TSTP Solution File: NUM926+1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n012.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 : 600s
% DateTime : Mon Jul 18 11:03:28 EDT 2022
% Result : Theorem 2.08s 2.28s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(fact_122_rel__simps_I32_J,axiom,
! [K,L] :
( ord_less_eq_int(bit0(K),bit1(L))
<=> ord_less_eq_int(K,L) ),
input ).
fof(fact_122_rel__simps_I32_J_0,plain,
! [K,L] :
( ord_less_eq_int(bit0(K),bit1(L))
| ~ ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_122_rel__simps_I32_J]) ).
fof(fact_122_rel__simps_I32_J_1,plain,
! [K,L] :
( ~ ord_less_eq_int(bit0(K),bit1(L))
| ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_122_rel__simps_I32_J]) ).
fof(fact_121_less__eq__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ),
input ).
fof(fact_121_less__eq__int__code_I14_J_0,plain,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_121_less__eq__int__code_I14_J]) ).
fof(fact_121_less__eq__int__code_I14_J_1,plain,
! [K1,K2] :
( ~ ord_less_eq_int(bit0(K1),bit1(K2))
| ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_121_less__eq__int__code_I14_J]) ).
fof(fact_120_rel__simps_I22_J,axiom,
! [K] :
( ord_less_eq_int(pls,bit1(K))
<=> ord_less_eq_int(pls,K) ),
input ).
fof(fact_120_rel__simps_I22_J_0,plain,
! [K] :
( ord_less_eq_int(pls,bit1(K))
| ~ ord_less_eq_int(pls,K) ),
inference(orientation,[status(thm)],[fact_120_rel__simps_I22_J]) ).
fof(fact_120_rel__simps_I22_J_1,plain,
! [K] :
( ~ ord_less_eq_int(pls,bit1(K))
| ord_less_eq_int(pls,K) ),
inference(orientation,[status(thm)],[fact_120_rel__simps_I22_J]) ).
fof(fact_119_rel__simps_I4_J,axiom,
! [K] :
( ord_less_int(pls,bit0(K))
<=> ord_less_int(pls,K) ),
input ).
fof(fact_119_rel__simps_I4_J_0,plain,
! [K] :
( ord_less_int(pls,bit0(K))
| ~ ord_less_int(pls,K) ),
inference(orientation,[status(thm)],[fact_119_rel__simps_I4_J]) ).
fof(fact_119_rel__simps_I4_J_1,plain,
! [K] :
( ~ ord_less_int(pls,bit0(K))
| ord_less_int(pls,K) ),
inference(orientation,[status(thm)],[fact_119_rel__simps_I4_J]) ).
fof(fact_118_rel__simps_I10_J,axiom,
! [K] :
( ord_less_int(bit0(K),pls)
<=> ord_less_int(K,pls) ),
input ).
fof(fact_118_rel__simps_I10_J_0,plain,
! [K] :
( ord_less_int(bit0(K),pls)
| ~ ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_118_rel__simps_I10_J]) ).
fof(fact_118_rel__simps_I10_J_1,plain,
! [K] :
( ~ ord_less_int(bit0(K),pls)
| ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_118_rel__simps_I10_J]) ).
fof(fact_117_rel__simps_I16_J,axiom,
! [K,L] :
( ord_less_int(bit1(K),bit0(L))
<=> ord_less_int(K,L) ),
input ).
fof(fact_117_rel__simps_I16_J_0,plain,
! [K,L] :
( ord_less_int(bit1(K),bit0(L))
| ~ ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_117_rel__simps_I16_J]) ).
fof(fact_117_rel__simps_I16_J_1,plain,
! [K,L] :
( ~ ord_less_int(bit1(K),bit0(L))
| ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_117_rel__simps_I16_J]) ).
fof(fact_116_less__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_int(bit1(K1),bit0(K2))
<=> ord_less_int(K1,K2) ),
input ).
fof(fact_116_less__int__code_I15_J_0,plain,
! [K1,K2] :
( ord_less_int(bit1(K1),bit0(K2))
| ~ ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_116_less__int__code_I15_J]) ).
fof(fact_116_less__int__code_I15_J_1,plain,
! [K1,K2] :
( ~ ord_less_int(bit1(K1),bit0(K2))
| ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_116_less__int__code_I15_J]) ).
fof(fact_115_rel__simps_I12_J,axiom,
! [K] :
( ord_less_int(bit1(K),pls)
<=> ord_less_int(K,pls) ),
input ).
fof(fact_115_rel__simps_I12_J_0,plain,
! [K] :
( ord_less_int(bit1(K),pls)
| ~ ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_115_rel__simps_I12_J]) ).
fof(fact_115_rel__simps_I12_J_1,plain,
! [K] :
( ~ ord_less_int(bit1(K),pls)
| ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_115_rel__simps_I12_J]) ).
fof(fact_114_zadd__commute,axiom,
! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z),
input ).
fof(fact_114_zadd__commute_0,plain,
! [W,Z] :
( plus_plus_int(Z,W) = plus_plus_int(W,Z)
| $false ),
inference(orientation,[status(thm)],[fact_114_zadd__commute]) ).
fof(fact_113_zadd__left__commute,axiom,
! [X_1,Y_1,Z] : plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z)),
input ).
fof(fact_113_zadd__left__commute_0,plain,
! [X_1,Y_1,Z] :
( plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z))
| $false ),
inference(orientation,[status(thm)],[fact_113_zadd__left__commute]) ).
fof(fact_112_zadd__assoc,axiom,
! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)),
input ).
fof(fact_112_zadd__assoc_0,plain,
! [Z1,Z2,Z3] :
( plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3))
| $false ),
inference(orientation,[status(thm)],[fact_112_zadd__assoc]) ).
fof(fact_111_number__of__is__id,axiom,
! [K_1] : number_number_of_int(K_1) = K_1,
input ).
fof(fact_111_number__of__is__id_0,plain,
! [K_1] :
( number_number_of_int(K_1) = K_1
| $false ),
inference(orientation,[status(thm)],[fact_111_number__of__is__id]) ).
fof(fact_110_zmult__commute,axiom,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z),
input ).
fof(fact_110_zmult__commute_0,plain,
! [W,Z] :
( times_times_int(Z,W) = times_times_int(W,Z)
| $false ),
inference(orientation,[status(thm)],[fact_110_zmult__commute]) ).
fof(fact_109_zmult__assoc,axiom,
! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)),
input ).
fof(fact_109_zmult__assoc_0,plain,
! [Z1,Z2,Z3] :
( times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3))
| $false ),
inference(orientation,[status(thm)],[fact_109_zmult__assoc]) ).
fof(fact_108_rel__simps_I48_J,axiom,
! [K,L] :
( bit0(K) = bit0(L)
<=> K = L ),
input ).
fof(fact_108_rel__simps_I48_J_0,plain,
! [K,L] :
( bit0(K) = bit0(L)
| K != L ),
inference(orientation,[status(thm)],[fact_108_rel__simps_I48_J]) ).
fof(fact_108_rel__simps_I48_J_1,plain,
! [K,L] :
( bit0(K) != bit0(L)
| K = L ),
inference(orientation,[status(thm)],[fact_108_rel__simps_I48_J]) ).
fof(fact_107_rel__simps_I51_J,axiom,
! [K,L] :
( bit1(K) = bit1(L)
<=> K = L ),
input ).
fof(fact_107_rel__simps_I51_J_0,plain,
! [K,L] :
( bit1(K) = bit1(L)
| K != L ),
inference(orientation,[status(thm)],[fact_107_rel__simps_I51_J]) ).
fof(fact_107_rel__simps_I51_J_1,plain,
! [K,L] :
( bit1(K) != bit1(L)
| K = L ),
inference(orientation,[status(thm)],[fact_107_rel__simps_I51_J]) ).
fof(fact_106_number__of__reorient,axiom,
! [W_1,X_2] :
( number_number_of_int(W_1) = X_2
<=> X_2 = number_number_of_int(W_1) ),
input ).
fof(fact_106_number__of__reorient_0,plain,
! [W_1,X_2] :
( number_number_of_int(W_1) = X_2
| X_2 != number_number_of_int(W_1) ),
inference(orientation,[status(thm)],[fact_106_number__of__reorient]) ).
fof(fact_106_number__of__reorient_1,plain,
! [W_1,X_2] :
( number_number_of_int(W_1) != X_2
| X_2 = number_number_of_int(W_1) ),
inference(orientation,[status(thm)],[fact_106_number__of__reorient]) ).
fof(fact_105_number__of__reorient,axiom,
! [W_1,X_2] :
( number_number_of_nat(W_1) = X_2
<=> X_2 = number_number_of_nat(W_1) ),
input ).
fof(fact_105_number__of__reorient_0,plain,
! [W_1,X_2] :
( number_number_of_nat(W_1) = X_2
| X_2 != number_number_of_nat(W_1) ),
inference(orientation,[status(thm)],[fact_105_number__of__reorient]) ).
fof(fact_105_number__of__reorient_1,plain,
! [W_1,X_2] :
( number_number_of_nat(W_1) != X_2
| X_2 = number_number_of_nat(W_1) ),
inference(orientation,[status(thm)],[fact_105_number__of__reorient]) ).
fof(fact_104_eq__number__of,axiom,
! [X_2,Y_2] :
( number_number_of_int(X_2) = number_number_of_int(Y_2)
<=> X_2 = Y_2 ),
input ).
fof(fact_104_eq__number__of_0,plain,
! [X_2,Y_2] :
( number_number_of_int(X_2) = number_number_of_int(Y_2)
| X_2 != Y_2 ),
inference(orientation,[status(thm)],[fact_104_eq__number__of]) ).
fof(fact_104_eq__number__of_1,plain,
! [X_2,Y_2] :
( number_number_of_int(X_2) != number_number_of_int(Y_2)
| X_2 = Y_2 ),
inference(orientation,[status(thm)],[fact_104_eq__number__of]) ).
fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A,C] : plus_plus_nat(A,C) = plus_plus_nat(C,A),
input ).
fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J_0,plain,
! [A,C] :
( plus_plus_nat(A,C) = plus_plus_nat(C,A)
| $false ),
inference(orientation,[status(thm)],[fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A,C] : plus_plus_int(A,C) = plus_plus_int(C,A),
input ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J_0,plain,
! [A,C] :
( plus_plus_int(A,C) = plus_plus_int(C,A)
| $false ),
inference(orientation,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_1,C_1,D] : plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D)),
input ).
fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J_0,plain,
! [A_1,C_1,D] :
( plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D))
| $false ),
inference(orientation,[status(thm)],[fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_1,C_1,D] : plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D)),
input ).
fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J_0,plain,
! [A_1,C_1,D] :
( plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D))
| $false ),
inference(orientation,[status(thm)],[fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_2,C_2,D_1] : plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1),
input ).
fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J_0,plain,
! [A_2,C_2,D_1] :
( plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1)
| $false ),
inference(orientation,[status(thm)],[fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_2,C_2,D_1] : plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1),
input ).
fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J_0,plain,
! [A_2,C_2,D_1] :
( plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1)
| $false ),
inference(orientation,[status(thm)],[fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_3,B,C_3] : plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3)),
input ).
fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J_0,plain,
! [A_3,B,C_3] :
( plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3))
| $false ),
inference(orientation,[status(thm)],[fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_3,B,C_3] : plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3)),
input ).
fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J_0,plain,
! [A_3,B,C_3] :
( plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3))
| $false ),
inference(orientation,[status(thm)],[fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_4,B_1,C_4] : plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1),
input ).
fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J_0,plain,
! [A_4,B_1,C_4] :
( plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1)
| $false ),
inference(orientation,[status(thm)],[fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_4,B_1,C_4] : plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1),
input ).
fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J_0,plain,
! [A_4,B_1,C_4] :
( plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1)
| $false ),
inference(orientation,[status(thm)],[fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_5,B_2,C_5,D_2] : plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2)),
input ).
fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J_0,plain,
! [A_5,B_2,C_5,D_2] :
( plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2))
| $false ),
inference(orientation,[status(thm)],[fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_5,B_2,C_5,D_2] : plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2)),
input ).
fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J_0,plain,
! [A_5,B_2,C_5,D_2] :
( plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2))
| $false ),
inference(orientation,[status(thm)],[fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_6,B_3] : times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6),
input ).
fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J_0,plain,
! [A_6,B_3] :
( times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6)
| $false ),
inference(orientation,[status(thm)],[fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_6,B_3] : times_times_int(A_6,B_3) = times_times_int(B_3,A_6),
input ).
fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J_0,plain,
! [A_6,B_3] :
( times_times_int(A_6,B_3) = times_times_int(B_3,A_6)
| $false ),
inference(orientation,[status(thm)],[fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx,Rx,Ry] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)),
input ).
fof(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J_0,plain,
! [Lx,Rx,Ry] :
( times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry))
| $false ),
inference(orientation,[status(thm)],[fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx,Rx,Ry] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)),
input ).
fof(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J_0,plain,
! [Lx,Rx,Ry] :
( times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry))
| $false ),
inference(orientation,[status(thm)],[fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_1,Rx_1,Ry_1] : times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1),
input ).
fof(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J_0,plain,
! [Lx_1,Rx_1,Ry_1] :
( times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1)
| $false ),
inference(orientation,[status(thm)],[fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_1,Rx_1,Ry_1] : times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1),
input ).
fof(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J_0,plain,
! [Lx_1,Rx_1,Ry_1] :
( times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1)
| $false ),
inference(orientation,[status(thm)],[fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_2,Ly,Rx_2] : times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2)),
input ).
fof(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J_0,plain,
! [Lx_2,Ly,Rx_2] :
( times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2))
| $false ),
inference(orientation,[status(thm)],[fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_2,Ly,Rx_2] : times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2)),
input ).
fof(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J_0,plain,
! [Lx_2,Ly,Rx_2] :
( times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2))
| $false ),
inference(orientation,[status(thm)],[fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_1,Rx_3] : times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1),
input ).
fof(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J_0,plain,
! [Lx_3,Ly_1,Rx_3] :
( times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1)
| $false ),
inference(orientation,[status(thm)],[fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_1,Rx_3] : times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1),
input ).
fof(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J_0,plain,
! [Lx_3,Ly_1,Rx_3] :
( times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1)
| $false ),
inference(orientation,[status(thm)],[fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,times_times_nat(Rx_4,Ry_2))),
input ).
fof(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J_0,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] :
( times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,times_times_nat(Rx_4,Ry_2)))
| $false ),
inference(orientation,[status(thm)],[fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2))),
input ).
fof(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J_0,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] :
( times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2)))
| $false ),
inference(orientation,[status(thm)],[fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_nat(times_times_nat(Lx_5,Ly_3),Ry_3)),
input ).
fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J_0,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] :
( times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_nat(times_times_nat(Lx_5,Ly_3),Ry_3))
| $false ),
inference(orientation,[status(thm)],[fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3)),
input ).
fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J_0,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] :
( times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3))
| $false ),
inference(orientation,[status(thm)],[fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4)),
input ).
fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J_0,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] :
( times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4))
| $false ),
inference(orientation,[status(thm)],[fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4)),
input ).
fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J_0,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] :
( times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4))
| $false ),
inference(orientation,[status(thm)],[fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(fact_75_is__mult__sum2sq,axiom,
! [Y_1,X_1] :
( twoSqu526106917sum2sq(X_1)
=> ( twoSqu526106917sum2sq(Y_1)
=> twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ),
input ).
fof(fact_75_is__mult__sum2sq_0,plain,
! [X_1,Y_1] :
( ~ twoSqu526106917sum2sq(X_1)
| ( twoSqu526106917sum2sq(Y_1)
=> twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ),
inference(orientation,[status(thm)],[fact_75_is__mult__sum2sq]) ).
fof(fact_74_zprime__2,axiom,
zprime(number_number_of_int(bit0(bit1(pls)))),
input ).
fof(fact_74_zprime__2_0,plain,
( zprime(number_number_of_int(bit0(bit1(pls))))
| $false ),
inference(orientation,[status(thm)],[fact_74_zprime__2]) ).
fof(fact_73_zle__add1__eq__le,axiom,
! [W_1,Z_1] :
( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
<=> ord_less_eq_int(W_1,Z_1) ),
input ).
fof(fact_73_zle__add1__eq__le_0,plain,
! [W_1,Z_1] :
( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
| ~ ord_less_eq_int(W_1,Z_1) ),
inference(orientation,[status(thm)],[fact_73_zle__add1__eq__le]) ).
fof(fact_73_zle__add1__eq__le_1,plain,
! [W_1,Z_1] :
( ~ ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
| ord_less_eq_int(W_1,Z_1) ),
inference(orientation,[status(thm)],[fact_73_zle__add1__eq__le]) ).
fof(fact_72_add1__zle__eq,axiom,
! [W_1,Z_1] :
( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
<=> ord_less_int(W_1,Z_1) ),
input ).
fof(fact_72_add1__zle__eq_0,plain,
! [W_1,Z_1] :
( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
| ~ ord_less_int(W_1,Z_1) ),
inference(orientation,[status(thm)],[fact_72_add1__zle__eq]) ).
fof(fact_72_add1__zle__eq_1,plain,
! [W_1,Z_1] :
( ~ ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
| ord_less_int(W_1,Z_1) ),
inference(orientation,[status(thm)],[fact_72_add1__zle__eq]) ).
fof(fact_71_zless__imp__add1__zle,axiom,
! [W,Z] :
( ord_less_int(W,Z)
=> ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ),
input ).
fof(fact_71_zless__imp__add1__zle_0,plain,
! [W,Z] :
( ~ ord_less_int(W,Z)
| ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ),
inference(orientation,[status(thm)],[fact_71_zless__imp__add1__zle]) ).
fof(fact_70_rel__simps_I15_J,axiom,
! [K,L] :
( ord_less_int(bit0(K),bit1(L))
<=> ord_less_eq_int(K,L) ),
input ).
fof(fact_70_rel__simps_I15_J_0,plain,
! [K,L] :
( ord_less_int(bit0(K),bit1(L))
| ~ ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_70_rel__simps_I15_J]) ).
fof(fact_70_rel__simps_I15_J_1,plain,
! [K,L] :
( ~ ord_less_int(bit0(K),bit1(L))
| ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_70_rel__simps_I15_J]) ).
fof(fact_69_less__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_int(bit0(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ),
input ).
fof(fact_69_less__int__code_I14_J_0,plain,
! [K1,K2] :
( ord_less_int(bit0(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_69_less__int__code_I14_J]) ).
fof(fact_69_less__int__code_I14_J_1,plain,
! [K1,K2] :
( ~ ord_less_int(bit0(K1),bit1(K2))
| ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_69_less__int__code_I14_J]) ).
fof(fact_68_rel__simps_I33_J,axiom,
! [K,L] :
( ord_less_eq_int(bit1(K),bit0(L))
<=> ord_less_int(K,L) ),
input ).
fof(fact_68_rel__simps_I33_J_0,plain,
! [K,L] :
( ord_less_eq_int(bit1(K),bit0(L))
| ~ ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_68_rel__simps_I33_J]) ).
fof(fact_68_rel__simps_I33_J_1,plain,
! [K,L] :
( ~ ord_less_eq_int(bit1(K),bit0(L))
| ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_68_rel__simps_I33_J]) ).
