nat,number_number_of(nat,X13),number_number_of(nat,X32)) = number_number_of(nat,plus_plus(int,X13,X32)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_52_add__nat__number__of]) ).
fof(i_0_144,plain,
! [X367,X368] : power_power(int,plus_plus(int,X367,X368),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,X367,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,X367,number_number_of(nat,bit0(bit1(pls))))),X368)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),X367),power_power(int,X368,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,X368,number_number_of(nat,bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[fact_8_zadd__power3]) ).
fof(i_0_145,plain,
! [X365,X366] : power_power(int,plus_plus(int,X365,X366),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,X365,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X365),X366)),power_power(int,X366,number_number_of(nat,bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[fact_7_zadd__power2]) ).
fof(i_0_146,plain,
! [X369,X370,X371] :
( ~ number_semiring(X369)
| power_power(X369,plus_plus(X369,X370,X371),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X369,plus_plus(X369,power_power(X369,X370,number_number_of(nat,bit0(bit1(pls)))),power_power(X369,X371,number_number_of(nat,bit0(bit1(pls))))),times_times(X369,times_times(X369,number_number_of(X369,bit0(bit1(pls))),X370),X371)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_power2__sum])])]) ).
fof(i_0_147,negated_conjecture,
! [X574,X575] : plus_plus(int,power_power(int,X574,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X575,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_141])]) ).
fof(i_0_148,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_19__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_149,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_150,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_151,plain,
! [X483,X484,X485,X486,X487] :
( ~ comm_semiring_1(X483)
| times_times(X483,times_times(X483,X484,X485),times_times(X483,X486,X487)) = times_times(X483,X486,times_times(X483,times_times(X483,X484,X485),X487)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])])]) ).
fof(i_0_152,plain,
! [X488,X489,X490,X491,X492] :
( ~ comm_semiring_1(X488)
| times_times(X488,times_times(X488,X489,X490),times_times(X488,X491,X492)) = times_times(X488,X489,times_times(X488,X490,times_times(X488,X491,X492))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])])]) ).
fof(i_0_153,plain,
! [X478,X479,X480,X481,X482] :
( ~ comm_semiring_1(X478)
| times_times(X478,times_times(X478,X479,X480),times_times(X478,X481,X482)) = times_times(X478,times_times(X478,X479,X481),times_times(X478,X480,X482)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])]) ).
fof(i_0_154,plain,
! [X512,X513,X514,X515,X516] :
( ~ comm_semiring_1(X512)
| plus_plus(X512,plus_plus(X512,X513,X514),plus_plus(X512,X515,X516)) = plus_plus(X512,plus_plus(X512,X513,X515),plus_plus(X512,X514,X516)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])]) ).
fof(i_0_155,plain,
! [X380,X381,X382] :
( ~ comm_semiring_1(X380)
| power_power(X380,X381,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X382)) = times_times(X380,power_power(X380,X381,X382),power_power(X380,X381,X382)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])])]) ).
fof(i_0_156,plain,
! [X423,X424,X425,X426] :
( ~ comm_semiring_1(X423)
| times_times(X423,power_power(X423,X424,X425),power_power(X423,X424,X426)) = power_power(X423,X424,plus_plus(nat,X425,X426)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])])]) ).
fof(i_0_157,plain,
! [X419,X420,X421,X422] :
( ~ ord_less(int,X421,X422)
| ~ ord_less_eq(int,X419,X420)
| ord_less(int,plus_plus(int,X421,X419),plus_plus(int,X422,X420)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_zadd__zless__mono])]) ).
fof(i_0_158,plain,
! [X427,X428,X429] : power_power(int,X427,plus_plus(nat,X428,X429)) = times_times(int,power_power(int,X427,X428),power_power(int,X427,X429)),
inference(variable_rename,[status(thm)],[fact_34_zpower__zadd__distrib]) ).
fof(i_0_159,plain,
! [X374] : times_times(int,X374,power_power(int,X374,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,X374,number_number_of(nat,bit1(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_11_cube__square]) ).
fof(i_0_160,plain,
! [X410,X411,X412] :
( ( ~ ord_less_eq(X410,number_number_of(X410,X411),number_number_of(X410,X412))
| ~ ord_less(X410,number_number_of(X410,X412),number_number_of(X410,X411))
| ~ number(X410)
| ~ linorder(X410) )
& ( ord_less(X410,number_number_of(X410,X412),number_number_of(X410,X411))
| ord_less_eq(X410,number_number_of(X410,X411),number_number_of(X410,X412))
| ~ number(X410)
| ~ linorder(X410) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_142])])])]) ).
fof(i_0_161,plain,
! [X455,X456,X457] :
( ~ ord_less_eq(int,X456,X457)
| ord_less_eq(int,plus_plus(int,X455,X456),plus_plus(int,X455,X457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_zadd__left__mono])]) ).
fof(i_0_162,plain,
! [X452,X453,X454] :
( ~ ord_less(int,X453,X454)
| ord_less(int,plus_plus(int,X453,X452),plus_plus(int,X454,X452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_zadd__strict__right__mono])]) ).
fof(i_0_163,plain,
! [X493,X494,X495,X496] :
( ~ comm_semiring_1(X493)
| times_times(X493,times_times(X493,X494,X495),X496) = times_times(X493,times_times(X493,X494,X496),X495) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])]) ).
fof(i_0_164,plain,
! [X517,X518,X519,X520] :
( ~ comm_semiring_1(X517)
| plus_plus(X517,plus_plus(X517,X518,X519),X520) = plus_plus(X517,plus_plus(X517,X518,X520),X519) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])]) ).
fof(i_0_165,plain,
! [X497,X498,X499,X500] :
( ~ comm_semiring_1(X497)
| times_times(X497,times_times(X497,X498,X499),X500) = times_times(X497,X498,times_times(X497,X499,X500)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])]) ).
fof(i_0_166,plain,
! [X521,X522,X523,X524] :
( ~ comm_semiring_1(X521)
| plus_plus(X521,plus_plus(X521,X522,X523),X524) = plus_plus(X521,X522,plus_plus(X521,X523,X524)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])]) ).
fof(i_0_167,plain,
! [X501,X502,X503,X504] :
( ~ comm_semiring_1(X501)
| times_times(X501,X502,times_times(X501,X503,X504)) = times_times(X501,times_times(X501,X502,X503),X504) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])])]) ).
fof(i_0_168,plain,
! [X525,X526,X527,X528] :
( ~ comm_semiring_1(X525)
| plus_plus(X525,X526,plus_plus(X525,X527,X528)) = plus_plus(X525,plus_plus(X525,X526,X527),X528) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])])]) ).
fof(i_0_169,plain,
! [X505,X506,X507,X508] :
( ~ comm_semiring_1(X505)
| times_times(X505,X506,times_times(X505,X507,X508)) = times_times(X505,X507,times_times(X505,X506,X508)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])]) ).
fof(i_0_170,plain,
! [X529,X530,X531,X532] :
( ~ comm_semiring_1(X529)
| plus_plus(X529,X530,plus_plus(X529,X531,X532)) = plus_plus(X529,X531,plus_plus(X529,X530,X532)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])]) ).
fof(i_0_171,plain,
! [X401,X402,X403,X404] :
( ~ comm_semiring_1(X401)
| power_power(X401,power_power(X401,X402,X403),X404) = power_power(X401,X402,times_times(nat,X403,X404)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])])]) ).
fof(i_0_172,plain,
! [X458,X459] :
( ( ~ ord_less(int,X459,pls)
| plus_plus(nat,number_number_of(nat,X459),number_number_of(nat,X458)) = number_number_of(nat,X458) )
& ( ~ ord_less(int,X458,pls)
| plus_plus(nat,number_number_of(nat,X459),number_number_of(nat,X458)) = number_number_of(nat,X459)
| ord_less(int,X459,pls) )
& ( ord_less(int,X458,pls)
| plus_plus(nat,number_number_of(nat,X459),number_number_of(nat,X458)) = number_number_of(nat,plus_plus(int,X459,X458))
| ord_less(int,X459,pls) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_143])])]) ).
fof(i_0_173,plain,
! [X407,X408,X409] : power_power(int,power_power(int,X407,X408),X409) = power_power(int,X407,times_times(nat,X408,X409)),
inference(variable_rename,[status(thm)],[fact_28_zpower__zpower]) ).
fof(i_0_174,plain,
! [X546,X547,X548] : times_times(int,times_times(int,X546,X547),X548) = times_times(int,X546,times_times(int,X547,X548)),
inference(variable_rename,[status(thm)],[fact_84_zmult__assoc]) ).