fof(fact_67_less__eq__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit0(K2))
<=> ord_less_int(K1,K2) ),
input ).
fof(fact_67_less__eq__int__code_I15_J_0,plain,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit0(K2))
| ~ ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_67_less__eq__int__code_I15_J]) ).
fof(fact_67_less__eq__int__code_I15_J_1,plain,
! [K1,K2] :
( ~ ord_less_eq_int(bit1(K1),bit0(K2))
| ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_67_less__eq__int__code_I15_J]) ).
fof(fact_66_rel__simps_I5_J,axiom,
! [K] :
( ord_less_int(pls,bit1(K))
<=> ord_less_eq_int(pls,K) ),
input ).
fof(fact_66_rel__simps_I5_J_0,plain,
! [K] :
( ord_less_int(pls,bit1(K))
| ~ ord_less_eq_int(pls,K) ),
inference(orientation,[status(thm)],[fact_66_rel__simps_I5_J]) ).
fof(fact_66_rel__simps_I5_J_1,plain,
! [K] :
( ~ ord_less_int(pls,bit1(K))
| ord_less_eq_int(pls,K) ),
inference(orientation,[status(thm)],[fact_66_rel__simps_I5_J]) ).
fof(fact_65_rel__simps_I29_J,axiom,
! [K] :
( ord_less_eq_int(bit1(K),pls)
<=> ord_less_int(K,pls) ),
input ).
fof(fact_65_rel__simps_I29_J_0,plain,
! [K] :
( ord_less_eq_int(bit1(K),pls)
| ~ ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_65_rel__simps_I29_J]) ).
fof(fact_65_rel__simps_I29_J_1,plain,
! [K] :
( ~ ord_less_eq_int(bit1(K),pls)
| ord_less_int(K,pls) ),
inference(orientation,[status(thm)],[fact_65_rel__simps_I29_J]) ).
fof(fact_64_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
input ).
fof(fact_64_Numeral1__eq1__nat_0,plain,
( one_one_nat = number_number_of_nat(bit1(pls))
| $false ),
inference(orientation,[status(thm)],[fact_64_Numeral1__eq1__nat]) ).
fof(fact_63_nat__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
input ).
fof(fact_63_nat__numeral__1__eq__1_0,plain,
( number_number_of_nat(bit1(pls)) = one_one_nat
| $false ),
inference(orientation,[status(thm)],[fact_63_nat__numeral__1__eq__1]) ).
fof(fact_62_add__nat__number__of,axiom,
! [V_1,V] :
( ( ord_less_int(V,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) )
& ( ~ ord_less_int(V,pls)
=> ( ( ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) )
& ( ~ ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ) ),
input ).
fof(fact_62_add__nat__number__of_0,plain,
! [V,V_1] :
( ~ ord_less_int(V,pls)
| plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) ),
inference(orientation,[status(thm)],[fact_62_add__nat__number__of]) ).
fof(fact_62_add__nat__number__of_1,plain,
! [V,V_1] :
( ord_less_int(V,pls)
| ( ( ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) )
& ( ~ ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ),
inference(orientation,[status(thm)],[fact_62_add__nat__number__of]) ).
fof(fact_61_zadd__left__mono,axiom,
! [K_1,I,J] :
( ord_less_eq_int(I,J)
=> ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ),
input ).
fof(fact_61_zadd__left__mono_0,plain,
! [I,J,K_1] :
( ~ ord_less_eq_int(I,J)
| ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ),
inference(orientation,[status(thm)],[fact_61_zadd__left__mono]) ).
fof(fact_60_zadd__strict__right__mono,axiom,
! [K_1,I,J] :
( ord_less_int(I,J)
=> ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ),
input ).
fof(fact_60_zadd__strict__right__mono_0,plain,
! [I,J,K_1] :
( ~ ord_less_int(I,J)
| ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ),
inference(orientation,[status(thm)],[fact_60_zadd__strict__right__mono]) ).
fof(fact_59_less__eq__number__of__int__code,axiom,
! [K,L] :
( ord_less_eq_int(number_number_of_int(K),number_number_of_int(L))
<=> ord_less_eq_int(K,L) ),
input ).
fof(fact_59_less__eq__number__of__int__code_0,plain,
! [K,L] :
( ord_less_eq_int(number_number_of_int(K),number_number_of_int(L))
| ~ ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_59_less__eq__number__of__int__code]) ).
fof(fact_59_less__eq__number__of__int__code_1,plain,
! [K,L] :
( ~ ord_less_eq_int(number_number_of_int(K),number_number_of_int(L))
| ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_59_less__eq__number__of__int__code]) ).
fof(fact_58_less__number__of__int__code,axiom,
! [K,L] :
( ord_less_int(number_number_of_int(K),number_number_of_int(L))
<=> ord_less_int(K,L) ),
input ).
fof(fact_58_less__number__of__int__code_0,plain,
! [K,L] :
( ord_less_int(number_number_of_int(K),number_number_of_int(L))
| ~ ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_58_less__number__of__int__code]) ).
fof(fact_58_less__number__of__int__code_1,plain,
! [K,L] :
( ~ ord_less_int(number_number_of_int(K),number_number_of_int(L))
| ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_58_less__number__of__int__code]) ).
fof(fact_57_rel__simps_I31_J,axiom,
! [K,L] :
( ord_less_eq_int(bit0(K),bit0(L))
<=> ord_less_eq_int(K,L) ),
input ).
fof(fact_57_rel__simps_I31_J_0,plain,
! [K,L] :
( ord_less_eq_int(bit0(K),bit0(L))
| ~ ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_57_rel__simps_I31_J]) ).
fof(fact_57_rel__simps_I31_J_1,plain,
! [K,L] :
( ~ ord_less_eq_int(bit0(K),bit0(L))
| ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_57_rel__simps_I31_J]) ).
fof(fact_56_less__eq__int__code_I13_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit0(K2))
<=> ord_less_eq_int(K1,K2) ),
input ).
fof(fact_56_less__eq__int__code_I13_J_0,plain,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit0(K2))
| ~ ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_56_less__eq__int__code_I13_J]) ).
fof(fact_56_less__eq__int__code_I13_J_1,plain,
! [K1,K2] :
( ~ ord_less_eq_int(bit0(K1),bit0(K2))
| ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_56_less__eq__int__code_I13_J]) ).
fof(fact_55_rel__simps_I19_J,axiom,
ord_less_eq_int(pls,pls),
input ).
fof(fact_55_rel__simps_I19_J_0,plain,
( ord_less_eq_int(pls,pls)
| $false ),
inference(orientation,[status(thm)],[fact_55_rel__simps_I19_J]) ).
fof(fact_54_rel__simps_I14_J,axiom,
! [K,L] :
( ord_less_int(bit0(K),bit0(L))
<=> ord_less_int(K,L) ),
input ).
fof(fact_54_rel__simps_I14_J_0,plain,
! [K,L] :
( ord_less_int(bit0(K),bit0(L))
| ~ ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_54_rel__simps_I14_J]) ).
fof(fact_54_rel__simps_I14_J_1,plain,
! [K,L] :
( ~ ord_less_int(bit0(K),bit0(L))
| ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_54_rel__simps_I14_J]) ).
fof(fact_53_less__int__code_I13_J,axiom,
! [K1,K2] :
( ord_less_int(bit0(K1),bit0(K2))
<=> ord_less_int(K1,K2) ),
input ).
fof(fact_53_less__int__code_I13_J_0,plain,
! [K1,K2] :
( ord_less_int(bit0(K1),bit0(K2))
| ~ ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_53_less__int__code_I13_J]) ).
fof(fact_53_less__int__code_I13_J_1,plain,
! [K1,K2] :
( ~ ord_less_int(bit0(K1),bit0(K2))
| ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_53_less__int__code_I13_J]) ).
fof(fact_52_rel__simps_I2_J,axiom,
~ ord_less_int(pls,pls),
input ).
fof(fact_52_rel__simps_I2_J_0,plain,
( ~ ord_less_int(pls,pls)
| $false ),
inference(orientation,[status(thm)],[fact_52_rel__simps_I2_J]) ).
fof(fact_51_rel__simps_I34_J,axiom,
! [K,L] :
( ord_less_eq_int(bit1(K),bit1(L))
<=> ord_less_eq_int(K,L) ),
input ).
fof(fact_51_rel__simps_I34_J_0,plain,
! [K,L] :
( ord_less_eq_int(bit1(K),bit1(L))
| ~ ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_51_rel__simps_I34_J]) ).
fof(fact_51_rel__simps_I34_J_1,plain,
! [K,L] :
( ~ ord_less_eq_int(bit1(K),bit1(L))
| ord_less_eq_int(K,L) ),
inference(orientation,[status(thm)],[fact_51_rel__simps_I34_J]) ).
fof(fact_50_less__eq__int__code_I16_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ),
input ).
fof(fact_50_less__eq__int__code_I16_J_0,plain,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_50_less__eq__int__code_I16_J]) ).
fof(fact_50_less__eq__int__code_I16_J_1,plain,
! [K1,K2] :
( ~ ord_less_eq_int(bit1(K1),bit1(K2))
| ord_less_eq_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_50_less__eq__int__code_I16_J]) ).
fof(fact_49_rel__simps_I17_J,axiom,
! [K,L] :
( ord_less_int(bit1(K),bit1(L))
<=> ord_less_int(K,L) ),
input ).
fof(fact_49_rel__simps_I17_J_0,plain,
! [K,L] :
( ord_less_int(bit1(K),bit1(L))
| ~ ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_49_rel__simps_I17_J]) ).
fof(fact_49_rel__simps_I17_J_1,plain,
! [K,L] :
( ~ ord_less_int(bit1(K),bit1(L))
| ord_less_int(K,L) ),
inference(orientation,[status(thm)],[fact_49_rel__simps_I17_J]) ).
fof(fact_48_less__int__code_I16_J,axiom,
! [K1,K2] :
( ord_less_int(bit1(K1),bit1(K2))
<=> ord_less_int(K1,K2) ),
input ).
fof(fact_48_less__int__code_I16_J_0,plain,
! [K1,K2] :
( ord_less_int(bit1(K1),bit1(K2))
| ~ ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_48_less__int__code_I16_J]) ).
fof(fact_48_less__int__code_I16_J_1,plain,
! [K1,K2] :
( ~ ord_less_int(bit1(K1),bit1(K2))
| ord_less_int(K1,K2) ),
inference(orientation,[status(thm)],[fact_48_less__int__code_I16_J]) ).
fof(fact_47_nat__1__add__1,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
input ).
fof(fact_47_nat__1__add__1_0,plain,
( plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls)))
| $false ),
inference(orientation,[status(thm)],[fact_47_nat__1__add__1]) ).
fof(fact_46_nat__mult__2__right,axiom,
! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z),
input ).
fof(fact_46_nat__mult__2__right_0,plain,
! [Z] :
( times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z)
| $false ),
inference(orientation,[status(thm)],[fact_46_nat__mult__2__right]) ).
fof(fact_45_nat__mult__2,axiom,
! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z),
input ).
fof(fact_45_nat__mult__2_0,plain,
! [Z] :
( times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z)
| $false ),
inference(orientation,[status(thm)],[fact_45_nat__mult__2]) ).
fof(fact_44_zpower__zadd__distrib,axiom,
! [X_1,Y_1,Z] : power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z)),
input ).
fof(fact_44_zpower__zadd__distrib_0,plain,
! [X_1,Y_1,Z] :
( power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z))
| $false ),
inference(orientation,[status(thm)],[fact_44_zpower__zadd__distrib]) ).
fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_3,P,Q] : times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q)),
input ).
fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J_0,plain,
! [P,Q,X_3] :
( times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q))
| $false ),
inference(orientation,[status(thm)],[fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_3,P,Q] : times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q)),
input ).
fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J_0,plain,
! [P,Q,X_3] :
( times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q))
| $false ),
inference(orientation,[status(thm)],[fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(fact_41_zadd__zless__mono,axiom,
! [Z_2,Z,W_2,W] :
( ord_less_int(W_2,W)
=> ( ord_less_eq_int(Z_2,Z)
=> ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ),
input ).
fof(fact_41_zadd__zless__mono_0,plain,
! [W,W_2,Z,Z_2] :
( ~ ord_less_int(W_2,W)
| ( ord_less_eq_int(Z_2,Z)
=> ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ),
inference(orientation,[status(thm)],[fact_41_zadd__zless__mono]) ).
fof(fact_40_le__number__of,axiom,
! [X_2,Y_2] :
( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
<=> ord_less_eq_int(X_2,Y_2) ),
input ).
fof(fact_40_le__number__of_0,plain,
! [X_2,Y_2] :
( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ~ ord_less_eq_int(X_2,Y_2) ),
inference(orientation,[status(thm)],[fact_40_le__number__of]) ).
fof(fact_40_le__number__of_1,plain,
! [X_2,Y_2] :
( ~ ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ord_less_eq_int(X_2,Y_2) ),
inference(orientation,[status(thm)],[fact_40_le__number__of]) ).
fof(fact_39_less__number__of,axiom,
! [X_2,Y_2] :
( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
<=> ord_less_int(X_2,Y_2) ),
input ).
fof(fact_39_less__number__of_0,plain,
! [X_2,Y_2] :
( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ~ ord_less_int(X_2,Y_2) ),
inference(orientation,[status(thm)],[fact_39_less__number__of]) ).
fof(fact_39_less__number__of_1,plain,
! [X_2,Y_2] :
( ~ ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ord_less_int(X_2,Y_2) ),
inference(orientation,[status(thm)],[fact_39_less__number__of]) ).
fof(fact_38_le__number__of__eq__not__less,axiom,
! [V_2,W_1] :
( ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1))
<=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ),
input ).
fof(fact_38_le__number__of__eq__not__less_0,plain,
! [V_2,W_1] :
( ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1))
| ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ),
inference(orientation,[status(thm)],[fact_38_le__number__of__eq__not__less]) ).
fof(fact_38_le__number__of__eq__not__less_1,plain,
! [V_2,W_1] :
( ~ ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1))
| ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ),
inference(orientation,[status(thm)],[fact_38_le__number__of__eq__not__less]) ).
fof(fact_37_le__number__of__eq__not__less,axiom,
! [V_2,W_1] :
( ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1))
<=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ),
input ).
fof(fact_37_le__number__of__eq__not__less_0,plain,
! [V_2,W_1] :
( ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1))
| ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ),
inference(orientation,[status(thm)],[fact_37_le__number__of__eq__not__less]) ).
fof(fact_37_le__number__of__eq__not__less_1,plain,
! [V_2,W_1] :
( ~ ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1))
| ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ),
inference(orientation,[status(thm)],[fact_37_le__number__of__eq__not__less]) ).
fof(fact_36_zpower__zpower,axiom,
! [X_1,Y_1,Z] : power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z)),
input ).
fof(fact_36_zpower__zpower_0,plain,
! [X_1,Y_1,Z] :
( power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z))
| $false ),
inference(orientation,[status(thm)],[fact_36_zpower__zpower]) ).
fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_4] : power_power_nat(X_4,one_one_nat) = X_4,
input ).
fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J_0,plain,
! [X_4] :
( power_power_nat(X_4,one_one_nat) = X_4
| $false ),
inference(orientation,[status(thm)],[fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_4] : power_power_int(X_4,one_one_nat) = X_4,
input ).
fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J_0,plain,
! [X_4] :
( power_power_int(X_4,one_one_nat) = X_4
| $false ),
inference(orientation,[status(thm)],[fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_5,P_1,Q_1] : power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1)),
input ).
fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J_0,plain,
! [P_1,Q_1,X_5] :
( power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1))
| $false ),
inference(orientation,[status(thm)],[fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_5,P_1,Q_1] : power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1)),
input ).
fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J_0,plain,
! [P_1,Q_1,X_5] :
( power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1))
| $false ),
inference(orientation,[status(thm)],[fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(fact_31_zle__antisym,axiom,
! [Z,W] :
( ord_less_eq_int(Z,W)
=> ( ord_less_eq_int(W,Z)
=> Z = W ) ),
input ).
fof(fact_31_zle__antisym_0,plain,
! [W,Z] :
( ~ ord_less_eq_int(Z,W)
| ( ord_less_eq_int(W,Z)
=> Z = W ) ),
inference(orientation,[status(thm)],[fact_31_zle__antisym]) ).
fof(fact_30_zle__trans,axiom,
! [K_1,I,J] :
( ord_less_eq_int(I,J)
=> ( ord_less_eq_int(J,K_1)
=> ord_less_eq_int(I,K_1) ) ),
input ).
fof(fact_30_zle__trans_0,plain,
! [I,J,K_1] :
( ~ ord_less_eq_int(I,J)
| ( ord_less_eq_int(J,K_1)
=> ord_less_eq_int(I,K_1) ) ),
inference(orientation,[status(thm)],[fact_30_zle__trans]) ).
fof(fact_28_zless__le,axiom,
! [Z_1,W_1] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ),
input ).
fof(fact_28_zless__le_0,plain,
! [W_1,Z_1] :
( ord_less_int(Z_1,W_1)
| ~ ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ),
inference(orientation,[status(thm)],[fact_28_zless__le]) ).
fof(fact_28_zless__le_1,plain,
! [W_1,Z_1] :
( ~ ord_less_int(Z_1,W_1)
| ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ),
inference(orientation,[status(thm)],[fact_28_zless__le]) ).
fof(fact_26_zle__refl,axiom,
! [W] : ord_less_eq_int(W,W),
input ).
fof(fact_26_zle__refl_0,plain,
! [W] :
( ord_less_eq_int(W,W)
| $false ),
inference(orientation,[status(thm)],[fact_26_zle__refl]) ).
fof(fact_24_one__add__one__is__two,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
input ).
fof(fact_24_one__add__one__is__two_0,plain,
( plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls)))
| $false ),
inference(orientation,[status(thm)],[fact_24_one__add__one__is__two]) ).
fof(fact_23_add__special_I3_J,axiom,
! [V_3] : plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls))),
input ).
fof(fact_23_add__special_I3_J_0,plain,
! [V_3] :
( plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls)))
| $false ),
inference(orientation,[status(thm)],[fact_23_add__special_I3_J]) ).
fof(fact_22_add__special_I2_J,axiom,
! [W_3] : plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3)),
input ).
fof(fact_22_add__special_I2_J_0,plain,
! [W_3] :
( plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3))
| $false ),
inference(orientation,[status(thm)],[fact_22_add__special_I2_J]) ).
fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_6,N] : power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N)),
input ).
fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J_0,plain,
! [N,X_6] :
( power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N))
| $false ),
inference(orientation,[status(thm)],[fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_6,N] : power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N)),
input ).
fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J_0,plain,
! [N,X_6] :
( power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N))
| $false ),
inference(orientation,[status(thm)],[fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(fact_19_power2__eq__square,axiom,
! [A_7] : power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7),
input ).
fof(fact_19_power2__eq__square_0,plain,
! [A_7] :
( power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7)
| $false ),
inference(orientation,[status(thm)],[fact_19_power2__eq__square]) ).
fof(fact_18_power2__eq__square,axiom,
! [A_7] : power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7),
input ).
fof(fact_18_power2__eq__square_0,plain,
! [A_7] :
( power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7)
| $false ),
inference(orientation,[status(thm)],[fact_18_power2__eq__square]) ).
fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_7] : times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))),
input ).
fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J_0,plain,
! [X_7] :
( times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls))))
| $false ),
inference(orientation,[status(thm)],[fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_7] : times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))),
input ).
fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J_0,plain,
! [X_7] :
( times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls))))
| $false ),
inference(orientation,[status(thm)],[fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(fact_15_one__power2,axiom,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
input ).
fof(fact_15_one__power2_0,plain,
( power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int
| $false ),
inference(orientation,[status(thm)],[fact_15_one__power2]) ).
fof(fact_14_one__power2,axiom,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
input ).
fof(fact_14_one__power2_0,plain,
( power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat
| $false ),
inference(orientation,[status(thm)],[fact_14_one__power2]) ).
fof(fact_13_cube__square,axiom,
! [A_8] : times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),
input ).
fof(fact_13_cube__square_0,plain,
! [A_8] :
( times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls))))
| $false ),
inference(orientation,[status(thm)],[fact_13_cube__square]) ).
fof(fact_12_power2__eq__square__number__of,axiom,
! [W_4] : power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4)),
input ).
fof(fact_12_power2__eq__square__number__of_0,plain,
! [W_4] :
( power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4))
| $false ),
inference(orientation,[status(thm)],[fact_12_power2__eq__square__number__of]) ).
fof(fact_11_power2__eq__square__number__of,axiom,
! [W_4] : power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4)),
input ).
fof(fact_11_power2__eq__square__number__of_0,plain,
! [W_4] :
( power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4))
| $false ),
inference(orientation,[status(thm)],[fact_11_power2__eq__square__number__of]) ).
fof(fact_10_power2__sum,axiom,
! [X_2,Y_2] : power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)),
input ).
fof(fact_10_power2__sum_0,plain,
! [X_2,Y_2] :
( power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2))
| $false ),
inference(orientation,[status(thm)],[fact_10_power2__sum]) ).
fof(fact_9_power2__sum,axiom,
! [X_2,Y_2] : power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X_2),Y_2)),
input ).
fof(fact_9_power2__sum_0,plain,
! [X_2,Y_2] :
( power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X_2),Y_2))
| $false ),
inference(orientation,[status(thm)],[fact_9_power2__sum]) ).
fof(fact_8_zadd__power3,axiom,
! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls))))),
input ).
fof(fact_8_zadd__power3_0,plain,
! [A_8,B_4] :
( power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls)))))
| $false ),
inference(orientation,[status(thm)],[fact_8_zadd__power3]) ).
fof(fact_7_zadd__power2,axiom,
! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls))))),
input ).
fof(fact_7_zadd__power2_0,plain,
! [A_8,B_4] :
( power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))
| $false ),
inference(orientation,[status(thm)],[fact_7_zadd__power2]) ).
fof(fact_6_qf1pt,axiom,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
input ).
fof(fact_6_qf1pt_0,plain,
( twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t))
| $false ),
inference(orientation,[status(thm)],[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),
input ).
fof(fact_5_t_0,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)
| $false ),
inference(orientation,[status(thm)],[fact_5_t]) ).
fof(fact_4_p,axiom,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
input ).
fof(fact_4_p_0,plain,
( zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| $false ),
inference(orientation,[status(thm)],[fact_4_p]) ).
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)),
input ).
fof(fact_3_t__l__p_0,plain,
( ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| $false ),
inference(orientation,[status(thm)],[fact_3_t__l__p]) ).
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)
=> ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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) ),
input ).
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_0,plain,
( ~ ord_less_int(one_one_int,t)
| ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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(orientation,[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(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
=> ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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) ),
input ).
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_0,plain,
( t != one_one_int
| ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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(orientation,[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(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
input ).
fof(fact_0_tpos_0,plain,
( ord_less_eq_int(one_one_int,t)
| $false ),
inference(orientation,[status(thm)],[fact_0_tpos]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> ord_less_eq_int(one_one_int,t) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[fact_0_tpos_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> t != one_one_int ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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(fold_definition,[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_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
( lhs_atom3
<=> ~ ord_less_int(one_one_int,t) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
( lhs_atom3
| ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,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(fold_definition,[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_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
( lhs_atom4
<=> ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
( lhs_atom4
| $false ),
inference(fold_definition,[status(thm)],[fact_3_t__l__p_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
( lhs_atom5
<=> zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
( lhs_atom5
| $false ),
inference(fold_definition,[status(thm)],[fact_4_p_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
( lhs_atom6
<=> 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(definition,[],]) ).
fof(to_be_clausified_5,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[fact_5_t_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fact_6_qf1pt_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [B_4,A_8] :
( lhs_atom8(B_4,A_8)
<=> power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A_8,B_4] :
( lhs_atom8(B_4,A_8)
| $false ),
inference(fold_definition,[status(thm)],[fact_7_zadd__power2_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [B_4,A_8] :
( lhs_atom9(B_4,A_8)
<=> power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls))))) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A_8,B_4] :
( lhs_atom9(B_4,A_8)
| $false ),
inference(fold_definition,[status(thm)],[fact_8_zadd__power3_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [Y_2,X_2] :
( lhs_atom10(Y_2,X_2)
<=> power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X_2),Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [X_2,Y_2] :
( lhs_atom10(Y_2,X_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_9_power2__sum_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [Y_2,X_2] :
( lhs_atom11(Y_2,X_2)
<=> power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [X_2,Y_2] :
( lhs_atom11(Y_2,X_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_10_power2__sum_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [W_4] :
( lhs_atom12(W_4)
<=> power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [W_4] :
( lhs_atom12(W_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_11_power2__eq__square__number__of_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [W_4] :
( lhs_atom13(W_4)
<=> power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4)) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [W_4] :
( lhs_atom13(W_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_12_power2__eq__square__number__of_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [A_8] :
( lhs_atom14(A_8)
<=> times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A_8] :
( lhs_atom14(A_8)
| $false ),
inference(fold_definition,[status(thm)],[fact_13_cube__square_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[fact_14_one__power2_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[fact_15_one__power2_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [X_7] :
( lhs_atom17(X_7)
<=> times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [X_7] :
( lhs_atom17(X_7)
| $false ),
inference(fold_definition,[status(thm)],[fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [X_7] :
( lhs_atom18(X_7)
<=> times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [X_7] :
( lhs_atom18(X_7)
| $false ),
inference(fold_definition,[status(thm)],[fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [A_7] :
( lhs_atom19(A_7)
<=> power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [A_7] :
( lhs_atom19(A_7)
| $false ),
inference(fold_definition,[status(thm)],[fact_18_power2__eq__square_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [A_7] :
( lhs_atom20(A_7)
<=> power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A_7] :
( lhs_atom20(A_7)
| $false ),
inference(fold_definition,[status(thm)],[fact_19_power2__eq__square_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [X_6,N] :
( lhs_atom21(X_6,N)
<=> power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N)) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [N,X_6] :
( lhs_atom21(X_6,N)
| $false ),
inference(fold_definition,[status(thm)],[fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [X_6,N] :
( lhs_atom22(X_6,N)
<=> power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N)) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [N,X_6] :
( lhs_atom22(X_6,N)
| $false ),
inference(fold_definition,[status(thm)],[fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [W_3] :
( lhs_atom23(W_3)
<=> plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [W_3] :
( lhs_atom23(W_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_22_add__special_I2_J_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_3] :
( lhs_atom24(V_3)
<=> plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls))) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [V_3] :
( lhs_atom24(V_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_23_add__special_I3_J_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
( lhs_atom25
<=> plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
( lhs_atom25
| $false ),
inference(fold_definition,[status(thm)],[fact_24_one__add__one__is__two_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [W] :
( lhs_atom26(W)
<=> ord_less_eq_int(W,W) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [W] :
( lhs_atom26(W)
| $false ),
inference(fold_definition,[status(thm)],[fact_26_zle__refl_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [Z_1,W_1] :
( lhs_atom27(Z_1,W_1)
<=> ~ ord_less_int(Z_1,W_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [W_1,Z_1] :
( lhs_atom27(Z_1,W_1)
| ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ),
inference(fold_definition,[status(thm)],[fact_28_zless__le_1,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [Z_1,W_1] :
( lhs_atom28(Z_1,W_1)
<=> ord_less_int(Z_1,W_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [W_1,Z_1] :
( lhs_atom28(Z_1,W_1)
| ~ ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ),
inference(fold_definition,[status(thm)],[fact_28_zless__le_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [J,I] :
( lhs_atom29(J,I)
<=> ~ ord_less_eq_int(I,J) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [I,J,K_1] :
( lhs_atom29(J,I)
| ( ord_less_eq_int(J,K_1)
=> ord_less_eq_int(I,K_1) ) ),
inference(fold_definition,[status(thm)],[fact_30_zle__trans_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [Z,W] :
( lhs_atom30(Z,W)
<=> ~ ord_less_eq_int(Z,W) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [W,Z] :
( lhs_atom30(Z,W)
| ( ord_less_eq_int(W,Z)
=> Z = W ) ),
inference(fold_definition,[status(thm)],[fact_31_zle__antisym_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [X_5,Q_1,P_1] :
( lhs_atom31(X_5,Q_1,P_1)
<=> power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [P_1,Q_1,X_5] :
( lhs_atom31(X_5,Q_1,P_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [X_5,Q_1,P_1] :
( lhs_atom32(X_5,Q_1,P_1)
<=> power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [P_1,Q_1,X_5] :
( lhs_atom32(X_5,Q_1,P_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [X_4] :
( lhs_atom33(X_4)
<=> power_power_int(X_4,one_one_nat) = X_4 ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [X_4] :
( lhs_atom33(X_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [X_4] :
( lhs_atom34(X_4)
<=> power_power_nat(X_4,one_one_nat) = X_4 ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [X_4] :
( lhs_atom34(X_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [Z,Y_1,X_1] :
( lhs_atom35(Z,Y_1,X_1)
<=> power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z)) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [X_1,Y_1,Z] :
( lhs_atom35(Z,Y_1,X_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_36_zpower__zpower_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [W_1,V_2] :
( lhs_atom36(W_1,V_2)
<=> ~ ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [V_2,W_1] :
( lhs_atom36(W_1,V_2)
| ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ),
inference(fold_definition,[status(thm)],[fact_37_le__number__of__eq__not__less_1,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [W_1,V_2] :
( lhs_atom37(W_1,V_2)
<=> ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [V_2,W_1] :
( lhs_atom37(W_1,V_2)
| ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ),
inference(fold_definition,[status(thm)],[fact_37_le__number__of__eq__not__less_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [W_1,V_2] :
( lhs_atom38(W_1,V_2)
<=> ~ ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [V_2,W_1] :
( lhs_atom38(W_1,V_2)
| ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ),
inference(fold_definition,[status(thm)],[fact_38_le__number__of__eq__not__less_1,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [W_1,V_2] :
( lhs_atom39(W_1,V_2)
<=> ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [V_2,W_1] :
( lhs_atom39(W_1,V_2)
| ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ),
inference(fold_definition,[status(thm)],[fact_38_le__number__of__eq__not__less_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [Y_2,X_2] :
( lhs_atom40(Y_2,X_2)
<=> ~ ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [X_2,Y_2] :
( lhs_atom40(Y_2,X_2)
| ord_less_int(X_2,Y_2) ),
inference(fold_definition,[status(thm)],[fact_39_less__number__of_1,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [Y_2,X_2] :
( lhs_atom41(Y_2,X_2)
<=> ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [X_2,Y_2] :
( lhs_atom41(Y_2,X_2)
| ~ ord_less_int(X_2,Y_2) ),
inference(fold_definition,[status(thm)],[fact_39_less__number__of_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [Y_2,X_2] :
( lhs_atom42(Y_2,X_2)
<=> ~ ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [X_2,Y_2] :
( lhs_atom42(Y_2,X_2)
| ord_less_eq_int(X_2,Y_2) ),
inference(fold_definition,[status(thm)],[fact_40_le__number__of_1,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [Y_2,X_2] :
( lhs_atom43(Y_2,X_2)
<=> ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [X_2,Y_2] :
( lhs_atom43(Y_2,X_2)
| ~ ord_less_eq_int(X_2,Y_2) ),
inference(fold_definition,[status(thm)],[fact_40_le__number__of_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [W_2,W] :
( lhs_atom44(W_2,W)
<=> ~ ord_less_int(W_2,W) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [W,W_2,Z,Z_2] :
( lhs_atom44(W_2,W)
| ( ord_less_eq_int(Z_2,Z)
=> ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ),
inference(fold_definition,[status(thm)],[fact_41_zadd__zless__mono_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [X_3,Q,P] :
( lhs_atom45(X_3,Q,P)
<=> times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q)) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [P,Q,X_3] :
( lhs_atom45(X_3,Q,P)
| $false ),
inference(fold_definition,[status(thm)],[fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [X_3,Q,P] :
( lhs_atom46(X_3,Q,P)
<=> times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q)) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [P,Q,X_3] :
( lhs_atom46(X_3,Q,P)
| $false ),
inference(fold_definition,[status(thm)],[fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [Z,Y_1,X_1] :
( lhs_atom47(Z,Y_1,X_1)
<=> power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z)) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
! [X_1,Y_1,Z] :
( lhs_atom47(Z,Y_1,X_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_44_zpower__zadd__distrib_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [Z] :
( lhs_atom48(Z)
<=> times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [Z] :
( lhs_atom48(Z)
| $false ),
inference(fold_definition,[status(thm)],[fact_45_nat__mult__2_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [Z] :
( lhs_atom49(Z)
<=> times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [Z] :
( lhs_atom49(Z)
| $false ),
inference(fold_definition,[status(thm)],[fact_46_nat__mult__2__right_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
( lhs_atom50
<=> plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
( lhs_atom50
| $false ),
inference(fold_definition,[status(thm)],[fact_47_nat__1__add__1_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [K2,K1] :
( lhs_atom51(K2,K1)
<=> ~ ord_less_int(bit1(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_50,plain,
! [K1,K2] :
( lhs_atom51(K2,K1)
| ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_48_less__int__code_I16_J_1,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [K2,K1] :
( lhs_atom52(K2,K1)
<=> ord_less_int(bit1(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
! [K1,K2] :
( lhs_atom52(K2,K1)
| ~ ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_48_less__int__code_I16_J_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [L,K] :
( lhs_atom53(L,K)
<=> ~ ord_less_int(bit1(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_52,plain,
! [K,L] :
( lhs_atom53(L,K)
| ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_49_rel__simps_I17_J_1,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [L,K] :
( lhs_atom54(L,K)
<=> ord_less_int(bit1(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_53,plain,
! [K,L] :
( lhs_atom54(L,K)
| ~ ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_49_rel__simps_I17_J_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [K2,K1] :
( lhs_atom55(K2,K1)
<=> ~ ord_less_eq_int(bit1(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_54,plain,
! [K1,K2] :
( lhs_atom55(K2,K1)
| ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_50_less__eq__int__code_I16_J_1,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [K2,K1] :
( lhs_atom56(K2,K1)
<=> ord_less_eq_int(bit1(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_55,plain,
! [K1,K2] :
( lhs_atom56(K2,K1)
| ~ ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_50_less__eq__int__code_I16_J_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [L,K] :
( lhs_atom57(L,K)
<=> ~ ord_less_eq_int(bit1(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
! [K,L] :
( lhs_atom57(L,K)
| ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_51_rel__simps_I34_J_1,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [L,K] :
( lhs_atom58(L,K)
<=> ord_less_eq_int(bit1(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_57,plain,
! [K,L] :
( lhs_atom58(L,K)
| ~ ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_51_rel__simps_I34_J_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
( lhs_atom59
<=> ~ ord_less_int(pls,pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
( lhs_atom59
| $false ),
inference(fold_definition,[status(thm)],[fact_52_rel__simps_I2_J_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [K2,K1] :
( lhs_atom60(K2,K1)
<=> ~ ord_less_int(bit0(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_59,plain,
! [K1,K2] :
( lhs_atom60(K2,K1)
| ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_53_less__int__code_I13_J_1,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [K2,K1] :
( lhs_atom61(K2,K1)
<=> ord_less_int(bit0(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
! [K1,K2] :
( lhs_atom61(K2,K1)
| ~ ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_53_less__int__code_I13_J_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [L,K] :
( lhs_atom62(L,K)
<=> ~ ord_less_int(bit0(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_61,plain,
! [K,L] :
( lhs_atom62(L,K)
| ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_54_rel__simps_I14_J_1,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [L,K] :
( lhs_atom63(L,K)
<=> ord_less_int(bit0(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
! [K,L] :
( lhs_atom63(L,K)
| ~ ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_54_rel__simps_I14_J_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
( lhs_atom64
<=> ord_less_eq_int(pls,pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_63,plain,
( lhs_atom64
| $false ),
inference(fold_definition,[status(thm)],[fact_55_rel__simps_I19_J_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [K2,K1] :
( lhs_atom65(K2,K1)
<=> ~ ord_less_eq_int(bit0(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
! [K1,K2] :
( lhs_atom65(K2,K1)
| ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_56_less__eq__int__code_I13_J_1,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [K2,K1] :
( lhs_atom66(K2,K1)
<=> ord_less_eq_int(bit0(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_65,plain,
! [K1,K2] :
( lhs_atom66(K2,K1)
| ~ ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_56_less__eq__int__code_I13_J_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [L,K] :
( lhs_atom67(L,K)
<=> ~ ord_less_eq_int(bit0(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_66,plain,
! [K,L] :
( lhs_atom67(L,K)
| ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_57_rel__simps_I31_J_1,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [L,K] :
( lhs_atom68(L,K)
<=> ord_less_eq_int(bit0(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
! [K,L] :
( lhs_atom68(L,K)
| ~ ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_57_rel__simps_I31_J_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [L,K] :
( lhs_atom69(L,K)
<=> ~ ord_less_int(number_number_of_int(K),number_number_of_int(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
! [K,L] :
( lhs_atom69(L,K)
| ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_58_less__number__of__int__code_1,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [L,K] :
( lhs_atom70(L,K)
<=> ord_less_int(number_number_of_int(K),number_number_of_int(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_69,plain,
! [K,L] :
( lhs_atom70(L,K)
| ~ ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_58_less__number__of__int__code_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [L,K] :
( lhs_atom71(L,K)
<=> ~ ord_less_eq_int(number_number_of_int(K),number_number_of_int(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_70,plain,
! [K,L] :
( lhs_atom71(L,K)
| ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_59_less__eq__number__of__int__code_1,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [L,K] :
( lhs_atom72(L,K)
<=> ord_less_eq_int(number_number_of_int(K),number_number_of_int(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_71,plain,
! [K,L] :
( lhs_atom72(L,K)
| ~ ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_59_less__eq__number__of__int__code_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [J,I] :
( lhs_atom73(J,I)
<=> ~ ord_less_int(I,J) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
! [I,J,K_1] :
( lhs_atom73(J,I)
| ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ),
inference(fold_definition,[status(thm)],[fact_60_zadd__strict__right__mono_0,def_lhs_atom73]) ).
fof(to_be_clausified_73,plain,
! [I,J,K_1] :
( lhs_atom29(J,I)
| ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ),
inference(fold_definition,[status(thm)],[fact_61_zadd__left__mono_0,def_lhs_atom29]) ).