fof(i_0_175,plain,
! [X552,X553,X554] : plus_plus(int,plus_plus(int,X552,X553),X554) = plus_plus(int,X552,plus_plus(int,X553,X554)),
inference(variable_rename,[status(thm)],[fact_87_zadd__assoc]) ).
fof(i_0_176,plain,
! [X555,X556,X557] : plus_plus(int,X555,plus_plus(int,X556,X557)) = plus_plus(int,X556,plus_plus(int,X555,X557)),
inference(variable_rename,[status(thm)],[fact_88_zadd__left__commute]) ).
fof(i_0_177,plain,
! [X472,X473] :
( ( ~ ord_less_eq(int,plus_plus(int,X472,one_one(int)),X473)
| ord_less(int,X472,X473) )
& ( ~ ord_less(int,X472,X473)
| ord_less_eq(int,plus_plus(int,X472,one_one(int)),X473) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_add1__zle__eq])]) ).
fof(i_0_178,plain,
! [X474,X475] :
( ( ~ ord_less(int,X474,plus_plus(int,X475,one_one(int)))
| ord_less_eq(int,X474,X475) )
& ( ~ ord_less_eq(int,X474,X475)
| ord_less(int,X474,plus_plus(int,X475,one_one(int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_zle__add1__eq__le])]) ).
fof(i_0_179,plain,
! [X372,X373] :
( ~ monoid_mult(X372)
| ~ number(X372)
| power_power(X372,number_number_of(X372,X373),number_number_of(nat,bit0(bit1(pls)))) = times_times(X372,number_number_of(X372,X373),number_number_of(X372,X373)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_power2__eq__square__number__of])])]) ).
fof(i_0_180,plain,
! [X470,X471] :
( ~ ord_less(int,X470,X471)
| ord_less_eq(int,plus_plus(int,X470,one_one(int)),X471) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_zless__imp__add1__zle])]) ).
fof(i_0_181,plain,
! [X416,X417,X418] :
( ( ~ ord_less_eq(X416,number_number_of(X416,X417),number_number_of(X416,X418))
| ord_less_eq(int,X417,X418)
| ~ number_ring(X416)
| ~ linordered_idom(X416) )
& ( ~ ord_less_eq(int,X417,X418)
| ord_less_eq(X416,number_number_of(X416,X417),number_number_of(X416,X418))
| ~ number_ring(X416)
| ~ linordered_idom(X416) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_le__number__of])])])]) ).
fof(i_0_182,plain,
! [X413,X414,X415] :
( ( ~ ord_less(X413,number_number_of(X413,X414),number_number_of(X413,X415))
| ord_less(int,X414,X415)
| ~ number_ring(X413)
| ~ linordered_idom(X413) )
& ( ~ ord_less(int,X414,X415)
| ord_less(X413,number_number_of(X413,X414),number_number_of(X413,X415))
| ~ number_ring(X413)
| ~ linordered_idom(X413) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_less__number__of])])])]) ).
fof(i_0_183,plain,
! [X396,X397,X398] :
( ~ ord_less_eq(int,X397,X398)
| ~ ord_less_eq(int,X398,X396)
| ord_less_eq(int,X397,X396) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_zle__trans])]) ).
fof(i_0_184,plain,
! [X385,X386] :
( ~ number_ring(X385)
| plus_plus(X385,number_number_of(X385,X386),one_one(X385)) = number_number_of(X385,plus_plus(int,X386,bit1(pls))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_add__special_I3_J])])]) ).
fof(i_0_185,plain,
! [X383,X384] :
( ~ number_ring(X383)
| plus_plus(X383,one_one(X383),number_number_of(X383,X384)) = number_number_of(X383,plus_plus(int,bit1(pls),X384)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_add__special_I2_J])])]) ).
fof(i_0_186,plain,
! [X450,X451] :
( ( ~ ord_less_eq(int,number_number_of(int,X450),number_number_of(int,X451))
| ord_less_eq(int,X450,X451) )
& ( ~ ord_less_eq(int,X450,X451)
| ord_less_eq(int,number_number_of(int,X450),number_number_of(int,X451)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_less__eq__number__of__int__code])]) ).
fof(i_0_187,plain,
! [X448,X449] :
( ( ~ ord_less(int,number_number_of(int,X448),number_number_of(int,X449))
| ord_less(int,X448,X449) )
& ( ~ ord_less(int,X448,X449)
| ord_less(int,number_number_of(int,X448),number_number_of(int,X449)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_less__number__of__int__code])]) ).
fof(i_0_188,plain,
! [X345,X346,X347] :
( ( ~ ord_less_eq(X347,ti(X347,X345),X346)
| ord_less_eq(X347,X345,X346)
| ~ number(X347)
| ~ linorder(X347) )
& ( ~ ord_less_eq(X347,X345,X346)
| ord_less_eq(X347,ti(X347,X345),X346)
| ~ number(X347)
| ~ linorder(X347) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_arg1])])]) ).
fof(i_0_189,plain,
! [X339,X340,X341] :
( ( ~ ord_less(X341,ti(X341,X339),X340)
| ord_less(X341,X339,X340)
| ~ number(X341)
| ~ linorder(X341) )
& ( ~ ord_less(X341,X339,X340)
| ord_less(X341,ti(X341,X339),X340)
| ~ number(X341)
| ~ linorder(X341) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_arg1])])]) ).
fof(i_0_190,plain,
! [X348,X349,X350] :
( ( ~ ord_less_eq(X350,X348,ti(X350,X349))
| ord_less_eq(X350,X348,X349)
| ~ number(X350)
| ~ linorder(X350) )
& ( ~ ord_less_eq(X350,X348,X349)
| ord_less_eq(X350,X348,ti(X350,X349))
| ~ number(X350)
| ~ linorder(X350) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_arg2])])]) ).
fof(i_0_191,plain,
! [X342,X343,X344] :
( ( ~ ord_less(X344,X342,ti(X344,X343))
| ord_less(X344,X342,X343)
| ~ number(X344)
| ~ linorder(X344) )
& ( ~ ord_less(X344,X342,X343)
| ord_less(X344,X342,ti(X344,X343))
| ~ number(X344)
| ~ linorder(X344) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_arg2])])]) ).
fof(i_0_192,plain,
! [X357,X358,X359] :
( ~ monoid_mult(X359)
| ti(X359,power_power(X359,X357,X358)) = power_power(X359,X357,X358) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Power_Opower__class_Opower_res])]) ).
fof(i_0_193,plain,
! [X326,X327,X328] :
( ~ monoid_mult(X328)
| ti(X328,times_times(X328,X326,X327)) = times_times(X328,X326,X327) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_res])]) ).
fof(i_0_194,plain,
! [X317,X318,X319] :
( ~ comm_semiring_1(X319)
| ti(X319,plus_plus(X319,X317,X318)) = plus_plus(X319,X317,X318) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_res])]) ).
fof(i_0_195,plain,
! [X399,X400] :
( ~ ord_less_eq(int,X399,X400)
| ~ ord_less_eq(int,X400,X399)
| X399 = X400 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_zle__antisym])]) ).
fof(i_0_196,plain,
! [X378,X379] :
( ~ monoid_mult(X378)
| power_power(X378,X379,number_number_of(nat,bit0(bit1(pls)))) = times_times(X378,X379,X379) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_power2__eq__square])])]) ).
fof(i_0_197,plain,
! [X376,X377] :
( ~ comm_semiring_1(X376)
| times_times(X376,X377,X377) = power_power(X376,X377,number_number_of(nat,bit0(bit1(pls)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])])]) ).
fof(i_0_198,plain,
! [X438,X439] :
( ( ~ ord_less_eq(int,bit1(X438),bit1(X439))
| ord_less_eq(int,X438,X439) )
& ( ~ ord_less_eq(int,X438,X439)
| ord_less_eq(int,bit1(X438),bit1(X439)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_rel__simps_I34_J])]) ).
fof(i_0_199,plain,
! [X436,X437] :
( ( ~ ord_less_eq(int,bit1(X436),bit1(X437))
| ord_less_eq(int,X436,X437) )
& ( ~ ord_less_eq(int,X436,X437)
| ord_less_eq(int,bit1(X436),bit1(X437)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_less__eq__int__code_I16_J])]) ).
fof(i_0_200,plain,
! [X570,X571] :
( ( ~ ord_less_eq(int,bit0(X570),bit1(X571))
| ord_less_eq(int,X570,X571) )
& ( ~ ord_less_eq(int,X570,X571)
| ord_less_eq(int,bit0(X570),bit1(X571)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_rel__simps_I32_J])]) ).