fof(def_lhs_atom74,axiom,
! [V] :
( lhs_atom74(V)
<=> ord_less_int(V,pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_74,plain,
! [V,V_1] :
( lhs_atom74(V)
| ( ( ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) )
& ( ~ ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ),
inference(fold_definition,[status(thm)],[fact_62_add__nat__number__of_1,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V] :
( lhs_atom75(V)
<=> ~ ord_less_int(V,pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_75,plain,
! [V,V_1] :
( lhs_atom75(V)
| plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) ),
inference(fold_definition,[status(thm)],[fact_62_add__nat__number__of_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
( lhs_atom76
<=> number_number_of_nat(bit1(pls)) = one_one_nat ),
inference(definition,[],]) ).
fof(to_be_clausified_76,plain,
( lhs_atom76
| $false ),
inference(fold_definition,[status(thm)],[fact_63_nat__numeral__1__eq__1_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
( lhs_atom77
<=> one_one_nat = number_number_of_nat(bit1(pls)) ),
inference(definition,[],]) ).
fof(to_be_clausified_77,plain,
( lhs_atom77
| $false ),
inference(fold_definition,[status(thm)],[fact_64_Numeral1__eq1__nat_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [K] :
( lhs_atom78(K)
<=> ~ ord_less_eq_int(bit1(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_78,plain,
! [K] :
( lhs_atom78(K)
| ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_65_rel__simps_I29_J_1,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [K] :
( lhs_atom79(K)
<=> ord_less_eq_int(bit1(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_79,plain,
! [K] :
( lhs_atom79(K)
| ~ ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_65_rel__simps_I29_J_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [K] :
( lhs_atom80(K)
<=> ~ ord_less_int(pls,bit1(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_80,plain,
! [K] :
( lhs_atom80(K)
| ord_less_eq_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_66_rel__simps_I5_J_1,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [K] :
( lhs_atom81(K)
<=> ord_less_int(pls,bit1(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
! [K] :
( lhs_atom81(K)
| ~ ord_less_eq_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_66_rel__simps_I5_J_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [K2,K1] :
( lhs_atom82(K2,K1)
<=> ~ ord_less_eq_int(bit1(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
! [K1,K2] :
( lhs_atom82(K2,K1)
| ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_67_less__eq__int__code_I15_J_1,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [K2,K1] :
( lhs_atom83(K2,K1)
<=> ord_less_eq_int(bit1(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_83,plain,
! [K1,K2] :
( lhs_atom83(K2,K1)
| ~ ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_67_less__eq__int__code_I15_J_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [L,K] :
( lhs_atom84(L,K)
<=> ~ ord_less_eq_int(bit1(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_84,plain,
! [K,L] :
( lhs_atom84(L,K)
| ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_68_rel__simps_I33_J_1,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [L,K] :
( lhs_atom85(L,K)
<=> ord_less_eq_int(bit1(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_85,plain,
! [K,L] :
( lhs_atom85(L,K)
| ~ ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_68_rel__simps_I33_J_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [K2,K1] :
( lhs_atom86(K2,K1)
<=> ~ ord_less_int(bit0(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
! [K1,K2] :
( lhs_atom86(K2,K1)
| ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_69_less__int__code_I14_J_1,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [K2,K1] :
( lhs_atom87(K2,K1)
<=> ord_less_int(bit0(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
! [K1,K2] :
( lhs_atom87(K2,K1)
| ~ ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_69_less__int__code_I14_J_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [L,K] :
( lhs_atom88(L,K)
<=> ~ ord_less_int(bit0(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
! [K,L] :
( lhs_atom88(L,K)
| ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_70_rel__simps_I15_J_1,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [L,K] :
( lhs_atom89(L,K)
<=> ord_less_int(bit0(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_89,plain,
! [K,L] :
( lhs_atom89(L,K)
| ~ ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_70_rel__simps_I15_J_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [Z,W] :
( lhs_atom90(Z,W)
<=> ~ ord_less_int(W,Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_90,plain,
! [W,Z] :
( lhs_atom90(Z,W)
| ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ),
inference(fold_definition,[status(thm)],[fact_71_zless__imp__add1__zle_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [Z_1,W_1] :
( lhs_atom91(Z_1,W_1)
<=> ~ ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_91,plain,
! [W_1,Z_1] :
( lhs_atom91(Z_1,W_1)
| ord_less_int(W_1,Z_1) ),
inference(fold_definition,[status(thm)],[fact_72_add1__zle__eq_1,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [Z_1,W_1] :
( lhs_atom92(Z_1,W_1)
<=> ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_92,plain,
! [W_1,Z_1] :
( lhs_atom92(Z_1,W_1)
| ~ ord_less_int(W_1,Z_1) ),
inference(fold_definition,[status(thm)],[fact_72_add1__zle__eq_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [Z_1,W_1] :
( lhs_atom93(Z_1,W_1)
<=> ~ ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
! [W_1,Z_1] :
( lhs_atom93(Z_1,W_1)
| ord_less_eq_int(W_1,Z_1) ),
inference(fold_definition,[status(thm)],[fact_73_zle__add1__eq__le_1,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [Z_1,W_1] :
( lhs_atom94(Z_1,W_1)
<=> ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) ),
inference(definition,[],]) ).
fof(to_be_clausified_94,plain,
! [W_1,Z_1] :
( lhs_atom94(Z_1,W_1)
| ~ ord_less_eq_int(W_1,Z_1) ),
inference(fold_definition,[status(thm)],[fact_73_zle__add1__eq__le_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
( lhs_atom95
<=> zprime(number_number_of_int(bit0(bit1(pls)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_95,plain,
( lhs_atom95
| $false ),
inference(fold_definition,[status(thm)],[fact_74_zprime__2_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [X_1] :
( lhs_atom96(X_1)
<=> ~ twoSqu526106917sum2sq(X_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,plain,
! [X_1,Y_1] :
( lhs_atom96(X_1)
| ( twoSqu526106917sum2sq(Y_1)
=> twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ),
inference(fold_definition,[status(thm)],[fact_75_is__mult__sum2sq_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [Ry_4,Rx_6,Ly_4,Lx_6] :
( lhs_atom97(Ry_4,Rx_6,Ly_4,Lx_6)
<=> times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4)) ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] :
( lhs_atom97(Ry_4,Rx_6,Ly_4,Lx_6)
| $false ),
inference(fold_definition,[status(thm)],[fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [Ry_4,Rx_6,Ly_4,Lx_6] :
( lhs_atom98(Ry_4,Rx_6,Ly_4,Lx_6)
<=> times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4)) ),
inference(definition,[],]) ).
fof(to_be_clausified_98,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] :
( lhs_atom98(Ry_4,Rx_6,Ly_4,Lx_6)
| $false ),
inference(fold_definition,[status(thm)],[fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [Ry_3,Rx_5,Ly_3,Lx_5] :
( lhs_atom99(Ry_3,Rx_5,Ly_3,Lx_5)
<=> times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_99,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] :
( lhs_atom99(Ry_3,Rx_5,Ly_3,Lx_5)
| $false ),
inference(fold_definition,[status(thm)],[fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [Ry_3,Rx_5,Ly_3,Lx_5] :
( lhs_atom100(Ry_3,Rx_5,Ly_3,Lx_5)
<=> times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_nat(times_times_nat(Lx_5,Ly_3),Ry_3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_100,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] :
( lhs_atom100(Ry_3,Rx_5,Ly_3,Lx_5)
| $false ),
inference(fold_definition,[status(thm)],[fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [Ry_2,Rx_4,Ly_2,Lx_4] :
( lhs_atom101(Ry_2,Rx_4,Ly_2,Lx_4)
<=> times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2))) ),
inference(definition,[],]) ).
fof(to_be_clausified_101,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] :
( lhs_atom101(Ry_2,Rx_4,Ly_2,Lx_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [Ry_2,Rx_4,Ly_2,Lx_4] :
( lhs_atom102(Ry_2,Rx_4,Ly_2,Lx_4)
<=> times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,times_times_nat(Rx_4,Ry_2))) ),
inference(definition,[],]) ).
fof(to_be_clausified_102,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] :
( lhs_atom102(Ry_2,Rx_4,Ly_2,Lx_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [Rx_3,Ly_1,Lx_3] :
( lhs_atom103(Rx_3,Ly_1,Lx_3)
<=> times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_103,plain,
! [Lx_3,Ly_1,Rx_3] :
( lhs_atom103(Rx_3,Ly_1,Lx_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [Rx_3,Ly_1,Lx_3] :
( lhs_atom104(Rx_3,Ly_1,Lx_3)
<=> times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_104,plain,
! [Lx_3,Ly_1,Rx_3] :
( lhs_atom104(Rx_3,Ly_1,Lx_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [Rx_2,Ly,Lx_2] :
( lhs_atom105(Rx_2,Ly,Lx_2)
<=> times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_105,plain,
! [Lx_2,Ly,Rx_2] :
( lhs_atom105(Rx_2,Ly,Lx_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [Rx_2,Ly,Lx_2] :
( lhs_atom106(Rx_2,Ly,Lx_2)
<=> times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_106,plain,
! [Lx_2,Ly,Rx_2] :
( lhs_atom106(Rx_2,Ly,Lx_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [Ry_1,Rx_1,Lx_1] :
( lhs_atom107(Ry_1,Rx_1,Lx_1)
<=> times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_107,plain,
! [Lx_1,Rx_1,Ry_1] :
( lhs_atom107(Ry_1,Rx_1,Lx_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [Ry_1,Rx_1,Lx_1] :
( lhs_atom108(Ry_1,Rx_1,Lx_1)
<=> times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_108,plain,
! [Lx_1,Rx_1,Ry_1] :
( lhs_atom108(Ry_1,Rx_1,Lx_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [Ry,Rx,Lx] :
( lhs_atom109(Ry,Rx,Lx)
<=> times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)) ),
inference(definition,[],]) ).
fof(to_be_clausified_109,plain,
! [Lx,Rx,Ry] :
( lhs_atom109(Ry,Rx,Lx)
| $false ),
inference(fold_definition,[status(thm)],[fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [Ry,Rx,Lx] :
( lhs_atom110(Ry,Rx,Lx)
<=> times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)) ),
inference(definition,[],]) ).
fof(to_be_clausified_110,plain,
! [Lx,Rx,Ry] :
( lhs_atom110(Ry,Rx,Lx)
| $false ),
inference(fold_definition,[status(thm)],[fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [B_3,A_6] :
( lhs_atom111(B_3,A_6)
<=> times_times_int(A_6,B_3) = times_times_int(B_3,A_6) ),
inference(definition,[],]) ).
fof(to_be_clausified_111,plain,
! [A_6,B_3] :
( lhs_atom111(B_3,A_6)
| $false ),
inference(fold_definition,[status(thm)],[fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [B_3,A_6] :
( lhs_atom112(B_3,A_6)
<=> times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6) ),
inference(definition,[],]) ).
fof(to_be_clausified_112,plain,
! [A_6,B_3] :
( lhs_atom112(B_3,A_6)
| $false ),
inference(fold_definition,[status(thm)],[fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [D_2,C_5,B_2,A_5] :
( lhs_atom113(D_2,C_5,B_2,A_5)
<=> plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_113,plain,
! [A_5,B_2,C_5,D_2] :
( lhs_atom113(D_2,C_5,B_2,A_5)
| $false ),
inference(fold_definition,[status(thm)],[fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [D_2,C_5,B_2,A_5] :
( lhs_atom114(D_2,C_5,B_2,A_5)
<=> plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_114,plain,
! [A_5,B_2,C_5,D_2] :
( lhs_atom114(D_2,C_5,B_2,A_5)
| $false ),
inference(fold_definition,[status(thm)],[fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [C_4,B_1,A_4] :
( lhs_atom115(C_4,B_1,A_4)
<=> plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_115,plain,
! [A_4,B_1,C_4] :
( lhs_atom115(C_4,B_1,A_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [C_4,B_1,A_4] :
( lhs_atom116(C_4,B_1,A_4)
<=> plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_116,plain,
! [A_4,B_1,C_4] :
( lhs_atom116(C_4,B_1,A_4)
| $false ),
inference(fold_definition,[status(thm)],[fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [C_3,B,A_3] :
( lhs_atom117(C_3,B,A_3)
<=> plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_117,plain,
! [A_3,B,C_3] :
( lhs_atom117(C_3,B,A_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [C_3,B,A_3] :
( lhs_atom118(C_3,B,A_3)
<=> plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_118,plain,
! [A_3,B,C_3] :
( lhs_atom118(C_3,B,A_3)
| $false ),
inference(fold_definition,[status(thm)],[fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [D_1,C_2,A_2] :
( lhs_atom119(D_1,C_2,A_2)
<=> plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_119,plain,
! [A_2,C_2,D_1] :
( lhs_atom119(D_1,C_2,A_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [D_1,C_2,A_2] :
( lhs_atom120(D_1,C_2,A_2)
<=> plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1) ),
inference(definition,[],]) ).
fof(to_be_clausified_120,plain,
! [A_2,C_2,D_1] :
( lhs_atom120(D_1,C_2,A_2)
| $false ),
inference(fold_definition,[status(thm)],[fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [D,C_1,A_1] :
( lhs_atom121(D,C_1,A_1)
<=> plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D)) ),
inference(definition,[],]) ).
fof(to_be_clausified_121,plain,
! [A_1,C_1,D] :
( lhs_atom121(D,C_1,A_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [D,C_1,A_1] :
( lhs_atom122(D,C_1,A_1)
<=> plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D)) ),
inference(definition,[],]) ).
fof(to_be_clausified_122,plain,
! [A_1,C_1,D] :
( lhs_atom122(D,C_1,A_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [C,A] :
( lhs_atom123(C,A)
<=> plus_plus_int(A,C) = plus_plus_int(C,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_123,plain,
! [A,C] :
( lhs_atom123(C,A)
| $false ),
inference(fold_definition,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [C,A] :
( lhs_atom124(C,A)
<=> plus_plus_nat(A,C) = plus_plus_nat(C,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_124,plain,
! [A,C] :
( lhs_atom124(C,A)
| $false ),
inference(fold_definition,[status(thm)],[fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
! [Y_2,X_2] :
( lhs_atom125(Y_2,X_2)
<=> number_number_of_int(X_2) != number_number_of_int(Y_2) ),
inference(definition,[],]) ).
fof(to_be_clausified_125,plain,
! [X_2,Y_2] :
( lhs_atom125(Y_2,X_2)
| X_2 = Y_2 ),
inference(fold_definition,[status(thm)],[fact_104_eq__number__of_1,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
! [Y_2,X_2] :
( lhs_atom126(Y_2,X_2)
<=> number_number_of_int(X_2) = number_number_of_int(Y_2) ),
inference(definition,[],]) ).
fof(to_be_clausified_126,plain,
! [X_2,Y_2] :
( lhs_atom126(Y_2,X_2)
| X_2 != Y_2 ),
inference(fold_definition,[status(thm)],[fact_104_eq__number__of_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
! [X_2,W_1] :
( lhs_atom127(X_2,W_1)
<=> number_number_of_nat(W_1) != X_2 ),
inference(definition,[],]) ).
fof(to_be_clausified_127,plain,
! [W_1,X_2] :
( lhs_atom127(X_2,W_1)
| X_2 = number_number_of_nat(W_1) ),
inference(fold_definition,[status(thm)],[fact_105_number__of__reorient_1,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
! [X_2,W_1] :
( lhs_atom128(X_2,W_1)
<=> number_number_of_nat(W_1) = X_2 ),
inference(definition,[],]) ).
fof(to_be_clausified_128,plain,
! [W_1,X_2] :
( lhs_atom128(X_2,W_1)
| X_2 != number_number_of_nat(W_1) ),
inference(fold_definition,[status(thm)],[fact_105_number__of__reorient_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
! [X_2,W_1] :
( lhs_atom129(X_2,W_1)
<=> number_number_of_int(W_1) != X_2 ),
inference(definition,[],]) ).
fof(to_be_clausified_129,plain,
! [W_1,X_2] :
( lhs_atom129(X_2,W_1)
| X_2 = number_number_of_int(W_1) ),
inference(fold_definition,[status(thm)],[fact_106_number__of__reorient_1,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
! [X_2,W_1] :
( lhs_atom130(X_2,W_1)
<=> number_number_of_int(W_1) = X_2 ),
inference(definition,[],]) ).
fof(to_be_clausified_130,plain,
! [W_1,X_2] :
( lhs_atom130(X_2,W_1)
| X_2 != number_number_of_int(W_1) ),
inference(fold_definition,[status(thm)],[fact_106_number__of__reorient_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
! [L,K] :
( lhs_atom131(L,K)
<=> bit1(K) != bit1(L) ),
inference(definition,[],]) ).
fof(to_be_clausified_131,plain,
! [K,L] :
( lhs_atom131(L,K)
| K = L ),
inference(fold_definition,[status(thm)],[fact_107_rel__simps_I51_J_1,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
! [L,K] :
( lhs_atom132(L,K)
<=> bit1(K) = bit1(L) ),
inference(definition,[],]) ).
fof(to_be_clausified_132,plain,
! [K,L] :
( lhs_atom132(L,K)
| K != L ),
inference(fold_definition,[status(thm)],[fact_107_rel__simps_I51_J_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
! [L,K] :
( lhs_atom133(L,K)
<=> bit0(K) != bit0(L) ),
inference(definition,[],]) ).
fof(to_be_clausified_133,plain,
! [K,L] :
( lhs_atom133(L,K)
| K = L ),
inference(fold_definition,[status(thm)],[fact_108_rel__simps_I48_J_1,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
! [L,K] :
( lhs_atom134(L,K)
<=> bit0(K) = bit0(L) ),
inference(definition,[],]) ).
fof(to_be_clausified_134,plain,
! [K,L] :
( lhs_atom134(L,K)
| K != L ),
inference(fold_definition,[status(thm)],[fact_108_rel__simps_I48_J_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
! [Z3,Z2,Z1] :
( lhs_atom135(Z3,Z2,Z1)
<=> times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_135,plain,
! [Z1,Z2,Z3] :
( lhs_atom135(Z3,Z2,Z1)
| $false ),
inference(fold_definition,[status(thm)],[fact_109_zmult__assoc_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
! [Z,W] :
( lhs_atom136(Z,W)
<=> times_times_int(Z,W) = times_times_int(W,Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_136,plain,
! [W,Z] :
( lhs_atom136(Z,W)
| $false ),
inference(fold_definition,[status(thm)],[fact_110_zmult__commute_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
! [K_1] :
( lhs_atom137(K_1)
<=> number_number_of_int(K_1) = K_1 ),
inference(definition,[],]) ).
fof(to_be_clausified_137,plain,
! [K_1] :
( lhs_atom137(K_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_111_number__of__is__id_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
! [Z3,Z2,Z1] :
( lhs_atom138(Z3,Z2,Z1)
<=> plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)) ),
inference(definition,[],]) ).
fof(to_be_clausified_138,plain,
! [Z1,Z2,Z3] :
( lhs_atom138(Z3,Z2,Z1)
| $false ),
inference(fold_definition,[status(thm)],[fact_112_zadd__assoc_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
! [Z,Y_1,X_1] :
( lhs_atom139(Z,Y_1,X_1)
<=> plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z)) ),
inference(definition,[],]) ).
fof(to_be_clausified_139,plain,
! [X_1,Y_1,Z] :
( lhs_atom139(Z,Y_1,X_1)
| $false ),
inference(fold_definition,[status(thm)],[fact_113_zadd__left__commute_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
! [Z,W] :
( lhs_atom140(Z,W)
<=> plus_plus_int(Z,W) = plus_plus_int(W,Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_140,plain,
! [W,Z] :
( lhs_atom140(Z,W)
| $false ),
inference(fold_definition,[status(thm)],[fact_114_zadd__commute_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
! [K] :
( lhs_atom141(K)
<=> ~ ord_less_int(bit1(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_141,plain,
! [K] :
( lhs_atom141(K)
| ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_115_rel__simps_I12_J_1,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
! [K] :
( lhs_atom142(K)
<=> ord_less_int(bit1(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_142,plain,
! [K] :
( lhs_atom142(K)
| ~ ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_115_rel__simps_I12_J_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
! [K2,K1] :
( lhs_atom143(K2,K1)
<=> ~ ord_less_int(bit1(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_143,plain,
! [K1,K2] :
( lhs_atom143(K2,K1)
| ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_116_less__int__code_I15_J_1,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
! [K2,K1] :
( lhs_atom144(K2,K1)
<=> ord_less_int(bit1(K1),bit0(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_144,plain,
! [K1,K2] :
( lhs_atom144(K2,K1)
| ~ ord_less_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_116_less__int__code_I15_J_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
! [L,K] :
( lhs_atom145(L,K)
<=> ~ ord_less_int(bit1(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_145,plain,
! [K,L] :
( lhs_atom145(L,K)
| ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_117_rel__simps_I16_J_1,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
! [L,K] :
( lhs_atom146(L,K)
<=> ord_less_int(bit1(K),bit0(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_146,plain,
! [K,L] :
( lhs_atom146(L,K)
| ~ ord_less_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_117_rel__simps_I16_J_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
! [K] :
( lhs_atom147(K)
<=> ~ ord_less_int(bit0(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_147,plain,
! [K] :
( lhs_atom147(K)
| ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_118_rel__simps_I10_J_1,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
! [K] :
( lhs_atom148(K)
<=> ord_less_int(bit0(K),pls) ),
inference(definition,[],]) ).
fof(to_be_clausified_148,plain,
! [K] :
( lhs_atom148(K)
| ~ ord_less_int(K,pls) ),
inference(fold_definition,[status(thm)],[fact_118_rel__simps_I10_J_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
! [K] :
( lhs_atom149(K)
<=> ~ ord_less_int(pls,bit0(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_149,plain,
! [K] :
( lhs_atom149(K)
| ord_less_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_119_rel__simps_I4_J_1,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
! [K] :
( lhs_atom150(K)
<=> ord_less_int(pls,bit0(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_150,plain,
! [K] :
( lhs_atom150(K)
| ~ ord_less_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_119_rel__simps_I4_J_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
! [K] :
( lhs_atom151(K)
<=> ~ ord_less_eq_int(pls,bit1(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_151,plain,
! [K] :
( lhs_atom151(K)
| ord_less_eq_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_120_rel__simps_I22_J_1,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
! [K] :
( lhs_atom152(K)
<=> ord_less_eq_int(pls,bit1(K)) ),
inference(definition,[],]) ).
fof(to_be_clausified_152,plain,
! [K] :
( lhs_atom152(K)
| ~ ord_less_eq_int(pls,K) ),
inference(fold_definition,[status(thm)],[fact_120_rel__simps_I22_J_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
! [K2,K1] :
( lhs_atom153(K2,K1)
<=> ~ ord_less_eq_int(bit0(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_153,plain,
! [K1,K2] :
( lhs_atom153(K2,K1)
| ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_121_less__eq__int__code_I14_J_1,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
! [K2,K1] :
( lhs_atom154(K2,K1)
<=> ord_less_eq_int(bit0(K1),bit1(K2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_154,plain,
! [K1,K2] :
( lhs_atom154(K2,K1)
| ~ ord_less_eq_int(K1,K2) ),
inference(fold_definition,[status(thm)],[fact_121_less__eq__int__code_I14_J_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
! [L,K] :
( lhs_atom155(L,K)
<=> ~ ord_less_eq_int(bit0(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_155,plain,
! [K,L] :
( lhs_atom155(L,K)
| ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_122_rel__simps_I32_J_1,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
! [L,K] :
( lhs_atom156(L,K)
<=> ord_less_eq_int(bit0(K),bit1(L)) ),
inference(definition,[],]) ).
fof(to_be_clausified_156,plain,
! [K,L] :
( lhs_atom156(L,K)
| ~ ord_less_eq_int(K,L) ),
inference(fold_definition,[status(thm)],[fact_122_rel__simps_I32_J_0,def_lhs_atom156]) ).
% Start CNF derivation
fof(c_0_0,axiom,
( lhs_atom3
| ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_1,axiom,
( lhs_atom2
| ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_2,axiom,
! [X65,X66,X67,X68] :
( lhs_atom114(X65,X66,X67,X68)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_3,axiom,
! [X65,X66,X67,X68] :
( lhs_atom113(X65,X66,X67,X68)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_4,axiom,
! [X47,X48,X49,X50] :
( lhs_atom102(X47,X48,X49,X50)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_5,axiom,
! [X47,X48,X49,X50] :
( lhs_atom101(X47,X48,X49,X50)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_6,axiom,
! [X43,X44,X45,X46] :
( lhs_atom100(X43,X44,X45,X46)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_7,axiom,
! [X43,X44,X45,X46] :
( lhs_atom99(X43,X44,X45,X46)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_8,axiom,
! [X39,X40,X41,X42] :
( lhs_atom98(X39,X40,X41,X42)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_9,axiom,
! [X39,X40,X41,X42] :
( lhs_atom97(X39,X40,X41,X42)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_10,axiom,
! [X28,X20,X29,X14] :
( lhs_atom44(X29,X14)
| ( ord_less_eq_int(X28,X20)
=> ord_less_int(plus_plus_int(X29,X28),plus_plus_int(X14,X20)) ) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_11,axiom,
! [X17,X18,X19] :
( lhs_atom29(X18,X19)
| ord_less_eq_int(plus_plus_int(X17,X19),plus_plus_int(X17,X18)) ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_12,axiom,
! [X17,X18,X19] :
( lhs_atom73(X18,X19)
| ord_less_int(plus_plus_int(X19,X17),plus_plus_int(X18,X17)) ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_13,axiom,
! [X37,X38] :
( lhs_atom74(X38)
| ( ( ord_less_int(X37,pls)
=> plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(X38) )
& ( ~ ord_less_int(X37,pls)
=> plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(plus_plus_int(X38,X37)) ) ) ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_14,axiom,
! [X16,X27] :
( lhs_atom38(X16,X27)
| ~ ord_less_int(number_number_of_int(X16),number_number_of_int(X27)) ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_15,axiom,
! [X16,X27] :
( lhs_atom36(X16,X27)
| ~ ord_less_nat(number_number_of_nat(X16),number_number_of_nat(X27)) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_16,axiom,
! [X20,X25,X26] :
( lhs_atom139(X20,X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_17,axiom,
! [X83,X84,X85] :
( lhs_atom138(X83,X84,X85)
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_18,axiom,
! [X83,X84,X85] :
( lhs_atom135(X83,X84,X85)
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_19,axiom,
! [X78,X79,X80] :
( lhs_atom122(X78,X79,X80)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_20,axiom,
! [X78,X79,X80] :
( lhs_atom121(X78,X79,X80)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_21,axiom,
! [X75,X76,X77] :
( lhs_atom120(X75,X76,X77)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_22,axiom,
! [X75,X76,X77] :
( lhs_atom119(X75,X76,X77)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_23,axiom,
! [X72,X73,X74] :
( lhs_atom118(X72,X73,X74)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_24,axiom,
! [X72,X73,X74] :
( lhs_atom117(X72,X73,X74)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_25,axiom,
! [X69,X70,X71] :
( lhs_atom116(X69,X70,X71)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_26,axiom,
! [X69,X70,X71] :
( lhs_atom115(X69,X70,X71)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_27,axiom,
! [X60,X61,X62] :
( lhs_atom110(X60,X61,X62)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_28,axiom,
! [X60,X61,X62] :
( lhs_atom109(X60,X61,X62)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_29,axiom,
! [X57,X58,X59] :
( lhs_atom108(X57,X58,X59)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_30,axiom,
! [X57,X58,X59] :
( lhs_atom107(X57,X58,X59)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_31,axiom,
! [X54,X55,X56] :
( lhs_atom106(X54,X55,X56)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_32,axiom,
! [X54,X55,X56] :
( lhs_atom105(X54,X55,X56)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_33,axiom,
! [X51,X52,X53] :
( lhs_atom104(X51,X52,X53)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_34,axiom,
! [X51,X52,X53] :
( lhs_atom103(X51,X52,X53)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_35,axiom,
! [X20,X25,X26] :
( lhs_atom47(X20,X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_36,axiom,
! [X30,X31,X32] :
( lhs_atom46(X30,X31,X32)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_37,axiom,
! [X30,X31,X32] :
( lhs_atom45(X30,X31,X32)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_38,axiom,
! [X20,X25,X26] :
( lhs_atom35(X20,X25,X26)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_39,axiom,
! [X21,X22,X23] :
( lhs_atom32(X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_40,axiom,
! [X21,X22,X23] :
( lhs_atom31(X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_41,axiom,
! [X20,X14] :
( lhs_atom90(X20,X14)
| ord_less_eq_int(plus_plus_int(X14,one_one_int),X20) ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_42,axiom,
! [X17,X18,X19] :
( lhs_atom29(X18,X19)
| ( ord_less_eq_int(X18,X17)
=> ord_less_eq_int(X19,X17) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_43,axiom,
! [X25,X26] :
( lhs_atom96(X26)
| ( twoSqu526106917sum2sq(X25)
=> twoSqu526106917sum2sq(times_times_int(X26,X25)) ) ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_44,axiom,
! [X16,X27] :
( lhs_atom39(X16,X27)
| ord_less_int(number_number_of_int(X16),number_number_of_int(X27)) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_45,axiom,
! [X16,X27] :
( lhs_atom37(X16,X27)
| ord_less_nat(number_number_of_nat(X16),number_number_of_nat(X27)) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_46,axiom,
! [X20,X14] :
( lhs_atom30(X20,X14)
| ( ord_less_eq_int(X14,X20)
=> X20 = X14 ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_47,axiom,
! [X15,X16] :
( lhs_atom28(X15,X16)
| ~ ( ord_less_eq_int(X15,X16)
& X15 != X16 ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_48,axiom,
! [X35,X36] :
( lhs_atom156(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_49,axiom,
! [X33,X34] :
( lhs_atom154(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_50,axiom,
! [X35,X36] :
( lhs_atom146(X35,X36)
| ~ ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_51,axiom,
! [X33,X34] :
( lhs_atom144(X33,X34)
| ~ ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_52,axiom,
! [X15,X16] :
( lhs_atom94(X15,X16)
| ~ ord_less_eq_int(X16,X15) ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_53,axiom,
! [X15,X16] :
( lhs_atom92(X15,X16)
| ~ ord_less_int(X16,X15) ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_54,axiom,
! [X35,X36] :
( lhs_atom89(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_55,axiom,
! [X33,X34] :
( lhs_atom87(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_56,axiom,
! [X35,X36] :
( lhs_atom85(X35,X36)
| ~ ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_57,axiom,
! [X33,X34] :
( lhs_atom83(X33,X34)
| ~ ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_58,axiom,
! [X35,X36] :
( lhs_atom72(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_59,axiom,
! [X35,X36] :
( lhs_atom70(X35,X36)
| ~ ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_60,axiom,
! [X35,X36] :
( lhs_atom68(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_61,axiom,
! [X33,X34] :
( lhs_atom66(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_62,axiom,
! [X35,X36] :
( lhs_atom63(X35,X36)
| ~ ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_63,axiom,
! [X33,X34] :
( lhs_atom61(X33,X34)
| ~ ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_64,axiom,
! [X35,X36] :
( lhs_atom58(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_65,axiom,
! [X33,X34] :
( lhs_atom56(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_66,axiom,
! [X35,X36] :
( lhs_atom54(X35,X36)
| ~ ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_67,axiom,
! [X33,X34] :
( lhs_atom52(X33,X34)
| ~ ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_68,axiom,
! [X5,X6] :
( lhs_atom43(X5,X6)
| ~ ord_less_eq_int(X6,X5) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_69,axiom,
! [X5,X6] :
( lhs_atom41(X5,X6)
| ~ ord_less_int(X6,X5) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_70,axiom,
! [X37,X38] :
( lhs_atom75(X38)
| plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(X37) ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_71,axiom,
! [X35,X36] :
( lhs_atom155(X35,X36)
| ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_72,axiom,
! [X33,X34] :
( lhs_atom153(X33,X34)
| ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_73,axiom,
! [X35,X36] :
( lhs_atom145(X35,X36)
| ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_74,axiom,
! [X33,X34] :
( lhs_atom143(X33,X34)
| ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_75,axiom,
! [X15,X16] :
( lhs_atom93(X15,X16)
| ord_less_eq_int(X16,X15) ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_76,axiom,
! [X15,X16] :
( lhs_atom91(X15,X16)
| ord_less_int(X16,X15) ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_77,axiom,
! [X35,X36] :
( lhs_atom88(X35,X36)
| ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_78,axiom,
! [X33,X34] :
( lhs_atom86(X33,X34)
| ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_79,axiom,
! [X35,X36] :
( lhs_atom84(X35,X36)
| ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_80,axiom,
! [X33,X34] :
( lhs_atom82(X33,X34)
| ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_81,axiom,
! [X35,X36] :
( lhs_atom71(X35,X36)
| ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_82,axiom,
! [X35,X36] :
( lhs_atom69(X35,X36)
| ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_83,axiom,
! [X35,X36] :
( lhs_atom67(X35,X36)
| ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_84,axiom,
! [X33,X34] :
( lhs_atom65(X33,X34)
| ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_85,axiom,
! [X35,X36] :
( lhs_atom62(X35,X36)
| ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_86,axiom,
! [X33,X34] :
( lhs_atom60(X33,X34)
| ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_87,axiom,
! [X35,X36] :
( lhs_atom57(X35,X36)
| ord_less_eq_int(X36,X35) ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_88,axiom,
! [X33,X34] :
( lhs_atom55(X33,X34)
| ord_less_eq_int(X34,X33) ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_89,axiom,
! [X35,X36] :
( lhs_atom53(X35,X36)
| ord_less_int(X36,X35) ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_90,axiom,
! [X33,X34] :
( lhs_atom51(X33,X34)
| ord_less_int(X34,X33) ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_91,axiom,
! [X5,X6] :
( lhs_atom42(X5,X6)
| ord_less_eq_int(X6,X5) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_92,axiom,
! [X5,X6] :
( lhs_atom40(X5,X6)
| ord_less_int(X6,X5) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_93,axiom,
! [X15,X16] :
( lhs_atom27(X15,X16)
| ( ord_less_eq_int(X15,X16)
& X15 != X16 ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_94,axiom,
! [X36] :
( lhs_atom152(X36)
| ~ ord_less_eq_int(pls,X36) ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_95,axiom,
! [X36] :
( lhs_atom150(X36)
| ~ ord_less_int(pls,X36) ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_96,axiom,
! [X36] :
( lhs_atom148(X36)
| ~ ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_97,axiom,
! [X36] :
( lhs_atom142(X36)
| ~ ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_98,axiom,
! [X36] :
( lhs_atom81(X36)
| ~ ord_less_eq_int(pls,X36) ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_99,axiom,
! [X36] :
( lhs_atom79(X36)
| ~ ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_100,axiom,
! [X6,X16] :
( lhs_atom130(X6,X16)
| X6 != number_number_of_int(X16) ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_101,axiom,
! [X6,X16] :
( lhs_atom128(X6,X16)
| X6 != number_number_of_nat(X16) ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_102,axiom,
! [X6,X16] :
( lhs_atom129(X6,X16)
| X6 = number_number_of_int(X16) ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_103,axiom,
! [X6,X16] :
( lhs_atom127(X6,X16)
| X6 = number_number_of_nat(X16) ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_104,axiom,
! [X35,X36] :
( lhs_atom134(X35,X36)
| X36 != X35 ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_105,axiom,
! [X35,X36] :
( lhs_atom132(X35,X36)
| X36 != X35 ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_106,axiom,
! [X5,X6] :
( lhs_atom126(X5,X6)
| X6 != X5 ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_107,axiom,
! [X36] :
( lhs_atom151(X36)
| ord_less_eq_int(pls,X36) ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_108,axiom,
! [X36] :
( lhs_atom149(X36)
| ord_less_int(pls,X36) ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_109,axiom,
! [X36] :
( lhs_atom147(X36)
| ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_110,axiom,
! [X36] :
( lhs_atom141(X36)
| ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_111,axiom,
! [X36] :
( lhs_atom80(X36)
| ord_less_eq_int(pls,X36) ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_112,axiom,
! [X36] :
( lhs_atom78(X36)
| ord_less_int(X36,pls) ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_113,axiom,
! [X35,X36] :
( lhs_atom133(X35,X36)
| X36 = X35 ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_114,axiom,
! [X35,X36] :
( lhs_atom131(X35,X36)
| X36 = X35 ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_115,axiom,
! [X5,X6] :
( lhs_atom125(X5,X6)
| X6 = X5 ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_116,axiom,
! [X20,X14] :
( lhs_atom140(X20,X14)
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_117,axiom,
! [X20,X14] :
( lhs_atom136(X20,X14)
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_118,axiom,
! [X81,X82] :
( lhs_atom124(X81,X82)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_119,axiom,
! [X81,X82] :
( lhs_atom123(X81,X82)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_120,axiom,
! [X63,X64] :
( lhs_atom112(X63,X64)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_121,axiom,
! [X63,X64] :
( lhs_atom111(X63,X64)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_122,axiom,
! [X10,X11] :
( lhs_atom22(X10,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_123,axiom,
! [X10,X11] :
( lhs_atom21(X10,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_124,axiom,
! [X5,X6] :
( lhs_atom11(X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_125,axiom,
! [X5,X6] :
( lhs_atom10(X5,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_126,axiom,
! [X3,X4] :
( lhs_atom9(X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_127,axiom,
! [X3,X4] :
( lhs_atom8(X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_128,axiom,
! [X17] :
( lhs_atom137(X17)
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_129,axiom,
! [X20] :
( lhs_atom49(X20)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_130,axiom,
! [X20] :
( lhs_atom48(X20)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_131,axiom,
! [X24] :
( lhs_atom34(X24)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_132,axiom,
! [X24] :
( lhs_atom33(X24)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_133,axiom,
! [X14] :
( lhs_atom26(X14)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_134,axiom,
! [X13] :
( lhs_atom24(X13)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_135,axiom,
! [X12] :
( lhs_atom23(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_136,axiom,
! [X9] :
( lhs_atom20(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_137,axiom,
! [X9] :
( lhs_atom19(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_138,axiom,
! [X8] :
( lhs_atom18(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_139,axiom,
! [X8] :
( lhs_atom17(X8)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_140,axiom,
! [X4] :
( lhs_atom14(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_141,axiom,
! [X7] :
( lhs_atom13(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_142,axiom,
! [X7] :
( lhs_atom12(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_143,axiom,
( lhs_atom95
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_144,axiom,
( lhs_atom77
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_145,axiom,
( lhs_atom76
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_146,axiom,
( lhs_atom64
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_147,axiom,
( lhs_atom59
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_148,axiom,
( lhs_atom50
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_149,axiom,
( lhs_atom25
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_150,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_151,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_152,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_153,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_154,axiom,
( lhs_atom5
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_155,axiom,
( lhs_atom4
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_156,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_157,axiom,
( lhs_atom3
| ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
c_0_0 ).