fof(i_0_201,plain,
! [X568,X569] :
( ( ~ ord_less_eq(int,bit0(X568),bit1(X569))
| ord_less_eq(int,X568,X569) )
& ( ~ ord_less_eq(int,X568,X569)
| ord_less_eq(int,bit0(X568),bit1(X569)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_less__eq__int__code_I14_J])]) ).
fof(i_0_202,plain,
! [X446,X447] :
( ( ~ ord_less_eq(int,bit0(X446),bit0(X447))
| ord_less_eq(int,X446,X447) )
& ( ~ ord_less_eq(int,X446,X447)
| ord_less_eq(int,bit0(X446),bit0(X447)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_rel__simps_I31_J])]) ).
fof(i_0_203,plain,
! [X444,X445] :
( ( ~ ord_less_eq(int,bit0(X444),bit0(X445))
| ord_less_eq(int,X444,X445) )
& ( ~ ord_less_eq(int,X444,X445)
| ord_less_eq(int,bit0(X444),bit0(X445)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_less__eq__int__code_I13_J])]) ).
fof(i_0_204,plain,
! [X468,X469] :
( ( ~ ord_less(int,bit0(X468),bit1(X469))
| ord_less_eq(int,X468,X469) )
& ( ~ ord_less_eq(int,X468,X469)
| ord_less(int,bit0(X468),bit1(X469)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_rel__simps_I15_J])]) ).
fof(i_0_205,plain,
! [X466,X467] :
( ( ~ ord_less(int,bit0(X466),bit1(X467))
| ord_less_eq(int,X466,X467) )
& ( ~ ord_less_eq(int,X466,X467)
| ord_less(int,bit0(X466),bit1(X467)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_less__int__code_I14_J])]) ).
fof(i_0_206,plain,
! [X464,X465] :
( ( ~ ord_less_eq(int,bit1(X464),bit0(X465))
| ord_less(int,X464,X465) )
& ( ~ ord_less(int,X464,X465)
| ord_less_eq(int,bit1(X464),bit0(X465)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_rel__simps_I33_J])]) ).
fof(i_0_207,plain,
! [X462,X463] :
( ( ~ ord_less_eq(int,bit1(X462),bit0(X463))
| ord_less(int,X462,X463) )
& ( ~ ord_less(int,X462,X463)
| ord_less_eq(int,bit1(X462),bit0(X463)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_less__eq__int__code_I15_J])]) ).
fof(i_0_208,plain,
! [X434,X435] :
( ( ~ ord_less(int,bit1(X434),bit1(X435))
| ord_less(int,X434,X435) )
& ( ~ ord_less(int,X434,X435)
| ord_less(int,bit1(X434),bit1(X435)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_rel__simps_I17_J])]) ).
fof(i_0_209,plain,
! [X432,X433] :
( ( ~ ord_less(int,bit1(X432),bit1(X433))
| ord_less(int,X432,X433) )
& ( ~ ord_less(int,X432,X433)
| ord_less(int,bit1(X432),bit1(X433)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_less__int__code_I16_J])]) ).
fof(i_0_210,plain,
! [X563,X564] :
( ( ~ ord_less(int,bit1(X563),bit0(X564))
| ord_less(int,X563,X564) )
& ( ~ ord_less(int,X563,X564)
| ord_less(int,bit1(X563),bit0(X564)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_rel__simps_I16_J])]) ).
fof(i_0_211,plain,
! [X561,X562] :
( ( ~ ord_less(int,bit1(X561),bit0(X562))
| ord_less(int,X561,X562) )
& ( ~ ord_less(int,X561,X562)
| ord_less(int,bit1(X561),bit0(X562)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_less__int__code_I15_J])]) ).
fof(i_0_212,plain,
! [X442,X443] :
( ( ~ ord_less(int,bit0(X442),bit0(X443))
| ord_less(int,X442,X443) )
& ( ~ ord_less(int,X442,X443)
| ord_less(int,bit0(X442),bit0(X443)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_rel__simps_I14_J])]) ).
fof(i_0_213,plain,
! [X440,X441] :
( ( ~ ord_less(int,bit0(X440),bit0(X441))
| ord_less(int,X440,X441) )
& ( ~ ord_less(int,X440,X441)
| ord_less(int,bit0(X440),bit0(X441)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_less__int__code_I13_J])]) ).
fof(i_0_214,plain,
! [X430] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X430) = plus_plus(nat,X430,X430),
inference(variable_rename,[status(thm)],[fact_35_nat__mult__2]) ).
fof(i_0_215,plain,
! [X431] : times_times(nat,X431,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X431,X431),
inference(variable_rename,[status(thm)],[fact_36_nat__mult__2__right]) ).
fof(i_0_216,plain,
! [X567] :
( ( ~ ord_less_eq(int,pls,bit1(X567))
| ord_less_eq(int,pls,X567) )
& ( ~ ord_less_eq(int,pls,X567)
| ord_less_eq(int,pls,bit1(X567)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_rel__simps_I22_J])]) ).
fof(i_0_217,plain,
! [X461] :
( ( ~ ord_less(int,pls,bit1(X461))
| ord_less_eq(int,pls,X461) )
& ( ~ ord_less_eq(int,pls,X461)
| ord_less(int,pls,bit1(X461)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_rel__simps_I5_J])]) ).
fof(i_0_218,plain,
! [X566] :
( ( ~ ord_less(int,pls,bit0(X566))
| ord_less(int,pls,X566) )
& ( ~ ord_less(int,pls,X566)
| ord_less(int,pls,bit0(X566)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_rel__simps_I4_J])]) ).
fof(i_0_219,plain,
! [X460] :
( ( ~ ord_less_eq(int,bit1(X460),pls)
| ord_less(int,X460,pls) )
& ( ~ ord_less(int,X460,pls)
| ord_less_eq(int,bit1(X460),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_rel__simps_I29_J])]) ).
fof(i_0_220,plain,
! [X560] :
( ( ~ ord_less(int,bit1(X560),pls)
| ord_less(int,X560,pls) )
& ( ~ ord_less(int,X560,pls)
| ord_less(int,bit1(X560),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_rel__simps_I12_J])]) ).
fof(i_0_221,plain,
! [X565] :
( ( ~ ord_less(int,bit0(X565),pls)
| ord_less(int,X565,pls) )
& ( ~ ord_less(int,X565,pls)
| ord_less(int,bit0(X565),pls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_rel__simps_I10_J])]) ).
fof(i_0_222,plain,
! [X351,X352,X353] :
( ~ monoid_mult(X353)
| power_power(X353,ti(X353,X351),X352) = power_power(X353,X351,X352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Power_Opower__class_Opower_arg1])]) ).
fof(i_0_223,plain,
! [X320,X321,X322] :
( ~ monoid_mult(X322)
| times_times(X322,ti(X322,X320),X321) = times_times(X322,X320,X321) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_arg1])]) ).
fof(i_0_224,plain,
! [X311,X312,X313] :
( ~ comm_semiring_1(X313)
| plus_plus(X313,ti(X313,X311),X312) = plus_plus(X313,X311,X312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_arg1])]) ).
fof(i_0_225,plain,
! [X323,X324,X325] :
( ~ monoid_mult(X325)
| times_times(X325,X323,ti(X325,X324)) = times_times(X325,X323,X324) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_arg2])]) ).
fof(i_0_226,plain,
! [X314,X315,X316] :
( ~ comm_semiring_1(X316)
| plus_plus(X316,X314,ti(X316,X315)) = plus_plus(X316,X314,X315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_arg2])]) ).
fof(i_0_227,plain,
! [X392,X393] :
( ( ord_less_eq(int,X392,X393)
| ~ ord_less(int,X392,X393) )
& ( X392 != X393
| ~ ord_less(int,X392,X393) )
& ( ~ ord_less_eq(int,X392,X393)
| X392 = X393
| ord_less(int,X392,X393) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_zless__le])])]) ).
fof(i_0_228,plain,
! [X354,X355,X356] :
( ~ monoid_mult(X356)
| power_power(X356,X354,ti(nat,X355)) = power_power(X356,X354,X355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Power_Opower__class_Opower_arg2])]) ).
fof(i_0_229,plain,
! [X476,X477] :
( ~ twoSqu33214720sum2sq(X477)
| ~ twoSqu33214720sum2sq(X476)
| twoSqu33214720sum2sq(times_times(int,X477,X476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_is__mult__sum2sq])]) ).
fof(i_0_230,plain,
! [X375] :
( ~ semiring_1(X375)
| power_power(X375,one_one(X375),number_number_of(nat,bit0(bit1(pls)))) = one_one(X375) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_12_one__power2])]) ).
fof(i_0_231,plain,
! [X509,X510,X511] :
( ~ comm_semiring_1(X509)
| times_times(X509,X510,X511) = times_times(X509,X511,X510) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).
fof(i_0_232,plain,
! [X533,X534,X535] :
( ~ comm_semiring_1(X533)
| plus_plus(X533,X534,X535) = plus_plus(X533,X535,X534) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(i_0_233,plain,
! [X394,X395] :
( ord_less(int,X394,X395)
| X394 = X395
| ord_less(int,X395,X394) ),
inference(variable_rename,[status(thm)],[fact_23_zless__linear]) ).
fof(i_0_234,plain,
! [X390,X391] :
( ord_less_eq(int,X390,X391)
| ord_less_eq(int,X391,X390) ),
inference(variable_rename,[status(thm)],[fact_21_zle__linear]) ).
fof(i_0_235,plain,
! [X549,X550] : times_times(int,X549,X550) = times_times(int,X550,X549),
inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).
fof(i_0_236,plain,
! [X558,X559] : plus_plus(int,X558,X559) = plus_plus(int,X559,X558),
inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).
fof(i_0_237,plain,
! [X387] :
( ~ number_ring(X387)
| plus_plus(X387,one_one(X387),one_one(X387)) = number_number_of(X387,bit0(bit1(pls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_18_one__add__one__is__two])]) ).
fof(i_0_238,plain,
~ ord_less(int,pls,pls),
inference(fof_simplification,[status(thm)],[fact_42_rel__simps_I2_J]) ).
fof(i_0_239,plain,
! [X405,X406] :
( ~ comm_semiring_1(X405)
| power_power(X405,X406,one_one(nat)) = ti(X405,X406) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])])]) ).
fof(i_0_240,plain,
! [X337,X338] :
( ~ number(X338)
| ti(X338,number_number_of(X338,X337)) = number_number_of(X338,X337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Onumber__class_Onumber__of_res])]) ).
fof(i_0_241,plain,
! [X536,X537,X538] :
( ( number_number_of(X536,X537) != number_number_of(X536,X538)
| X537 = X538
| ~ number_ring(X536)
| ~ ring_char_0(X536) )
& ( X537 != X538
| number_number_of(X536,X537) = number_number_of(X536,X538)
| ~ number_ring(X536)
| ~ ring_char_0(X536) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_eq__number__of])])])]) ).
fof(i_0_242,plain,
! [X335,X336] :
( ~ number(X336)
| number_number_of(X336,ti(int,X335)) = number_number_of(X336,X335) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Onumber__class_Onumber__of_arg1])]) ).
fof(i_0_243,plain,
! [X572,X573] : ti(X572,ti(X572,X573)) = ti(X572,X573),
inference(variable_rename,[status(thm)],[help_ti_idem]) ).
fof(i_0_244,plain,
! [X389] : ord_less_eq(int,X389,X389),
inference(variable_rename,[status(thm)],[fact_20_zle__refl]) ).
fof(i_0_245,plain,
! [X360] :
( ( ~ twoSqu33214720sum2sq(ti(int,X360))
| twoSqu33214720sum2sq(X360) )
& ( ~ twoSqu33214720sum2sq(X360)
| twoSqu33214720sum2sq(ti(int,X360)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1])]) ).
fof(i_0_246,plain,
! [X330] :
( ( ~ zprime(ti(int,X330))
| zprime(X330) )
& ( ~ zprime(X330)
| zprime(ti(int,X330)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_IntPrimes_Ozprime_arg1])]) ).
fof(i_0_247,plain,
! [X310] :
( ~ semiring_1(X310)
| ti(X310,one_one(X310)) = one_one(X310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res])]) ).
fof(i_0_248,hypothesis,
! [X333] : bit1(ti(int,X333)) = bit1(X333),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_arg1]) ).
fof(i_0_249,hypothesis,
! [X331] : bit0(ti(int,X331)) = bit0(X331),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_arg1]) ).
fof(i_0_250,plain,
! [X329] : ti(X329,undefined(X329)) = undefined(X329),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
fof(i_0_251,hypothesis,
! [X334] : ti(int,bit1(X334)) = bit1(X334),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_res]) ).
fof(i_0_252,hypothesis,
! [X332] : ti(int,bit0(X332)) = bit0(X332),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_res]) ).
fof(i_0_253,plain,
! [X542,X543] :
( ( bit1(X542) != bit1(X543)
| X542 = X543 )
& ( X542 != X543
| bit1(X542) = bit1(X543) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_82_rel__simps_I51_J])]) ).
fof(i_0_254,plain,
! [X544,X545] :
( ( bit0(X544) != bit0(X545)
| X544 = X545 )
& ( X544 != X545
| bit0(X544) = bit0(X545) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_83_rel__simps_I48_J])]) ).
fof(i_0_255,plain,
! [X551] : number_number_of(int,X551) = X551,
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
cnf(i_0_256,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_144]),
[final] ).
cnf(i_0_257,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_145]),
[final] ).
cnf(i_0_258,plain,
( power_power(X1,plus_plus(X1,X2,X3),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X1,plus_plus(X1,power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X3,number_number_of(nat,bit0(bit1(pls))))),times_times(X1,times_times(X1,number_number_of(X1,bit0(bit1(pls))),X2),X3))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_259,plain,
twoSqu33214720sum2sq(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]),
[final] ).
cnf(i_0_260,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_147]),
[final] ).
cnf(i_0_261,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_148]),
[final] ).
cnf(i_0_262,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]),
[final] ).
cnf(i_0_263,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_149]),
[final] ).
cnf(i_0_264,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_150]),
[final] ).
cnf(i_0_265,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]),
[final] ).
cnf(i_0_266,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]),
[final] ).
cnf(i_0_267,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X4,times_times(X1,times_times(X1,X2,X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_268,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,X2,times_times(X1,X3,times_times(X1,X4,X5)))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_269,plain,
( times_times(X1,times_times(X1,X2,X3),times_times(X1,X4,X5)) = times_times(X1,times_times(X1,X2,X4),times_times(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_270,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),plus_plus(X1,X4,X5)) = plus_plus(X1,plus_plus(X1,X2,X4),plus_plus(X1,X3,X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_271,plain,
( power_power(X1,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X3)) = times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X3))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_272,plain,
( times_times(X1,power_power(X1,X2,X3),power_power(X1,X2,X4)) = power_power(X1,X2,plus_plus(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_273,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_274,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_158]),
[final] ).
cnf(i_0_275,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_159]),
[final] ).
cnf(i_0_276,plain,
( ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_277,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_161]),
[final] ).
cnf(i_0_278,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_162]),
[final] ).
cnf(i_0_279,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,times_times(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_280,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,plus_plus(X1,X2,X4),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_281,plain,
( times_times(X1,times_times(X1,X2,X3),X4) = times_times(X1,X2,times_times(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_282,plain,
( plus_plus(X1,plus_plus(X1,X2,X3),X4) = plus_plus(X1,X2,plus_plus(X1,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_283,plain,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,times_times(X1,X2,X3),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_284,plain,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,plus_plus(X1,X2,X3),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_285,plain,
( times_times(X1,X2,times_times(X1,X3,X4)) = times_times(X1,X3,times_times(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_286,plain,
( plus_plus(X1,X2,plus_plus(X1,X3,X4)) = plus_plus(X1,X3,plus_plus(X1,X2,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_170]),
[final] ).
cnf(i_0_287,plain,
( power_power(X1,power_power(X1,X2,X3),X4) = power_power(X1,X2,times_times(nat,X3,X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_288,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_172]),
[final] ).
cnf(i_0_289,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_173]),
[final] ).
cnf(i_0_290,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_174]),
[final] ).
cnf(i_0_291,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_292,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_176]),
[final] ).
cnf(i_0_293,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_177]),
[final] ).
cnf(i_0_294,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_178]),
[final] ).
cnf(i_0_295,plain,
( power_power(X1,number_number_of(X1,X2),number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,number_number_of(X1,X2),number_number_of(X1,X2))
| ~ monoid_mult(X1)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_296,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_177]),
[final] ).
cnf(i_0_297,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_180]),
[final] ).
cnf(i_0_298,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_178]),
[final] ).
cnf(i_0_299,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_172]),
[final] ).
cnf(i_0_300,plain,
( ord_less_eq(int,X2,X3)
| ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_301,plain,
( ord_less(int,X2,X3)
| ~ ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_302,plain,
( ord_less(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ord_less_eq(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_303,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_183]),
[final] ).