fof(c_0_158,axiom,
( lhs_atom2
| ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
c_0_1 ).
fof(c_0_159,plain,
! [X65,X66,X67,X68] : lhs_atom114(X65,X66,X67,X68),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_160,plain,
! [X65,X66,X67,X68] : lhs_atom113(X65,X66,X67,X68),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_161,plain,
! [X47,X48,X49,X50] : lhs_atom102(X47,X48,X49,X50),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_162,plain,
! [X47,X48,X49,X50] : lhs_atom101(X47,X48,X49,X50),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_163,plain,
! [X43,X44,X45,X46] : lhs_atom100(X43,X44,X45,X46),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_164,plain,
! [X43,X44,X45,X46] : lhs_atom99(X43,X44,X45,X46),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_165,plain,
! [X39,X40,X41,X42] : lhs_atom98(X39,X40,X41,X42),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_166,plain,
! [X39,X40,X41,X42] : lhs_atom97(X39,X40,X41,X42),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_167,axiom,
! [X28,X20,X29,X14] :
( lhs_atom44(X29,X14)
| ( ord_less_eq_int(X28,X20)
=> ord_less_int(plus_plus_int(X29,X28),plus_plus_int(X14,X20)) ) ),
c_0_10 ).
fof(c_0_168,axiom,
! [X17,X18,X19] :
( lhs_atom29(X18,X19)
| ord_less_eq_int(plus_plus_int(X17,X19),plus_plus_int(X17,X18)) ),
c_0_11 ).
fof(c_0_169,axiom,
! [X17,X18,X19] :
( lhs_atom73(X18,X19)
| ord_less_int(plus_plus_int(X19,X17),plus_plus_int(X18,X17)) ),
c_0_12 ).
fof(c_0_170,plain,
! [X37,X38] :
( lhs_atom74(X38)
| ( ( ord_less_int(X37,pls)
=> plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(X38) )
& ( ~ ord_less_int(X37,pls)
=> plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(plus_plus_int(X38,X37)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_171,plain,
! [X16,X27] :
( lhs_atom38(X16,X27)
| ~ ord_less_int(number_number_of_int(X16),number_number_of_int(X27)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_172,plain,
! [X16,X27] :
( lhs_atom36(X16,X27)
| ~ ord_less_nat(number_number_of_nat(X16),number_number_of_nat(X27)) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_173,plain,
! [X20,X25,X26] : lhs_atom139(X20,X25,X26),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_174,plain,
! [X83,X84,X85] : lhs_atom138(X83,X84,X85),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_175,plain,
! [X83,X84,X85] : lhs_atom135(X83,X84,X85),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_176,plain,
! [X78,X79,X80] : lhs_atom122(X78,X79,X80),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_177,plain,
! [X78,X79,X80] : lhs_atom121(X78,X79,X80),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_178,plain,
! [X75,X76,X77] : lhs_atom120(X75,X76,X77),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_179,plain,
! [X75,X76,X77] : lhs_atom119(X75,X76,X77),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_180,plain,
! [X72,X73,X74] : lhs_atom118(X72,X73,X74),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_181,plain,
! [X72,X73,X74] : lhs_atom117(X72,X73,X74),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_182,plain,
! [X69,X70,X71] : lhs_atom116(X69,X70,X71),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_183,plain,
! [X69,X70,X71] : lhs_atom115(X69,X70,X71),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_184,plain,
! [X60,X61,X62] : lhs_atom110(X60,X61,X62),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_185,plain,
! [X60,X61,X62] : lhs_atom109(X60,X61,X62),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_186,plain,
! [X57,X58,X59] : lhs_atom108(X57,X58,X59),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_187,plain,
! [X57,X58,X59] : lhs_atom107(X57,X58,X59),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_188,plain,
! [X54,X55,X56] : lhs_atom106(X54,X55,X56),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_189,plain,
! [X54,X55,X56] : lhs_atom105(X54,X55,X56),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_190,plain,
! [X51,X52,X53] : lhs_atom104(X51,X52,X53),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_191,plain,
! [X51,X52,X53] : lhs_atom103(X51,X52,X53),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_192,plain,
! [X20,X25,X26] : lhs_atom47(X20,X25,X26),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_193,plain,
! [X30,X31,X32] : lhs_atom46(X30,X31,X32),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_194,plain,
! [X30,X31,X32] : lhs_atom45(X30,X31,X32),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_195,plain,
! [X20,X25,X26] : lhs_atom35(X20,X25,X26),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_196,plain,
! [X21,X22,X23] : lhs_atom32(X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_197,plain,
! [X21,X22,X23] : lhs_atom31(X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_198,axiom,
! [X20,X14] :
( lhs_atom90(X20,X14)
| ord_less_eq_int(plus_plus_int(X14,one_one_int),X20) ),
c_0_41 ).
fof(c_0_199,axiom,
! [X17,X18,X19] :
( lhs_atom29(X18,X19)
| ( ord_less_eq_int(X18,X17)
=> ord_less_eq_int(X19,X17) ) ),
c_0_42 ).
fof(c_0_200,axiom,
! [X25,X26] :
( lhs_atom96(X26)
| ( twoSqu526106917sum2sq(X25)
=> twoSqu526106917sum2sq(times_times_int(X26,X25)) ) ),
c_0_43 ).
fof(c_0_201,axiom,
! [X16,X27] :
( lhs_atom39(X16,X27)
| ord_less_int(number_number_of_int(X16),number_number_of_int(X27)) ),
c_0_44 ).
fof(c_0_202,axiom,
! [X16,X27] :
( lhs_atom37(X16,X27)
| ord_less_nat(number_number_of_nat(X16),number_number_of_nat(X27)) ),
c_0_45 ).
fof(c_0_203,axiom,
! [X20,X14] :
( lhs_atom30(X20,X14)
| ( ord_less_eq_int(X14,X20)
=> X20 = X14 ) ),
c_0_46 ).
fof(c_0_204,axiom,
! [X15,X16] :
( lhs_atom28(X15,X16)
| ~ ( ord_less_eq_int(X15,X16)
& X15 != X16 ) ),
c_0_47 ).
fof(c_0_205,plain,
! [X35,X36] :
( lhs_atom156(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_206,plain,
! [X33,X34] :
( lhs_atom154(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_207,plain,
! [X35,X36] :
( lhs_atom146(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_208,plain,
! [X33,X34] :
( lhs_atom144(X33,X34)
| ~ ord_less_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_209,plain,
! [X15,X16] :
( lhs_atom94(X15,X16)
| ~ ord_less_eq_int(X16,X15) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_210,plain,
! [X15,X16] :
( lhs_atom92(X15,X16)
| ~ ord_less_int(X16,X15) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_211,plain,
! [X35,X36] :
( lhs_atom89(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_212,plain,
! [X33,X34] :
( lhs_atom87(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_213,plain,
! [X35,X36] :
( lhs_atom85(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_214,plain,
! [X33,X34] :
( lhs_atom83(X33,X34)
| ~ ord_less_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_215,plain,
! [X35,X36] :
( lhs_atom72(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_216,plain,
! [X35,X36] :
( lhs_atom70(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_217,plain,
! [X35,X36] :
( lhs_atom68(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_218,plain,
! [X33,X34] :
( lhs_atom66(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_219,plain,
! [X35,X36] :
( lhs_atom63(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_220,plain,
! [X33,X34] :
( lhs_atom61(X33,X34)
| ~ ord_less_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_221,plain,
! [X35,X36] :
( lhs_atom58(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_222,plain,
! [X33,X34] :
( lhs_atom56(X33,X34)
| ~ ord_less_eq_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_223,plain,
! [X35,X36] :
( lhs_atom54(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_224,plain,
! [X33,X34] :
( lhs_atom52(X33,X34)
| ~ ord_less_int(X34,X33) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_225,plain,
! [X5,X6] :
( lhs_atom43(X5,X6)
| ~ ord_less_eq_int(X6,X5) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_226,plain,
! [X5,X6] :
( lhs_atom41(X5,X6)
| ~ ord_less_int(X6,X5) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_227,axiom,
! [X37,X38] :
( lhs_atom75(X38)
| plus_plus_nat(number_number_of_nat(X38),number_number_of_nat(X37)) = number_number_of_nat(X37) ),
c_0_70 ).
fof(c_0_228,axiom,
! [X35,X36] :
( lhs_atom155(X35,X36)
| ord_less_eq_int(X36,X35) ),
c_0_71 ).
fof(c_0_229,axiom,
! [X33,X34] :
( lhs_atom153(X33,X34)
| ord_less_eq_int(X34,X33) ),
c_0_72 ).
fof(c_0_230,axiom,
! [X35,X36] :
( lhs_atom145(X35,X36)
| ord_less_int(X36,X35) ),
c_0_73 ).
fof(c_0_231,axiom,
! [X33,X34] :
( lhs_atom143(X33,X34)
| ord_less_int(X34,X33) ),
c_0_74 ).
fof(c_0_232,axiom,
! [X15,X16] :
( lhs_atom93(X15,X16)
| ord_less_eq_int(X16,X15) ),
c_0_75 ).
fof(c_0_233,axiom,
! [X15,X16] :
( lhs_atom91(X15,X16)
| ord_less_int(X16,X15) ),
c_0_76 ).
fof(c_0_234,axiom,
! [X35,X36] :
( lhs_atom88(X35,X36)
| ord_less_eq_int(X36,X35) ),
c_0_77 ).
fof(c_0_235,axiom,
! [X33,X34] :
( lhs_atom86(X33,X34)
| ord_less_eq_int(X34,X33) ),
c_0_78 ).
fof(c_0_236,axiom,
! [X35,X36] :
( lhs_atom84(X35,X36)
| ord_less_int(X36,X35) ),
c_0_79 ).
fof(c_0_237,axiom,
! [X33,X34] :
( lhs_atom82(X33,X34)
| ord_less_int(X34,X33) ),
c_0_80 ).
fof(c_0_238,axiom,
! [X35,X36] :
( lhs_atom71(X35,X36)
| ord_less_eq_int(X36,X35) ),
c_0_81 ).
fof(c_0_239,axiom,
! [X35,X36] :
( lhs_atom69(X35,X36)
| ord_less_int(X36,X35) ),
c_0_82 ).
fof(c_0_240,axiom,
! [X35,X36] :
( lhs_atom67(X35,X36)
| ord_less_eq_int(X36,X35) ),
c_0_83 ).
fof(c_0_241,axiom,
! [X33,X34] :
( lhs_atom65(X33,X34)
| ord_less_eq_int(X34,X33) ),
c_0_84 ).
fof(c_0_242,axiom,
! [X35,X36] :
( lhs_atom62(X35,X36)
| ord_less_int(X36,X35) ),
c_0_85 ).
fof(c_0_243,axiom,
! [X33,X34] :
( lhs_atom60(X33,X34)
| ord_less_int(X34,X33) ),
c_0_86 ).
fof(c_0_244,axiom,
! [X35,X36] :
( lhs_atom57(X35,X36)
| ord_less_eq_int(X36,X35) ),
c_0_87 ).
fof(c_0_245,axiom,
! [X33,X34] :
( lhs_atom55(X33,X34)
| ord_less_eq_int(X34,X33) ),
c_0_88 ).
fof(c_0_246,axiom,
! [X35,X36] :
( lhs_atom53(X35,X36)
| ord_less_int(X36,X35) ),
c_0_89 ).
fof(c_0_247,axiom,
! [X33,X34] :
( lhs_atom51(X33,X34)
| ord_less_int(X34,X33) ),
c_0_90 ).
fof(c_0_248,axiom,
! [X5,X6] :
( lhs_atom42(X5,X6)
| ord_less_eq_int(X6,X5) ),
c_0_91 ).
fof(c_0_249,axiom,
! [X5,X6] :
( lhs_atom40(X5,X6)
| ord_less_int(X6,X5) ),
c_0_92 ).
fof(c_0_250,axiom,
! [X15,X16] :
( lhs_atom27(X15,X16)
| ( ord_less_eq_int(X15,X16)
& X15 != X16 ) ),
c_0_93 ).
fof(c_0_251,plain,
! [X36] :
( lhs_atom152(X36)
| ~ ord_less_eq_int(pls,X36) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_252,plain,
! [X36] :
( lhs_atom150(X36)
| ~ ord_less_int(pls,X36) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_253,plain,
! [X36] :
( lhs_atom148(X36)
| ~ ord_less_int(X36,pls) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_254,plain,
! [X36] :
( lhs_atom142(X36)
| ~ ord_less_int(X36,pls) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_255,plain,
! [X36] :
( lhs_atom81(X36)
| ~ ord_less_eq_int(pls,X36) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_256,plain,
! [X36] :
( lhs_atom79(X36)
| ~ ord_less_int(X36,pls) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_257,plain,
! [X6,X16] :
( lhs_atom130(X6,X16)
| X6 != number_number_of_int(X16) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_258,plain,
! [X6,X16] :
( lhs_atom128(X6,X16)
| X6 != number_number_of_nat(X16) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_259,axiom,
! [X6,X16] :
( lhs_atom129(X6,X16)
| X6 = number_number_of_int(X16) ),
c_0_102 ).
fof(c_0_260,axiom,
! [X6,X16] :
( lhs_atom127(X6,X16)
| X6 = number_number_of_nat(X16) ),
c_0_103 ).
fof(c_0_261,plain,
! [X35,X36] :
( lhs_atom134(X35,X36)
| X36 != X35 ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_262,plain,
! [X35,X36] :
( lhs_atom132(X35,X36)
| X36 != X35 ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_263,plain,
! [X5,X6] :
( lhs_atom126(X5,X6)
| X6 != X5 ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_264,axiom,
! [X36] :
( lhs_atom151(X36)
| ord_less_eq_int(pls,X36) ),
c_0_107 ).
fof(c_0_265,axiom,
! [X36] :
( lhs_atom149(X36)
| ord_less_int(pls,X36) ),
c_0_108 ).
fof(c_0_266,axiom,
! [X36] :
( lhs_atom147(X36)
| ord_less_int(X36,pls) ),
c_0_109 ).
fof(c_0_267,axiom,
! [X36] :
( lhs_atom141(X36)
| ord_less_int(X36,pls) ),
c_0_110 ).
fof(c_0_268,axiom,
! [X36] :
( lhs_atom80(X36)
| ord_less_eq_int(pls,X36) ),
c_0_111 ).
fof(c_0_269,axiom,
! [X36] :
( lhs_atom78(X36)
| ord_less_int(X36,pls) ),
c_0_112 ).
fof(c_0_270,axiom,
! [X35,X36] :
( lhs_atom133(X35,X36)
| X36 = X35 ),
c_0_113 ).
fof(c_0_271,axiom,
! [X35,X36] :
( lhs_atom131(X35,X36)
| X36 = X35 ),
c_0_114 ).
fof(c_0_272,axiom,
! [X5,X6] :
( lhs_atom125(X5,X6)
| X6 = X5 ),
c_0_115 ).
fof(c_0_273,plain,
! [X20,X14] : lhs_atom140(X20,X14),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_274,plain,
! [X20,X14] : lhs_atom136(X20,X14),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_275,plain,
! [X81,X82] : lhs_atom124(X81,X82),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_276,plain,
! [X81,X82] : lhs_atom123(X81,X82),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_277,plain,
! [X63,X64] : lhs_atom112(X63,X64),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_278,plain,
! [X63,X64] : lhs_atom111(X63,X64),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_279,plain,
! [X10,X11] : lhs_atom22(X10,X11),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_280,plain,
! [X10,X11] : lhs_atom21(X10,X11),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_281,plain,
! [X5,X6] : lhs_atom11(X5,X6),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_282,plain,
! [X5,X6] : lhs_atom10(X5,X6),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_283,plain,
! [X3,X4] : lhs_atom9(X3,X4),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_284,plain,
! [X3,X4] : lhs_atom8(X3,X4),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_285,plain,
! [X17] : lhs_atom137(X17),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_286,plain,
! [X20] : lhs_atom49(X20),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_287,plain,
! [X20] : lhs_atom48(X20),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_288,plain,
! [X24] : lhs_atom34(X24),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_289,plain,
! [X24] : lhs_atom33(X24),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_290,plain,
! [X14] : lhs_atom26(X14),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_291,plain,
! [X13] : lhs_atom24(X13),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_292,plain,
! [X12] : lhs_atom23(X12),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_293,plain,
! [X9] : lhs_atom20(X9),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_294,plain,
! [X9] : lhs_atom19(X9),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_295,plain,
! [X8] : lhs_atom18(X8),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_296,plain,
! [X8] : lhs_atom17(X8),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_297,plain,
! [X4] : lhs_atom14(X4),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_298,plain,
! [X7] : lhs_atom13(X7),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_299,plain,
! [X7] : lhs_atom12(X7),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_300,plain,
lhs_atom95,
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_301,plain,
lhs_atom77,
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_302,plain,
lhs_atom76,
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_303,plain,
lhs_atom64,
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_304,plain,
lhs_atom59,
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_305,plain,
lhs_atom50,
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_306,plain,
lhs_atom25,
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_307,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_308,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_309,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_310,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_311,plain,
lhs_atom5,
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_312,plain,
lhs_atom4,
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_313,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_314,plain,
( lhs_atom3
| 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)],[c_0_157])]) ).
fof(c_0_315,plain,
( lhs_atom2
| 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)],[c_0_158])]) ).
fof(c_0_316,plain,
! [X69,X70,X71,X72] : lhs_atom114(X69,X70,X71,X72),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_317,plain,
! [X69,X70,X71,X72] : lhs_atom113(X69,X70,X71,X72),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_318,plain,
! [X51,X52,X53,X54] : lhs_atom102(X51,X52,X53,X54),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_319,plain,
! [X51,X52,X53,X54] : lhs_atom101(X51,X52,X53,X54),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_320,plain,
! [X47,X48,X49,X50] : lhs_atom100(X47,X48,X49,X50),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_321,plain,
! [X47,X48,X49,X50] : lhs_atom99(X47,X48,X49,X50),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_322,plain,
! [X43,X44,X45,X46] : lhs_atom98(X43,X44,X45,X46),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_323,plain,
! [X43,X44,X45,X46] : lhs_atom97(X43,X44,X45,X46),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_324,plain,
! [X30,X31,X32,X33] :
( lhs_atom44(X32,X33)
| ~ ord_less_eq_int(X30,X31)
| ord_less_int(plus_plus_int(X32,X30),plus_plus_int(X33,X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_167])]) ).