cnf(i_0_304,plain,
( plus_plus(X1,number_number_of(X1,X2),one_one(X1)) = number_number_of(X1,plus_plus(int,X2,bit1(pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_305,plain,
( plus_plus(X1,one_one(X1),number_number_of(X1,X2)) = number_number_of(X1,plus_plus(int,bit1(pls),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_306,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_307,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_308,plain,
( ord_less_eq(X3,number_number_of(X3,X1),number_number_of(X3,X2))
| ~ ord_less_eq(int,X1,X2)
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_309,plain,
( ord_less(X3,number_number_of(X3,X1),number_number_of(X3,X2))
| ~ ord_less(int,X1,X2)
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_310,plain,
( ord_less_eq(X1,X2,X3)
| ~ ord_less_eq(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_311,plain,
( ord_less(X1,X2,X3)
| ~ ord_less(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_312,plain,
( ord_less_eq(X1,X2,X3)
| ~ ord_less_eq(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_313,plain,
( ord_less(X1,X2,X3)
| ~ ord_less(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_191]),
[final] ).
cnf(i_0_314,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_172]),
[final] ).
cnf(i_0_315,plain,
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_316,plain,
( ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_317,plain,
( ti(X1,power_power(X1,X2,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_192]),
[final] ).
cnf(i_0_318,plain,
( ti(X1,times_times(X1,X2,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_319,plain,
( ti(X1,plus_plus(X1,X2,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_194]),
[final] ).
cnf(i_0_320,plain,
( ord_less_eq(X1,ti(X1,X2),X3)
| ~ ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_321,plain,
( ord_less(X1,ti(X1,X2),X3)
| ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_322,plain,
( ord_less_eq(X1,X2,ti(X1,X3))
| ~ ord_less_eq(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_323,plain,
( ord_less(X1,X2,ti(X1,X3))
| ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_191]),
[final] ).
cnf(i_0_324,plain,
( X1 = X2
| ~ ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_325,plain,
( power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) = times_times(X1,X2,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_326,plain,
( times_times(X1,X2,X2) = power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_197]),
[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_198]),
[final] ).
cnf(i_0_328,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_329,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_330,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_331,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_332,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_333,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_334,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_335,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_336,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_337,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_338,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_339,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_340,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit1(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_341,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_342,plain,
( ord_less(int,X1,X2)
| ~ ord_less(int,bit0(X1),bit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_343,plain,
times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) = plus_plus(nat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_344,plain,
times_times(nat,X1,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_215]),
[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_198]),
[final] ).
cnf(i_0_346,plain,
( ord_less_eq(int,bit1(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_347,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_348,plain,
( ord_less_eq(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_349,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_350,plain,
( ord_less_eq(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_351,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_352,plain,
( ord_less_eq(int,bit0(X1),bit0(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_353,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_354,plain,
( ord_less(int,bit1(X1),bit1(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_355,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_356,plain,
( ord_less(int,bit1(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_357,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_358,plain,
( ord_less(int,bit0(X1),bit1(X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_359,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_360,plain,
( ord_less(int,bit0(X1),bit0(X2))
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_361,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_362,plain,
( ord_less_eq(int,pls,X1)
| ~ ord_less(int,pls,bit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_217]),
[final] ).
cnf(i_0_363,plain,
( ord_less(int,pls,X1)
| ~ ord_less(int,pls,bit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_364,plain,
( ord_less(int,X1,pls)
| ~ ord_less_eq(int,bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_365,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit1(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_366,plain,
( ord_less(int,X1,pls)
| ~ ord_less(int,bit0(X1),pls) ),
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_367,plain,
( power_power(X1,ti(X1,X2),X3) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_222]),
[final] ).
cnf(i_0_368,plain,
( times_times(X1,ti(X1,X2),X3) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_369,plain,
( plus_plus(X1,ti(X1,X2),X3) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_370,plain,
( times_times(X1,X2,ti(X1,X3)) = times_times(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_371,plain,
( plus_plus(X1,X2,ti(X1,X3)) = plus_plus(X1,X2,X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_226]),
[final] ).
cnf(i_0_372,plain,
( X1 = X2
| ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_227]),
[final] ).
cnf(i_0_373,plain,
( ord_less_eq(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_374,plain,
( ord_less(int,bit1(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_375,plain,
( ord_less(int,bit0(X1),pls)
| ~ ord_less(int,X1,pls) ),
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_376,plain,
( ord_less_eq(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_377,plain,
( ord_less(int,pls,bit1(X1))
| ~ ord_less_eq(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_217]),
[final] ).
cnf(i_0_378,plain,
( ord_less(int,pls,bit0(X1))
| ~ ord_less(int,pls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_379,plain,
( power_power(X1,X2,ti(nat,X3)) = power_power(X1,X2,X3)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_380,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_227]),
[final] ).
cnf(i_0_381,plain,
( twoSqu33214720sum2sq(times_times(int,X1,X2))
| ~ twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(X2) ),
inference(split_conjunct,[status(thm)],[i_0_229]),
[final] ).
cnf(i_0_382,plain,
( power_power(X1,one_one(X1),number_number_of(nat,bit0(bit1(pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_383,plain,
( times_times(X1,X2,X3) = times_times(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_231]),
[final] ).
cnf(i_0_384,plain,
( plus_plus(X1,X2,X3) = plus_plus(X1,X3,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_232]),
[final] ).
cnf(i_0_385,plain,
( ord_less(int,X1,X2)
| X1 = X2
| ord_less(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_386,plain,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_387,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_388,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_236]),
[final] ).
cnf(i_0_389,plain,
( plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_390,plain,
( X1 != X2
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_227]),
[final] ).
cnf(i_0_391,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_37_nat__1__add__1]),
[final] ).
cnf(i_0_392,plain,
~ ord_less(int,pls,pls),
inference(split_conjunct,[status(thm)],[i_0_238]),
[final] ).
cnf(i_0_393,plain,
( power_power(X1,X2,one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_239]),
[final] ).
cnf(i_0_394,plain,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[i_0_240]),
[final] ).
cnf(i_0_395,plain,
( X2 = X3
| number_number_of(X1,X2) != number_number_of(X1,X3)
| ~ number_ring(X1)
| ~ ring_char_0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_241]),
[final] ).
cnf(i_0_396,plain,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[i_0_242]),
[final] ).
cnf(i_0_397,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]),
[final] ).
cnf(i_0_398,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_243]),
[final] ).
cnf(i_0_399,plain,
ord_less_eq(int,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_244]),
[final] ).
cnf(i_0_400,plain,
zprime(number_number_of(int,bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[fact_64_zprime__2]),
[final] ).
cnf(i_0_401,plain,
ord_less_eq(int,pls,pls),
inference(split_conjunct,[status(thm)],[fact_45_rel__simps_I19_J]),
[final] ).
cnf(i_0_402,plain,
( twoSqu33214720sum2sq(X1)
| ~ twoSqu33214720sum2sq(ti(int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_403,plain,
( zprime(X1)
| ~ zprime(ti(int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_246]),
[final] ).
cnf(i_0_404,plain,
( twoSqu33214720sum2sq(ti(int,X1))
| ~ twoSqu33214720sum2sq(X1) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_405,plain,
( zprime(ti(int,X1))
| ~ zprime(X1) ),
inference(split_conjunct,[status(thm)],[i_0_246]),
[final] ).
cnf(i_0_406,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_247]),
[final] ).
cnf(i_0_407,hypothesis,
bit1(ti(int,X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[i_0_248]),
[final] ).
cnf(i_0_408,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[i_0_249]),
[final] ).
cnf(i_0_409,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_410,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[i_0_251]),
[final] ).
cnf(i_0_411,hypothesis,
ti(int,bit0(X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[i_0_252]),
[final] ).
cnf(i_0_412,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(split_conjunct,[status(thm)],[fact_53_nat__numeral__1__eq__1]),
[final] ).
cnf(i_0_413,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_54_Numeral1__eq1__nat]),
[final] ).
cnf(i_0_414,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_415,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_416,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_255]),
[final] ).
cnf(i_0_417,plain,
ti(int,t) = t,
inference(split_conjunct,[status(thm)],[tsy_v_t_____res]),
[final] ).
cnf(i_0_418,plain,
ti(int,s) = s,
inference(split_conjunct,[status(thm)],[tsy_v_s_____res]),
[final] ).
cnf(i_0_419,hypothesis,
ti(int,m) = m,
inference(split_conjunct,[status(thm)],[tsy_v_m_res]),
[final] ).
cnf(i_0_420,hypothesis,
ti(int,pls) = pls,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OPls_res]),
[final] ).
cnf(i_0_421,plain,
ring_char_0(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Oring__char__0]),
[final] ).
cnf(i_0_422,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]),
[final] ).
cnf(i_0_423,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]),
[final] ).
cnf(i_0_424,plain,
number_semiring(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Int_Onumber__semiring]),
[final] ).
cnf(i_0_425,plain,
number_semiring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__semiring]),
[final] ).
cnf(i_0_426,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]),
[final] ).
cnf(i_0_427,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]),
[final] ).
cnf(i_0_428,plain,
number(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Int_Onumber]),
[final] ).
cnf(i_0_429,plain,
number(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber]),
[final] ).
cnf(i_0_430,plain,
monoid_mult(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__mult]),
[final] ).
cnf(i_0_431,plain,
monoid_mult(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Groups_Omonoid__mult]),
[final] ).
cnf(i_0_432,plain,
comm_semiring_1(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_433,plain,
comm_semiring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_434,plain,
semiring_1(nat),
inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Osemiring__1]),
[final] ).
cnf(i_0_435,plain,
semiring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Osemiring__1]),
[final] ).
cnf(i_0_436,axiom,
X1 = X1 ).
cnf(i_0_437,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_438,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_439,axiom,
( X1 != X2
| power_power(X1,X3,X4) = power_power(X2,X3,X4) ) ).
cnf(i_0_440,axiom,
( X1 != X2
| power_power(X3,X1,X4) = power_power(X3,X2,X4) ) ).
cnf(i_0_441,axiom,
( X1 != X2
| power_power(X3,X4,X1) = power_power(X3,X4,X2) ) ).
cnf(i_0_442,axiom,
( X1 != X2
| plus_plus(X1,X3,X4) = plus_plus(X2,X3,X4) ) ).
cnf(i_0_443,axiom,
( X1 != X2
| plus_plus(X3,X1,X4) = plus_plus(X3,X2,X4) ) ).
cnf(i_0_444,axiom,
( X1 != X2
| plus_plus(X3,X4,X1) = plus_plus(X3,X4,X2) ) ).
cnf(i_0_445,axiom,
( X1 != X2
| number_number_of(X1,X3) = number_number_of(X2,X3) ) ).
cnf(i_0_446,axiom,
( X1 != X2
| number_number_of(X3,X1) = number_number_of(X3,X2) ) ).
cnf(i_0_447,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ) ).
cnf(i_0_448,axiom,
( X1 != X2
| times_times(X1,X3,X4) = times_times(X2,X3,X4) ) ).
cnf(i_0_449,axiom,
( X1 != X2
| times_times(X3,X1,X4) = times_times(X3,X2,X4) ) ).
cnf(i_0_450,axiom,
( X1 != X2
| times_times(X3,X4,X1) = times_times(X3,X4,X2) ) ).
cnf(i_0_451,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ) ).
cnf(i_0_452,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_453,axiom,
( X1 != X2
| ti(X1,X3) = ti(X2,X3) ) ).
cnf(i_0_454,axiom,
( X1 != X2
| ti(X3,X1) = ti(X3,X2) ) ).
cnf(i_0_455,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_456,axiom,
( X1 != X2
| ~ number_semiring(X1)
| number_semiring(X2) ) ).
cnf(i_0_457,axiom,
( X1 != X2
| ~ number_ring(X1)
| number_ring(X2) ) ).
cnf(i_0_458,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_459,axiom,
( X1 != X2
| ~ semiring_1(X1)
| semiring_1(X2) ) ).
cnf(i_0_460,axiom,
( X1 != X2
| ~ ring_char_0(X1)
| ring_char_0(X2) ) ).
cnf(i_0_461,axiom,
( X1 != X2
| ~ twoSqu33214720sum2sq(X1)
| twoSqu33214720sum2sq(X2) ) ).
cnf(i_0_462,axiom,
( X1 != X2
| ~ ord_less(X1,X3,X4)
| ord_less(X2,X3,X4) ) ).
cnf(i_0_463,axiom,
( X1 != X2
| ~ ord_less(X3,X1,X4)
| ord_less(X3,X2,X4) ) ).
cnf(i_0_464,axiom,
( X1 != X2
| ~ ord_less(X3,X4,X1)
| ord_less(X3,X4,X2) ) ).
cnf(i_0_465,axiom,
( X1 != X2
| ~ zprime(X1)
| zprime(X2) ) ).
cnf(i_0_466,axiom,
( X1 != X2
| ~ comm_semiring_1(X1)
| comm_semiring_1(X2) ) ).
cnf(i_0_467,axiom,
( X1 != X2
| ~ ord_less_eq(X1,X3,X4)
| ord_less_eq(X2,X3,X4) ) ).
cnf(i_0_468,axiom,
( X1 != X2
| ~ ord_less_eq(X3,X1,X4)
| ord_less_eq(X3,X2,X4) ) ).
cnf(i_0_469,axiom,
( X1 != X2
| ~ ord_less_eq(X3,X4,X1)
| ord_less_eq(X3,X4,X2) ) ).
cnf(i_0_470,axiom,
( X1 != X2
| ~ number(X1)
| number(X2) ) ).
cnf(i_0_471,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_472,axiom,
( X1 != X2
| ~ monoid_mult(X1)
| monoid_mult(X2) ) ).
cnf(i_0_436_001,axiom,
X1 = X1 ).
cnf(i_0_437_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_438_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_439_004,axiom,
( X1 != X2
| power_power(X1,X3,X4) = power_power(X2,X3,X4) ) ).
cnf(i_0_440_005,axiom,
( X1 != X2
| power_power(X3,X1,X4) = power_power(X3,X2,X4) ) ).
cnf(i_0_441_006,axiom,
( X1 != X2
| power_power(X3,X4,X1) = power_power(X3,X4,X2) ) ).
cnf(i_0_442_007,axiom,
( X1 != X2
| plus_plus(X1,X3,X4) = plus_plus(X2,X3,X4) ) ).
cnf(i_0_443_008,axiom,
( X1 != X2
| plus_plus(X3,X1,X4) = plus_plus(X3,X2,X4) ) ).
cnf(i_0_444_009,axiom,
( X1 != X2
| plus_plus(X3,X4,X1) = plus_plus(X3,X4,X2) ) ).
cnf(i_0_445_010,axiom,
( X1 != X2
| number_number_of(X1,X3) = number_number_of(X2,X3) ) ).
cnf(i_0_446_011,axiom,
( X1 != X2
| number_number_of(X3,X1) = number_number_of(X3,X2) ) ).
cnf(i_0_447_012,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ) ).
cnf(i_0_448_013,axiom,
( X1 != X2
| times_times(X1,X3,X4) = times_times(X2,X3,X4) ) ).
cnf(i_0_449_014,axiom,
( X1 != X2
| times_times(X3,X1,X4) = times_times(X3,X2,X4) ) ).
cnf(i_0_450_015,axiom,
( X1 != X2
| times_times(X3,X4,X1) = times_times(X3,X4,X2) ) ).
cnf(i_0_451_016,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ) ).
cnf(i_0_452_017,axiom,
( X1 != X2
| one_one(X1) = one_one(X2) ) ).
cnf(i_0_453_018,axiom,
( X1 != X2
| ti(X1,X3) = ti(X2,X3) ) ).
cnf(i_0_454_019,axiom,
( X1 != X2
| ti(X3,X1) = ti(X3,X2) ) ).
cnf(i_0_455_020,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_456_021,axiom,
( X1 != X2
| ~ number_semiring(X1)
| number_semiring(X2) ) ).
cnf(i_0_457_022,axiom,
( X1 != X2
| ~ number_ring(X1)
| number_ring(X2) ) ).
cnf(i_0_458_023,axiom,
( X1 != X2
| ~ linordered_idom(X1)
| linordered_idom(X2) ) ).
cnf(i_0_459_024,axiom,
( X1 != X2
| ~ semiring_1(X1)
| semiring_1(X2) ) ).
cnf(i_0_460_025,axiom,
( X1 != X2
| ~ ring_char_0(X1)
| ring_char_0(X2) ) ).
cnf(i_0_461_026,axiom,
( X1 != X2
| ~ twoSqu33214720sum2sq(X1)
| twoSqu33214720sum2sq(X2) ) ).
cnf(i_0_462_027,axiom,
( X1 != X2
| ~ ord_less(X1,X3,X4)
| ord_less(X2,X3,X4) ) ).
cnf(i_0_463_028,axiom,
( X1 != X2
| ~ ord_less(X3,X1,X4)
| ord_less(X3,X2,X4) ) ).
cnf(i_0_464_029,axiom,
( X1 != X2
| ~ ord_less(X3,X4,X1)
| ord_less(X3,X4,X2) ) ).
cnf(i_0_465_030,axiom,
( X1 != X2
| ~ zprime(X1)
| zprime(X2) ) ).
cnf(i_0_466_031,axiom,
( X1 != X2
| ~ comm_semiring_1(X1)
| comm_semiring_1(X2) ) ).
cnf(i_0_467_032,axiom,
( X1 != X2
| ~ ord_less_eq(X1,X3,X4)
| ord_less_eq(X2,X3,X4) ) ).