fof(c_0_325,plain,
! [X20,X21,X22] :
( lhs_atom29(X21,X22)
| ord_less_eq_int(plus_plus_int(X20,X22),plus_plus_int(X20,X21)) ),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_326,plain,
! [X20,X21,X22] :
( lhs_atom73(X21,X22)
| ord_less_int(plus_plus_int(X22,X20),plus_plus_int(X21,X20)) ),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_327,plain,
! [X39,X40] :
( ( ~ ord_less_int(X39,pls)
| plus_plus_nat(number_number_of_nat(X40),number_number_of_nat(X39)) = number_number_of_nat(X40)
| lhs_atom74(X40) )
& ( ord_less_int(X39,pls)
| plus_plus_nat(number_number_of_nat(X40),number_number_of_nat(X39)) = number_number_of_nat(plus_plus_int(X40,X39))
| lhs_atom74(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])])]) ).
fof(c_0_328,plain,
! [X28,X29] :
( lhs_atom38(X28,X29)
| ~ ord_less_int(number_number_of_int(X28),number_number_of_int(X29)) ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_329,plain,
! [X28,X29] :
( lhs_atom36(X28,X29)
| ~ ord_less_nat(number_number_of_nat(X28),number_number_of_nat(X29)) ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_330,plain,
! [X27,X28,X29] : lhs_atom139(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_331,plain,
! [X86,X87,X88] : lhs_atom138(X86,X87,X88),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_332,plain,
! [X86,X87,X88] : lhs_atom135(X86,X87,X88),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_333,plain,
! [X81,X82,X83] : lhs_atom122(X81,X82,X83),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_334,plain,
! [X81,X82,X83] : lhs_atom121(X81,X82,X83),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_335,plain,
! [X78,X79,X80] : lhs_atom120(X78,X79,X80),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_336,plain,
! [X78,X79,X80] : lhs_atom119(X78,X79,X80),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_337,plain,
! [X75,X76,X77] : lhs_atom118(X75,X76,X77),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_338,plain,
! [X75,X76,X77] : lhs_atom117(X75,X76,X77),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_339,plain,
! [X72,X73,X74] : lhs_atom116(X72,X73,X74),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_340,plain,
! [X72,X73,X74] : lhs_atom115(X72,X73,X74),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_341,plain,
! [X63,X64,X65] : lhs_atom110(X63,X64,X65),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_342,plain,
! [X63,X64,X65] : lhs_atom109(X63,X64,X65),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_343,plain,
! [X60,X61,X62] : lhs_atom108(X60,X61,X62),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_344,plain,
! [X60,X61,X62] : lhs_atom107(X60,X61,X62),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_345,plain,
! [X57,X58,X59] : lhs_atom106(X57,X58,X59),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_346,plain,
! [X57,X58,X59] : lhs_atom105(X57,X58,X59),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_347,plain,
! [X54,X55,X56] : lhs_atom104(X54,X55,X56),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_348,plain,
! [X54,X55,X56] : lhs_atom103(X54,X55,X56),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_349,plain,
! [X27,X28,X29] : lhs_atom47(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_350,plain,
! [X33,X34,X35] : lhs_atom46(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_351,plain,
! [X33,X34,X35] : lhs_atom45(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_352,plain,
! [X27,X28,X29] : lhs_atom35(X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_353,plain,
! [X24,X25,X26] : lhs_atom32(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_354,plain,
! [X24,X25,X26] : lhs_atom31(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_355,plain,
! [X21,X22] :
( lhs_atom90(X21,X22)
| ord_less_eq_int(plus_plus_int(X22,one_one_int),X21) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_356,plain,
! [X20,X21,X22] :
( lhs_atom29(X21,X22)
| ~ ord_less_eq_int(X21,X20)
| ord_less_eq_int(X22,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])]) ).
fof(c_0_357,plain,
! [X27,X28] :
( lhs_atom96(X28)
| ~ twoSqu526106917sum2sq(X27)
| twoSqu526106917sum2sq(times_times_int(X28,X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])]) ).
fof(c_0_358,plain,
! [X28,X29] :
( lhs_atom39(X28,X29)
| ord_less_int(number_number_of_int(X28),number_number_of_int(X29)) ),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_359,plain,
! [X28,X29] :
( lhs_atom37(X28,X29)
| ord_less_nat(number_number_of_nat(X28),number_number_of_nat(X29)) ),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_360,plain,
! [X21,X22] :
( lhs_atom30(X21,X22)
| ~ ord_less_eq_int(X22,X21)
| X21 = X22 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])]) ).
fof(c_0_361,plain,
! [X17,X18] :
( lhs_atom28(X17,X18)
| ~ ord_less_eq_int(X17,X18)
| X17 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])]) ).
fof(c_0_362,plain,
! [X37,X38] :
( lhs_atom156(X37,X38)
| ~ ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_363,plain,
! [X35,X36] :
( lhs_atom154(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_364,plain,
! [X37,X38] :
( lhs_atom146(X37,X38)
| ~ ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_365,plain,
! [X35,X36] :
( lhs_atom144(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_366,plain,
! [X17,X18] :
( lhs_atom94(X17,X18)
| ~ ord_less_eq_int(X18,X17) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_367,plain,
! [X17,X18] :
( lhs_atom92(X17,X18)
| ~ ord_less_int(X18,X17) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_368,plain,
! [X37,X38] :
( lhs_atom89(X37,X38)
| ~ ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_369,plain,
! [X35,X36] :
( lhs_atom87(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_370,plain,
! [X37,X38] :
( lhs_atom85(X37,X38)
| ~ ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_371,plain,
! [X35,X36] :
( lhs_atom83(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_372,plain,
! [X37,X38] :
( lhs_atom72(X37,X38)
| ~ ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_373,plain,
! [X37,X38] :
( lhs_atom70(X37,X38)
| ~ ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_374,plain,
! [X37,X38] :
( lhs_atom68(X37,X38)
| ~ ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_375,plain,
! [X35,X36] :
( lhs_atom66(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_376,plain,
! [X37,X38] :
( lhs_atom63(X37,X38)
| ~ ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_377,plain,
! [X35,X36] :
( lhs_atom61(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_378,plain,
! [X37,X38] :
( lhs_atom58(X37,X38)
| ~ ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_379,plain,
! [X35,X36] :
( lhs_atom56(X35,X36)
| ~ ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_380,plain,
! [X37,X38] :
( lhs_atom54(X37,X38)
| ~ ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_381,plain,
! [X35,X36] :
( lhs_atom52(X35,X36)
| ~ ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_382,plain,
! [X7,X8] :
( lhs_atom43(X7,X8)
| ~ ord_less_eq_int(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_383,plain,
! [X7,X8] :
( lhs_atom41(X7,X8)
| ~ ord_less_int(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_384,plain,
! [X39,X40] :
( lhs_atom75(X40)
| plus_plus_nat(number_number_of_nat(X40),number_number_of_nat(X39)) = number_number_of_nat(X39) ),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_385,plain,
! [X37,X38] :
( lhs_atom155(X37,X38)
| ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_386,plain,
! [X35,X36] :
( lhs_atom153(X35,X36)
| ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_387,plain,
! [X37,X38] :
( lhs_atom145(X37,X38)
| ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_388,plain,
! [X35,X36] :
( lhs_atom143(X35,X36)
| ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_389,plain,
! [X17,X18] :
( lhs_atom93(X17,X18)
| ord_less_eq_int(X18,X17) ),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_390,plain,
! [X17,X18] :
( lhs_atom91(X17,X18)
| ord_less_int(X18,X17) ),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_391,plain,
! [X37,X38] :
( lhs_atom88(X37,X38)
| ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_392,plain,
! [X35,X36] :
( lhs_atom86(X35,X36)
| ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_393,plain,
! [X37,X38] :
( lhs_atom84(X37,X38)
| ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_394,plain,
! [X35,X36] :
( lhs_atom82(X35,X36)
| ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_395,plain,
! [X37,X38] :
( lhs_atom71(X37,X38)
| ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_396,plain,
! [X37,X38] :
( lhs_atom69(X37,X38)
| ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_397,plain,
! [X37,X38] :
( lhs_atom67(X37,X38)
| ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_398,plain,
! [X35,X36] :
( lhs_atom65(X35,X36)
| ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_399,plain,
! [X37,X38] :
( lhs_atom62(X37,X38)
| ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_400,plain,
! [X35,X36] :
( lhs_atom60(X35,X36)
| ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_401,plain,
! [X37,X38] :
( lhs_atom57(X37,X38)
| ord_less_eq_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_402,plain,
! [X35,X36] :
( lhs_atom55(X35,X36)
| ord_less_eq_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_403,plain,
! [X37,X38] :
( lhs_atom53(X37,X38)
| ord_less_int(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_404,plain,
! [X35,X36] :
( lhs_atom51(X35,X36)
| ord_less_int(X36,X35) ),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_405,plain,
! [X7,X8] :
( lhs_atom42(X7,X8)
| ord_less_eq_int(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_406,plain,
! [X7,X8] :
( lhs_atom40(X7,X8)
| ord_less_int(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_407,plain,
! [X17,X18] :
( ( ord_less_eq_int(X17,X18)
| lhs_atom27(X17,X18) )
& ( X17 != X18
| lhs_atom27(X17,X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_250])]) ).
fof(c_0_408,plain,
! [X37] :
( lhs_atom152(X37)
| ~ ord_less_eq_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_409,plain,
! [X37] :
( lhs_atom150(X37)
| ~ ord_less_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_410,plain,
! [X37] :
( lhs_atom148(X37)
| ~ ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_411,plain,
! [X37] :
( lhs_atom142(X37)
| ~ ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_412,plain,
! [X37] :
( lhs_atom81(X37)
| ~ ord_less_eq_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_413,plain,
! [X37] :
( lhs_atom79(X37)
| ~ ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_414,plain,
! [X17,X18] :
( lhs_atom130(X17,X18)
| X17 != number_number_of_int(X18) ),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_415,plain,
! [X17,X18] :
( lhs_atom128(X17,X18)
| X17 != number_number_of_nat(X18) ),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_416,plain,
! [X17,X18] :
( lhs_atom129(X17,X18)
| X17 = number_number_of_int(X18) ),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_417,plain,
! [X17,X18] :
( lhs_atom127(X17,X18)
| X17 = number_number_of_nat(X18) ),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_418,plain,
! [X37,X38] :
( lhs_atom134(X37,X38)
| X38 != X37 ),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_419,plain,
! [X37,X38] :
( lhs_atom132(X37,X38)
| X38 != X37 ),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_420,plain,
! [X7,X8] :
( lhs_atom126(X7,X8)
| X8 != X7 ),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_421,plain,
! [X37] :
( lhs_atom151(X37)
| ord_less_eq_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_422,plain,
! [X37] :
( lhs_atom149(X37)
| ord_less_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_423,plain,
! [X37] :
( lhs_atom147(X37)
| ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_424,plain,
! [X37] :
( lhs_atom141(X37)
| ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_425,plain,
! [X37] :
( lhs_atom80(X37)
| ord_less_eq_int(pls,X37) ),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_426,plain,
! [X37] :
( lhs_atom78(X37)
| ord_less_int(X37,pls) ),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_427,plain,
! [X37,X38] :
( lhs_atom133(X37,X38)
| X38 = X37 ),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_428,plain,
! [X37,X38] :
( lhs_atom131(X37,X38)
| X38 = X37 ),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_429,plain,
! [X7,X8] :
( lhs_atom125(X7,X8)
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_430,plain,
! [X21,X22] : lhs_atom140(X21,X22),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_431,plain,
! [X21,X22] : lhs_atom136(X21,X22),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_432,plain,
! [X83,X84] : lhs_atom124(X83,X84),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_433,plain,
! [X83,X84] : lhs_atom123(X83,X84),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_434,plain,
! [X65,X66] : lhs_atom112(X65,X66),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_435,plain,
! [X65,X66] : lhs_atom111(X65,X66),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_436,plain,
! [X12,X13] : lhs_atom22(X12,X13),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_437,plain,
! [X12,X13] : lhs_atom21(X12,X13),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_438,plain,
! [X7,X8] : lhs_atom11(X7,X8),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_439,plain,
! [X7,X8] : lhs_atom10(X7,X8),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_440,plain,
! [X5,X6] : lhs_atom9(X5,X6),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_441,plain,
! [X5,X6] : lhs_atom8(X5,X6),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_442,plain,
! [X18] : lhs_atom137(X18),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_443,plain,
! [X21] : lhs_atom49(X21),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_444,plain,
! [X21] : lhs_atom48(X21),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_445,plain,
! [X25] : lhs_atom34(X25),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_446,plain,
! [X25] : lhs_atom33(X25),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_447,plain,
! [X15] : lhs_atom26(X15),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_448,plain,
! [X14] : lhs_atom24(X14),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_449,plain,
! [X13] : lhs_atom23(X13),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_450,plain,
! [X10] : lhs_atom20(X10),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_451,plain,
! [X10] : lhs_atom19(X10),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_452,plain,
! [X9] : lhs_atom18(X9),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_453,plain,
! [X9] : lhs_atom17(X9),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_454,plain,
! [X5] : lhs_atom14(X5),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_455,plain,
! [X8] : lhs_atom13(X8),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_456,plain,
! [X8] : lhs_atom12(X8),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_457,plain,
lhs_atom95,
c_0_300 ).
fof(c_0_458,plain,
lhs_atom77,
c_0_301 ).
fof(c_0_459,plain,
lhs_atom76,
c_0_302 ).
fof(c_0_460,plain,
lhs_atom64,
c_0_303 ).
fof(c_0_461,plain,
lhs_atom59,
c_0_304 ).
fof(c_0_462,plain,
lhs_atom50,
c_0_305 ).
fof(c_0_463,plain,
lhs_atom25,
c_0_306 ).
fof(c_0_464,plain,
lhs_atom16,
c_0_307 ).
fof(c_0_465,plain,
lhs_atom15,
c_0_308 ).
fof(c_0_466,plain,
lhs_atom7,
c_0_309 ).
fof(c_0_467,plain,
lhs_atom6,
c_0_310 ).
fof(c_0_468,plain,
lhs_atom5,
c_0_311 ).
fof(c_0_469,plain,
lhs_atom4,
c_0_312 ).
fof(c_0_470,plain,
lhs_atom1,
c_0_313 ).
cnf(c_0_471,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)
| lhs_atom3 ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_472,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)
| lhs_atom2 ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_473,plain,
lhs_atom114(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_474,plain,
lhs_atom113(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_475,plain,
lhs_atom102(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_476,plain,
lhs_atom101(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_477,plain,
lhs_atom100(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_478,plain,
lhs_atom99(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_479,plain,
lhs_atom98(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_480,plain,
lhs_atom97(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_481,plain,
( ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X4))
| lhs_atom44(X1,X3)
| ~ ord_less_eq_int(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_482,plain,
( ord_less_eq_int(plus_plus_int(X1,X2),plus_plus_int(X1,X3))
| lhs_atom29(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_483,plain,
( ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X2))
| lhs_atom73(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_484,plain,
( lhs_atom74(X1)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(plus_plus_int(X1,X2))
| ord_less_int(X2,pls) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_485,plain,
( lhs_atom38(X1,X2)
| ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_486,plain,
( lhs_atom36(X1,X2)
| ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_487,plain,
( lhs_atom74(X1)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ ord_less_int(X2,pls) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_488,plain,
lhs_atom139(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_489,plain,
lhs_atom138(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_490,plain,
lhs_atom135(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_491,plain,
lhs_atom122(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_492,plain,
lhs_atom121(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_493,plain,
lhs_atom120(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_494,plain,
lhs_atom119(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_495,plain,
lhs_atom118(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_496,plain,
lhs_atom117(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_497,plain,
lhs_atom116(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_498,plain,
lhs_atom115(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_499,plain,
lhs_atom110(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_500,plain,
lhs_atom109(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_501,plain,
lhs_atom108(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_502,plain,
lhs_atom107(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_503,plain,
lhs_atom106(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_504,plain,
lhs_atom105(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_505,plain,
lhs_atom104(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_506,plain,
lhs_atom103(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_507,plain,
lhs_atom47(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_508,plain,
lhs_atom46(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_509,plain,
lhs_atom45(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_510,plain,
lhs_atom35(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_511,plain,
lhs_atom32(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_512,plain,
lhs_atom31(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_513,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| lhs_atom90(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_514,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom29(X3,X1)
| ~ ord_less_eq_int(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_515,plain,
( twoSqu526106917sum2sq(times_times_int(X1,X2))
| lhs_atom96(X1)
| ~ twoSqu526106917sum2sq(X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_516,plain,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| lhs_atom39(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_517,plain,
( ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2))
| lhs_atom37(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_518,plain,
( X1 = X2
| lhs_atom30(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_519,plain,
( X1 = X2
| lhs_atom28(X1,X2)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_520,plain,
( lhs_atom156(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_521,plain,
( lhs_atom154(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_522,plain,
( lhs_atom146(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_523,plain,
( lhs_atom144(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_524,plain,
( lhs_atom94(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_525,plain,
( lhs_atom92(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_526,plain,
( lhs_atom89(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_527,plain,
( lhs_atom87(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_528,plain,
( lhs_atom85(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_529,plain,
( lhs_atom83(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_530,plain,
( lhs_atom72(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_531,plain,
( lhs_atom70(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_532,plain,
( lhs_atom68(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_533,plain,
( lhs_atom66(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_534,plain,
( lhs_atom63(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_535,plain,
( lhs_atom61(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_536,plain,
( lhs_atom58(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_537,plain,
( lhs_atom56(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_538,plain,
( lhs_atom54(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_539,plain,
( lhs_atom52(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_540,plain,
( lhs_atom43(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_541,plain,
( lhs_atom41(X2,X1)
| ~ ord_less_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_542,plain,
( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X2)
| lhs_atom75(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_543,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom155(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_544,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom153(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_545,plain,
( ord_less_int(X1,X2)
| lhs_atom145(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_546,plain,
( ord_less_int(X1,X2)
| lhs_atom143(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_547,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom93(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_548,plain,
( ord_less_int(X1,X2)
| lhs_atom91(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_549,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom88(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_550,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom86(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_551,plain,
( ord_less_int(X1,X2)
| lhs_atom84(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_552,plain,
( ord_less_int(X1,X2)
| lhs_atom82(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_553,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom71(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_554,plain,
( ord_less_int(X1,X2)
| lhs_atom69(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_555,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom67(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_556,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom65(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_557,plain,
( ord_less_int(X1,X2)
| lhs_atom62(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_558,plain,
( ord_less_int(X1,X2)
| lhs_atom60(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_559,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom57(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_560,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom55(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_561,plain,
( ord_less_int(X1,X2)
| lhs_atom53(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_562,plain,
( ord_less_int(X1,X2)
| lhs_atom51(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_563,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom42(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_564,plain,
( ord_less_int(X1,X2)
| lhs_atom40(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_565,plain,
( lhs_atom27(X1,X2)
| ord_less_eq_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_566,plain,
( lhs_atom152(X1)
| ~ ord_less_eq_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_567,plain,
( lhs_atom150(X1)
| ~ ord_less_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_568,plain,
( lhs_atom148(X1)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_569,plain,
( lhs_atom142(X1)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_570,plain,
( lhs_atom81(X1)
| ~ ord_less_eq_int(pls,X1) ),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_571,plain,
( lhs_atom79(X1)
| ~ ord_less_int(X1,pls) ),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_572,plain,
( lhs_atom130(X1,X2)
| X1 != number_number_of_int(X2) ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_573,plain,
( lhs_atom128(X1,X2)
| X1 != number_number_of_nat(X2) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_574,plain,
( X1 = number_number_of_int(X2)
| lhs_atom129(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_575,plain,
( X1 = number_number_of_nat(X2)
| lhs_atom127(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_576,plain,
( lhs_atom134(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_577,plain,
( lhs_atom132(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_578,plain,
( lhs_atom126(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_579,plain,
( lhs_atom27(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_580,plain,
( ord_less_eq_int(pls,X1)
| lhs_atom151(X1) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_581,plain,
( ord_less_int(pls,X1)
| lhs_atom149(X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_582,plain,
( ord_less_int(X1,pls)
| lhs_atom147(X1) ),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_583,plain,
( ord_less_int(X1,pls)
| lhs_atom141(X1) ),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_584,plain,
( ord_less_eq_int(pls,X1)
| lhs_atom80(X1) ),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_585,plain,
( ord_less_int(X1,pls)
| lhs_atom78(X1) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_586,plain,
( X1 = X2
| lhs_atom133(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_587,plain,
( X1 = X2
| lhs_atom131(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_588,plain,
( X1 = X2
| lhs_atom125(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_589,plain,
lhs_atom140(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_590,plain,
lhs_atom136(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_591,plain,
lhs_atom124(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_592,plain,
lhs_atom123(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_593,plain,
lhs_atom112(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_594,plain,
lhs_atom111(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_595,plain,
lhs_atom22(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_596,plain,
lhs_atom21(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_597,plain,
lhs_atom11(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_598,plain,
lhs_atom10(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_599,plain,
lhs_atom9(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_600,plain,
lhs_atom8(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_601,plain,
lhs_atom137(X1),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_602,plain,
lhs_atom49(X1),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_603,plain,
lhs_atom48(X1),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_604,plain,
lhs_atom34(X1),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_605,plain,
lhs_atom33(X1),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_606,plain,
lhs_atom26(X1),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_607,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_608,plain,
lhs_atom23(X1),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_609,plain,
lhs_atom20(X1),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_610,plain,
lhs_atom19(X1),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_611,plain,
lhs_atom18(X1),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_612,plain,
lhs_atom17(X1),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_613,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_614,plain,
lhs_atom13(X1),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_615,plain,
lhs_atom12(X1),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_616,plain,
lhs_atom95,
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_617,plain,
lhs_atom77,
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_618,plain,
lhs_atom76,
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_619,plain,
lhs_atom64,
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_620,plain,
lhs_atom59,
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_621,plain,
lhs_atom50,
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_622,plain,
lhs_atom25,
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_623,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_624,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_625,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_626,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_627,plain,
lhs_atom5,
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_628,plain,
lhs_atom4,
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_629,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_630,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)
| lhs_atom3 ),
c_0_471,
[final] ).