cnf(i_0_468_033,axiom,
( X1 != X2
| ~ ord_less_eq(X3,X1,X4)
| ord_less_eq(X3,X2,X4) ) ).
cnf(i_0_469_034,axiom,
( X1 != X2
| ~ ord_less_eq(X3,X4,X1)
| ord_less_eq(X3,X4,X2) ) ).
cnf(i_0_470_035,axiom,
( X1 != X2
| ~ number(X1)
| number(X2) ) ).
cnf(i_0_471_036,axiom,
( X1 != X2
| ~ linorder(X1)
| linorder(X2) ) ).
cnf(i_0_472_037,axiom,
( X1 != X2
| ~ monoid_mult(X1)
| monoid_mult(X2) ) ).
cnf(i_0_473,plain,
~ ord_less(int,X1,X1),
inference(equality_inference,[],[390]) ).
cnf(i_0_474,plain,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X2 ),
inference(equality_inference,[],[395]) ).
cnf(i_0_475,plain,
X1 = X1,
inference(equality_inference,[],[414]) ).
cnf(i_0_476,plain,
X1 = X1,
inference(equality_inference,[],[415]) ).
cnf(i_0_477,plain,
~ ord_less(int,one_one(int),t),
inference(scs_inference,[],[i_0_260,i_0_263]) ).
cnf(i_0_478,plain,
t != one_one(int),
inference(scs_inference,[],[i_0_260,i_0_264]) ).
cnf(i_0_479,plain,
t != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(scs_inference,[],[i_0_265,i_0_390]) ).
cnf(i_0_480,plain,
( ~ ord_less(int,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_390]) ).
cnf(i_0_481,plain,
ti(int,X1) = X1,
inference(scs_inference,[],[i_0_407,i_0_265,i_0_390,i_0_414]) ).
cnf(i_0_482,plain,
( bit1(X1) != bit1(X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_414]) ).
cnf(i_0_483,plain,
X1 = number_number_of(int,X1),
inference(scs_inference,[],[i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437]) ).
cnf(i_0_484,plain,
ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(scs_inference,[],[i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293]) ).
cnf(i_0_485,plain,
ord_less_eq(int,X1,X1),
inference(rename_variables,[],[i_0_399]) ).
cnf(i_0_486,plain,
( ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ord_less(int,X1,X2) ),
inference(rename_variables,[],[i_0_293]) ).
cnf(i_0_487,plain,
ord_less_eq(int,t,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)),
inference(scs_inference,[],[i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294]) ).
cnf(i_0_488,plain,
( ~ ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_294]) ).
cnf(i_0_489,plain,
~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X1),
inference(scs_inference,[],[i_0_473,i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298]) ).
cnf(i_0_490,plain,
~ ord_less(int,X1,X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_491,plain,
( ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ~ ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_298]) ).
cnf(i_0_492,plain,
ord_less_eq(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(scs_inference,[],[i_0_473,i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380]) ).
cnf(i_0_493,plain,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_380]) ).
cnf(i_0_494,plain,
ord_less_eq(int,X1,plus_plus(int,X1,one_one(int))),
inference(scs_inference,[],[i_0_473,i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386]) ).
cnf(i_0_495,plain,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
inference(rename_variables,[],[i_0_386]) ).
cnf(i_0_496,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(scs_inference,[],[i_0_473,i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324]) ).
cnf(i_0_497,plain,
( ~ ord_less_eq(int,X1,X2)
| ~ ord_less_eq(int,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_324]) ).
cnf(i_0_498,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))))) != number_number_of(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_399,i_0_416,i_0_407,i_0_265,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438]) ).
cnf(i_0_499,plain,
number_number_of(int,X1) = X1,
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_500,plain,
twoSqu33214720sum2sq(times_times(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_399,i_0_416,i_0_387,i_0_407,i_0_265,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461]) ).
cnf(i_0_501,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(rename_variables,[],[i_0_387]) ).
cnf(i_0_502,plain,
~ ord_less(number_number_of(int,int),X1,X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_399,i_0_416,i_0_499,i_0_387,i_0_407,i_0_265,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462]) ).
cnf(i_0_503,plain,
number_number_of(int,X1) = X1,
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_504,plain,
~ ord_less(int,number_number_of(int,X1),X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_399,i_0_416,i_0_499,i_0_503,i_0_387,i_0_407,i_0_265,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463]) ).
cnf(i_0_505,plain,
~ ord_less(int,X1,X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_506,plain,
~ ord_less(int,X1,number_number_of(int,X1)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_387,i_0_407,i_0_265,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464]) ).
cnf(i_0_507,plain,
~ ord_less(int,X1,X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_508,plain,
zprime(plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_387,i_0_388,i_0_407,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465]) ).
cnf(i_0_509,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(rename_variables,[],[i_0_388]) ).
cnf(i_0_510,plain,
~ ord_less_eq(number_number_of(int,int),plus_plus(int,X1,one_one(int)),X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_387,i_0_388,i_0_407,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467]) ).
cnf(i_0_511,plain,
number_number_of(int,X1) = X1,
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_512,plain,
~ ord_less_eq(int,number_number_of(int,plus_plus(int,X1,one_one(int))),X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_511,i_0_387,i_0_388,i_0_407,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468]) ).
cnf(i_0_513,plain,
number_number_of(int,X1) = X1,
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_514,plain,
~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),number_number_of(int,X1)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_407,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469]) ).
cnf(i_0_515,plain,
~ ord_less_eq(int,plus_plus(int,t,one_one(int)),one_one(int)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303]) ).
cnf(i_0_516,plain,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,X3,X2)
| ~ ord_less_eq(int,X3,X1) ),
inference(rename_variables,[],[i_0_303]) ).
cnf(i_0_517,plain,
ord_less_eq(int,number_number_of(int,one_one(int)),number_number_of(int,t)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308]) ).
cnf(i_0_518,plain,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(X3,number_number_of(X3,X1),number_number_of(X3,X2))
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(rename_variables,[],[i_0_308]) ).
cnf(i_0_519,plain,
ord_less(int,number_number_of(int,t),number_number_of(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309]) ).
cnf(i_0_520,plain,
( ~ ord_less(int,X1,X2)
| ord_less(X3,number_number_of(X3,X1),number_number_of(X3,X2))
| ~ number_ring(X3)
| ~ linordered_idom(X3) ),
inference(rename_variables,[],[i_0_309]) ).
cnf(i_0_521,plain,
ord_less_eq(int,X1,ti(int,X1)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_485,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310]) ).
cnf(i_0_522,plain,
ord_less_eq(int,X1,X1),
inference(rename_variables,[],[i_0_399]) ).
cnf(i_0_523,plain,
( ~ ord_less_eq(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_310]) ).
cnf(i_0_524,plain,
ord_less(int,X1,plus_plus(int,ti(int,X1),one_one(int))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_485,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311]) ).
cnf(i_0_525,plain,
( ~ ord_less(X1,ti(X1,X2),X3)
| ~ number(X1)
| ~ linorder(X1)
| ord_less(X1,X2,X3) ),
inference(rename_variables,[],[i_0_311]) ).
cnf(i_0_526,plain,
ord_less_eq(int,ti(int,X1),X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312]) ).
cnf(i_0_527,plain,
ord_less_eq(int,X1,X1),
inference(rename_variables,[],[i_0_399]) ).
cnf(i_0_528,plain,
( ~ ord_less_eq(X1,X2,ti(X1,X3))
| ~ number(X1)
| ~ linorder(X1)
| ord_less_eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_312]) ).
cnf(i_0_529,plain,
~ ord_less(int,X1,ti(int,X1)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321]) ).
cnf(i_0_530,plain,
~ ord_less(int,X1,X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_531,plain,
( ord_less(X1,ti(X1,X2),X3)
| ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(rename_variables,[],[i_0_321]) ).
cnf(i_0_532,plain,
~ ord_less(int,ti(int,X1),X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323]) ).
cnf(i_0_533,plain,
~ ord_less(int,X1,X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_534,plain,
( ord_less(X1,X2,ti(X1,X3))
| ~ ord_less(X1,X2,X3)
| ~ number(X1)
| ~ linorder(X1) ),
inference(rename_variables,[],[i_0_323]) ).
cnf(i_0_535,plain,
~ ord_less(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),t),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297]) ).
cnf(i_0_536,plain,
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ~ ord_less(int,X1,X2) ),
inference(rename_variables,[],[i_0_297]) ).
cnf(i_0_537,plain,
X1 = ti(int,X1),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372]) ).
cnf(i_0_538,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_372]) ).
cnf(i_0_539,plain,
( t = times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)
| ord_less(int,t,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)) ),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385]) ).
cnf(i_0_540,plain,
( ord_less(int,X1,X2)
| ord_less(int,X2,X1)
| X2 = X1 ),
inference(rename_variables,[],[i_0_385]) ).
cnf(i_0_541,plain,
number_semiring(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_427,i_0_429,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456]) ).
cnf(i_0_542,plain,
semiring_1(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_427,i_0_429,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459]) ).
cnf(i_0_543,plain,
comm_semiring_1(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_427,i_0_429,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466]) ).
cnf(i_0_544,plain,
number(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_427,i_0_428,i_0_429,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470]) ).
cnf(i_0_545,plain,
linorder(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471]) ).
cnf(i_0_546,plain,
monoid_mult(ti(int,nat)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472]) ).
cnf(i_0_547,plain,
~ ord_less(int,number_number_of(int,t),number_number_of(int,one_one(int))),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472,i_0_276]) ).
cnf(i_0_548,plain,
( ~ ord_less_eq(X1,number_number_of(X1,X2),number_number_of(X1,X3))
| ~ ord_less(X1,number_number_of(X1,X3),number_number_of(X1,X2))
| ~ number(X1)
| ~ linorder(X1) ),
inference(rename_variables,[],[i_0_276]) ).
cnf(i_0_549,plain,
~ ord_less(int,t,one_one(int)),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472,i_0_276,i_0_316]) ).
cnf(i_0_550,plain,
( ord_less(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less(int,X1,X2) ),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_551,plain,
( number_ring(X1)
| int != X1 ),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472,i_0_276,i_0_316,i_0_457]) ).
cnf(i_0_552,plain,
( linordered_idom(X1)
| int != X1 ),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472,i_0_276,i_0_316,i_0_457,i_0_458]) ).
cnf(i_0_553,plain,
( ring_char_0(X1)
| int != X1 ),
inference(scs_inference,[],[i_0_260,i_0_473,i_0_490,i_0_505,i_0_507,i_0_530,i_0_399,i_0_485,i_0_522,i_0_416,i_0_499,i_0_503,i_0_511,i_0_513,i_0_387,i_0_388,i_0_421,i_0_422,i_0_423,i_0_424,i_0_426,i_0_427,i_0_428,i_0_429,i_0_430,i_0_432,i_0_434,i_0_407,i_0_397,i_0_265,i_0_266,i_0_259,i_0_390,i_0_414,i_0_437,i_0_293,i_0_294,i_0_298,i_0_380,i_0_386,i_0_324,i_0_438,i_0_461,i_0_462,i_0_463,i_0_464,i_0_465,i_0_467,i_0_468,i_0_469,i_0_303,i_0_308,i_0_309,i_0_310,i_0_311,i_0_312,i_0_321,i_0_323,i_0_297,i_0_372,i_0_385,i_0_456,i_0_459,i_0_466,i_0_470,i_0_471,i_0_472,i_0_276,i_0_316,i_0_457,i_0_458,i_0_460]) ).
cnf(i_0_554,plain,
number_ring(int),
inference(equality_inference,[],[551]) ).
cnf(i_0_555,plain,
linordered_idom(int),
inference(equality_inference,[],[552]) ).
cnf(i_0_556,plain,
ring_char_0(int),
inference(equality_inference,[],[553]) ).
cnf(i_0_557,plain,
number_ring(number_number_of(int,int)),
inference(scs_inference,[],[i_0_483,i_0_551]) ).
cnf(i_0_558,plain,
X1 = number_number_of(int,X1),
inference(rename_variables,[],[i_0_483]) ).
cnf(i_0_559,plain,
linordered_idom(number_number_of(int,int)),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_551,i_0_552]) ).
cnf(i_0_560,plain,
X1 = number_number_of(int,X1),
inference(rename_variables,[],[i_0_483]) ).
cnf(i_0_561,plain,
ring_char_0(number_number_of(int,int)),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_551,i_0_552,i_0_553]) ).
cnf(i_0_562,plain,
X1 = number_number_of(int,X1),
inference(rename_variables,[],[i_0_483]) ).
cnf(i_0_563,plain,
~ ord_less_eq(int,plus_plus(int,number_number_of(int,X1),one_one(int)),X1),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_551,i_0_552,i_0_553,i_0_315]) ).
cnf(i_0_564,plain,
~ ord_less_eq(int,number_number_of(int,plus_plus(int,X1,one_one(int))),X1),
inference(rename_variables,[],[i_0_512]) ).
cnf(i_0_565,plain,
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_315]) ).
cnf(i_0_566,plain,
X1 != plus_plus(int,X1,one_one(int)),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_484,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390]) ).
cnf(i_0_567,plain,
( ~ ord_less(int,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_390]) ).
cnf(i_0_568,plain,
ord_less(int,X1,ti(int,plus_plus(int,X1,one_one(int)))),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_521,i_0_484,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293]) ).
cnf(i_0_569,plain,
ord_less_eq(int,X1,ti(int,X1)),
inference(rename_variables,[],[i_0_521]) ).
cnf(i_0_570,plain,
( ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X2)
| ord_less(int,X1,X2) ),
inference(rename_variables,[],[i_0_293]) ).
cnf(i_0_571,plain,
~ ord_less_eq(int,ti(int,plus_plus(int,X1,one_one(int))),X1),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_521,i_0_532,i_0_484,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298]) ).
cnf(i_0_572,plain,
~ ord_less(int,ti(int,X1),X1),
inference(rename_variables,[],[i_0_532]) ).
cnf(i_0_573,plain,
( ord_less(int,X1,plus_plus(int,X2,one_one(int)))
| ~ ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_298]) ).
cnf(i_0_574,plain,
ord_less_eq(int,X1,plus_plus(int,ti(int,X1),one_one(int))),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_521,i_0_532,i_0_484,i_0_524,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380]) ).
cnf(i_0_575,plain,
( ~ ord_less(int,X1,X2)
| ord_less_eq(int,X1,X2) ),
inference(rename_variables,[],[i_0_380]) ).
cnf(i_0_576,plain,
ord_less_eq(int,X1,number_number_of(int,plus_plus(int,X1,one_one(int)))),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_564,i_0_521,i_0_532,i_0_484,i_0_524,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380,i_0_386]) ).
cnf(i_0_577,plain,
( ord_less_eq(int,X1,X2)
| ord_less_eq(int,X2,X1) ),
inference(rename_variables,[],[i_0_386]) ).
cnf(i_0_578,plain,
bit0(X1) = bit0(ti(int,X1)),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_512,i_0_564,i_0_408,i_0_521,i_0_532,i_0_484,i_0_524,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380,i_0_386,i_0_437]) ).
cnf(i_0_579,plain,
one_one(int) = t,
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_477,i_0_512,i_0_564,i_0_408,i_0_521,i_0_532,i_0_484,i_0_524,i_0_397,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380,i_0_386,i_0_437,i_0_372]) ).
cnf(i_0_580,plain,
( ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_372]) ).
cnf(i_0_581,plain,
~ ord_less_eq(int,number_number_of(int,plus_plus(int,number_number_of(int,t),one_one(int))),number_number_of(int,one_one(int))),
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_477,i_0_512,i_0_564,i_0_408,i_0_517,i_0_521,i_0_532,i_0_484,i_0_524,i_0_397,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380,i_0_386,i_0_437,i_0_372,i_0_303]) ).
cnf(i_0_582,plain,
~ ord_less_eq(int,number_number_of(int,plus_plus(int,X1,one_one(int))),X1),
inference(rename_variables,[],[i_0_512]) ).
cnf(i_0_583,plain,
( ~ ord_less_eq(int,X1,X2)
| ord_less_eq(int,X3,X2)
| ~ ord_less_eq(int,X3,X1) ),
inference(rename_variables,[],[i_0_303]) ).
cnf(i_0_584,plain,
$false,
inference(scs_inference,[],[i_0_483,i_0_558,i_0_560,i_0_477,i_0_478,i_0_512,i_0_564,i_0_408,i_0_517,i_0_521,i_0_532,i_0_484,i_0_524,i_0_549,i_0_397,i_0_551,i_0_552,i_0_553,i_0_315,i_0_390,i_0_293,i_0_298,i_0_380,i_0_386,i_0_437,i_0_372,i_0_303,i_0_385]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+5 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:20:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.39/1.62 % Version : CSE_E---1.7
% 0.39/1.62 % Problem : theBenchmark.p
% 0.39/1.62 % SZS status Theorem for theBenchmark.p
% 0.39/1.62 % SZS output start CNFRefutation
% See solution above
% 0.91/2.14 % Total time : 1.274s
%------------------------------------------------------------------------------