cnf(c_0_631,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)
| lhs_atom2 ),
c_0_472,
[final] ).
cnf(c_0_632,plain,
lhs_atom114(X1,X2,X3,X4),
c_0_473,
[final] ).
cnf(c_0_633,plain,
lhs_atom113(X1,X2,X3,X4),
c_0_474,
[final] ).
cnf(c_0_634,plain,
lhs_atom102(X1,X2,X3,X4),
c_0_475,
[final] ).
cnf(c_0_635,plain,
lhs_atom101(X1,X2,X3,X4),
c_0_476,
[final] ).
cnf(c_0_636,plain,
lhs_atom100(X1,X2,X3,X4),
c_0_477,
[final] ).
cnf(c_0_637,plain,
lhs_atom99(X1,X2,X3,X4),
c_0_478,
[final] ).
cnf(c_0_638,plain,
lhs_atom98(X1,X2,X3,X4),
c_0_479,
[final] ).
cnf(c_0_639,plain,
lhs_atom97(X1,X2,X3,X4),
c_0_480,
[final] ).
cnf(c_0_640,plain,
( ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X4))
| lhs_atom44(X1,X3)
| ~ ord_less_eq_int(X2,X4) ),
c_0_481,
[final] ).
cnf(c_0_641,plain,
( ord_less_eq_int(plus_plus_int(X1,X2),plus_plus_int(X1,X3))
| lhs_atom29(X3,X2) ),
c_0_482,
[final] ).
cnf(c_0_642,plain,
( ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X2))
| lhs_atom73(X3,X1) ),
c_0_483,
[final] ).
cnf(c_0_643,plain,
( lhs_atom74(X1)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(plus_plus_int(X1,X2))
| ord_less_int(X2,pls) ),
c_0_484,
[final] ).
cnf(c_0_644,plain,
( lhs_atom38(X1,X2)
| ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X2)) ),
c_0_485,
[final] ).
cnf(c_0_645,plain,
( lhs_atom36(X1,X2)
| ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2)) ),
c_0_486,
[final] ).
cnf(c_0_646,plain,
( lhs_atom74(X1)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ ord_less_int(X2,pls) ),
c_0_487,
[final] ).
cnf(c_0_647,plain,
lhs_atom139(X1,X2,X3),
c_0_488,
[final] ).
cnf(c_0_648,plain,
lhs_atom138(X1,X2,X3),
c_0_489,
[final] ).
cnf(c_0_649,plain,
lhs_atom135(X1,X2,X3),
c_0_490,
[final] ).
cnf(c_0_650,plain,
lhs_atom122(X1,X2,X3),
c_0_491,
[final] ).
cnf(c_0_651,plain,
lhs_atom121(X1,X2,X3),
c_0_492,
[final] ).
cnf(c_0_652,plain,
lhs_atom120(X1,X2,X3),
c_0_493,
[final] ).
cnf(c_0_653,plain,
lhs_atom119(X1,X2,X3),
c_0_494,
[final] ).
cnf(c_0_654,plain,
lhs_atom118(X1,X2,X3),
c_0_495,
[final] ).
cnf(c_0_655,plain,
lhs_atom117(X1,X2,X3),
c_0_496,
[final] ).
cnf(c_0_656,plain,
lhs_atom116(X1,X2,X3),
c_0_497,
[final] ).
cnf(c_0_657,plain,
lhs_atom115(X1,X2,X3),
c_0_498,
[final] ).
cnf(c_0_658,plain,
lhs_atom110(X1,X2,X3),
c_0_499,
[final] ).
cnf(c_0_659,plain,
lhs_atom109(X1,X2,X3),
c_0_500,
[final] ).
cnf(c_0_660,plain,
lhs_atom108(X1,X2,X3),
c_0_501,
[final] ).
cnf(c_0_661,plain,
lhs_atom107(X1,X2,X3),
c_0_502,
[final] ).
cnf(c_0_662,plain,
lhs_atom106(X1,X2,X3),
c_0_503,
[final] ).
cnf(c_0_663,plain,
lhs_atom105(X1,X2,X3),
c_0_504,
[final] ).
cnf(c_0_664,plain,
lhs_atom104(X1,X2,X3),
c_0_505,
[final] ).
cnf(c_0_665,plain,
lhs_atom103(X1,X2,X3),
c_0_506,
[final] ).
cnf(c_0_666,plain,
lhs_atom47(X1,X2,X3),
c_0_507,
[final] ).
cnf(c_0_667,plain,
lhs_atom46(X1,X2,X3),
c_0_508,
[final] ).
cnf(c_0_668,plain,
lhs_atom45(X1,X2,X3),
c_0_509,
[final] ).
cnf(c_0_669,plain,
lhs_atom35(X1,X2,X3),
c_0_510,
[final] ).
cnf(c_0_670,plain,
lhs_atom32(X1,X2,X3),
c_0_511,
[final] ).
cnf(c_0_671,plain,
lhs_atom31(X1,X2,X3),
c_0_512,
[final] ).
cnf(c_0_672,plain,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| lhs_atom90(X2,X1) ),
c_0_513,
[final] ).
cnf(c_0_673,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom29(X3,X1)
| ~ ord_less_eq_int(X3,X2) ),
c_0_514,
[final] ).
cnf(c_0_674,plain,
( twoSqu526106917sum2sq(times_times_int(X1,X2))
| lhs_atom96(X1)
| ~ twoSqu526106917sum2sq(X2) ),
c_0_515,
[final] ).
cnf(c_0_675,plain,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| lhs_atom39(X1,X2) ),
c_0_516,
[final] ).
cnf(c_0_676,plain,
( ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2))
| lhs_atom37(X1,X2) ),
c_0_517,
[final] ).
cnf(c_0_677,plain,
( X1 = X2
| lhs_atom30(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
c_0_518,
[final] ).
cnf(c_0_678,plain,
( X1 = X2
| lhs_atom28(X1,X2)
| ~ ord_less_eq_int(X1,X2) ),
c_0_519,
[final] ).
cnf(c_0_679,plain,
( lhs_atom156(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_520,
[final] ).
cnf(c_0_680,plain,
( lhs_atom154(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_521,
[final] ).
cnf(c_0_681,plain,
( lhs_atom146(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_522,
[final] ).
cnf(c_0_682,plain,
( lhs_atom144(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_523,
[final] ).
cnf(c_0_683,plain,
( lhs_atom94(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_524,
[final] ).
cnf(c_0_684,plain,
( lhs_atom92(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_525,
[final] ).
cnf(c_0_685,plain,
( lhs_atom89(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_526,
[final] ).
cnf(c_0_686,plain,
( lhs_atom87(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_527,
[final] ).
cnf(c_0_687,plain,
( lhs_atom85(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_528,
[final] ).
cnf(c_0_688,plain,
( lhs_atom83(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_529,
[final] ).
cnf(c_0_689,plain,
( lhs_atom72(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_530,
[final] ).
cnf(c_0_690,plain,
( lhs_atom70(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_531,
[final] ).
cnf(c_0_691,plain,
( lhs_atom68(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_532,
[final] ).
cnf(c_0_692,plain,
( lhs_atom66(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_533,
[final] ).
cnf(c_0_693,plain,
( lhs_atom63(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_534,
[final] ).
cnf(c_0_694,plain,
( lhs_atom61(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_535,
[final] ).
cnf(c_0_695,plain,
( lhs_atom58(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_536,
[final] ).
cnf(c_0_696,plain,
( lhs_atom56(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_537,
[final] ).
cnf(c_0_697,plain,
( lhs_atom54(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_538,
[final] ).
cnf(c_0_698,plain,
( lhs_atom52(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_539,
[final] ).
cnf(c_0_699,plain,
( lhs_atom43(X2,X1)
| ~ ord_less_eq_int(X1,X2) ),
c_0_540,
[final] ).
cnf(c_0_700,plain,
( lhs_atom41(X2,X1)
| ~ ord_less_int(X1,X2) ),
c_0_541,
[final] ).
cnf(c_0_701,plain,
( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X2)
| lhs_atom75(X1) ),
c_0_542,
[final] ).
cnf(c_0_702,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom155(X2,X1) ),
c_0_543,
[final] ).
cnf(c_0_703,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom153(X2,X1) ),
c_0_544,
[final] ).
cnf(c_0_704,plain,
( ord_less_int(X1,X2)
| lhs_atom145(X2,X1) ),
c_0_545,
[final] ).
cnf(c_0_705,plain,
( ord_less_int(X1,X2)
| lhs_atom143(X2,X1) ),
c_0_546,
[final] ).
cnf(c_0_706,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom93(X2,X1) ),
c_0_547,
[final] ).
cnf(c_0_707,plain,
( ord_less_int(X1,X2)
| lhs_atom91(X2,X1) ),
c_0_548,
[final] ).
cnf(c_0_708,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom88(X2,X1) ),
c_0_549,
[final] ).
cnf(c_0_709,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom86(X2,X1) ),
c_0_550,
[final] ).
cnf(c_0_710,plain,
( ord_less_int(X1,X2)
| lhs_atom84(X2,X1) ),
c_0_551,
[final] ).
cnf(c_0_711,plain,
( ord_less_int(X1,X2)
| lhs_atom82(X2,X1) ),
c_0_552,
[final] ).
cnf(c_0_712,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom71(X2,X1) ),
c_0_553,
[final] ).
cnf(c_0_713,plain,
( ord_less_int(X1,X2)
| lhs_atom69(X2,X1) ),
c_0_554,
[final] ).
cnf(c_0_714,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom67(X2,X1) ),
c_0_555,
[final] ).
cnf(c_0_715,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom65(X2,X1) ),
c_0_556,
[final] ).
cnf(c_0_716,plain,
( ord_less_int(X1,X2)
| lhs_atom62(X2,X1) ),
c_0_557,
[final] ).
cnf(c_0_717,plain,
( ord_less_int(X1,X2)
| lhs_atom60(X2,X1) ),
c_0_558,
[final] ).
cnf(c_0_718,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom57(X2,X1) ),
c_0_559,
[final] ).
cnf(c_0_719,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom55(X2,X1) ),
c_0_560,
[final] ).
cnf(c_0_720,plain,
( ord_less_int(X1,X2)
| lhs_atom53(X2,X1) ),
c_0_561,
[final] ).
cnf(c_0_721,plain,
( ord_less_int(X1,X2)
| lhs_atom51(X2,X1) ),
c_0_562,
[final] ).
cnf(c_0_722,plain,
( ord_less_eq_int(X1,X2)
| lhs_atom42(X2,X1) ),
c_0_563,
[final] ).
cnf(c_0_723,plain,
( ord_less_int(X1,X2)
| lhs_atom40(X2,X1) ),
c_0_564,
[final] ).
cnf(c_0_724,plain,
( lhs_atom27(X1,X2)
| ord_less_eq_int(X1,X2) ),
c_0_565,
[final] ).
cnf(c_0_725,plain,
( lhs_atom152(X1)
| ~ ord_less_eq_int(pls,X1) ),
c_0_566,
[final] ).
cnf(c_0_726,plain,
( lhs_atom150(X1)
| ~ ord_less_int(pls,X1) ),
c_0_567,
[final] ).
cnf(c_0_727,plain,
( lhs_atom148(X1)
| ~ ord_less_int(X1,pls) ),
c_0_568,
[final] ).
cnf(c_0_728,plain,
( lhs_atom142(X1)
| ~ ord_less_int(X1,pls) ),
c_0_569,
[final] ).
cnf(c_0_729,plain,
( lhs_atom81(X1)
| ~ ord_less_eq_int(pls,X1) ),
c_0_570,
[final] ).
cnf(c_0_730,plain,
( lhs_atom79(X1)
| ~ ord_less_int(X1,pls) ),
c_0_571,
[final] ).
cnf(c_0_731,plain,
( lhs_atom130(X1,X2)
| X1 != number_number_of_int(X2) ),
c_0_572,
[final] ).
cnf(c_0_732,plain,
( lhs_atom128(X1,X2)
| X1 != number_number_of_nat(X2) ),
c_0_573,
[final] ).
cnf(c_0_733,plain,
( X1 = number_number_of_int(X2)
| lhs_atom129(X1,X2) ),
c_0_574,
[final] ).
cnf(c_0_734,plain,
( X1 = number_number_of_nat(X2)
| lhs_atom127(X1,X2) ),
c_0_575,
[final] ).
cnf(c_0_735,plain,
( lhs_atom134(X2,X1)
| X1 != X2 ),
c_0_576,
[final] ).
cnf(c_0_736,plain,
( lhs_atom132(X2,X1)
| X1 != X2 ),
c_0_577,
[final] ).
cnf(c_0_737,plain,
( lhs_atom126(X2,X1)
| X1 != X2 ),
c_0_578,
[final] ).
cnf(c_0_738,plain,
( lhs_atom27(X1,X2)
| X1 != X2 ),
c_0_579,
[final] ).
cnf(c_0_739,plain,
( ord_less_eq_int(pls,X1)
| lhs_atom151(X1) ),
c_0_580,
[final] ).
cnf(c_0_740,plain,
( ord_less_int(pls,X1)
| lhs_atom149(X1) ),
c_0_581,
[final] ).
cnf(c_0_741,plain,
( ord_less_int(X1,pls)
| lhs_atom147(X1) ),
c_0_582,
[final] ).
cnf(c_0_742,plain,
( ord_less_int(X1,pls)
| lhs_atom141(X1) ),
c_0_583,
[final] ).
cnf(c_0_743,plain,
( ord_less_eq_int(pls,X1)
| lhs_atom80(X1) ),
c_0_584,
[final] ).
cnf(c_0_744,plain,
( ord_less_int(X1,pls)
| lhs_atom78(X1) ),
c_0_585,
[final] ).
cnf(c_0_745,plain,
( X1 = X2
| lhs_atom133(X2,X1) ),
c_0_586,
[final] ).
cnf(c_0_746,plain,
( X1 = X2
| lhs_atom131(X2,X1) ),
c_0_587,
[final] ).
cnf(c_0_747,plain,
( X1 = X2
| lhs_atom125(X2,X1) ),
c_0_588,
[final] ).
cnf(c_0_748,plain,
lhs_atom140(X1,X2),
c_0_589,
[final] ).
cnf(c_0_749,plain,
lhs_atom136(X1,X2),
c_0_590,
[final] ).
cnf(c_0_750,plain,
lhs_atom124(X1,X2),
c_0_591,
[final] ).
cnf(c_0_751,plain,
lhs_atom123(X1,X2),
c_0_592,
[final] ).
cnf(c_0_752,plain,
lhs_atom112(X1,X2),
c_0_593,
[final] ).
cnf(c_0_753,plain,
lhs_atom111(X1,X2),
c_0_594,
[final] ).
cnf(c_0_754,plain,
lhs_atom22(X1,X2),
c_0_595,
[final] ).
cnf(c_0_755,plain,
lhs_atom21(X1,X2),
c_0_596,
[final] ).
cnf(c_0_756,plain,
lhs_atom11(X1,X2),
c_0_597,
[final] ).
cnf(c_0_757,plain,
lhs_atom10(X1,X2),
c_0_598,
[final] ).
cnf(c_0_758,plain,
lhs_atom9(X1,X2),
c_0_599,
[final] ).
cnf(c_0_759,plain,
lhs_atom8(X1,X2),
c_0_600,
[final] ).
cnf(c_0_760,plain,
lhs_atom137(X1),
c_0_601,
[final] ).
cnf(c_0_761,plain,
lhs_atom49(X1),
c_0_602,
[final] ).
cnf(c_0_762,plain,
lhs_atom48(X1),
c_0_603,
[final] ).
cnf(c_0_763,plain,
lhs_atom34(X1),
c_0_604,
[final] ).
cnf(c_0_764,plain,
lhs_atom33(X1),
c_0_605,
[final] ).
cnf(c_0_765,plain,
lhs_atom26(X1),
c_0_606,
[final] ).
cnf(c_0_766,plain,
lhs_atom24(X1),
c_0_607,
[final] ).
cnf(c_0_767,plain,
lhs_atom23(X1),
c_0_608,
[final] ).
cnf(c_0_768,plain,
lhs_atom20(X1),
c_0_609,
[final] ).
cnf(c_0_769,plain,
lhs_atom19(X1),
c_0_610,
[final] ).
cnf(c_0_770,plain,
lhs_atom18(X1),
c_0_611,
[final] ).
cnf(c_0_771,plain,
lhs_atom17(X1),
c_0_612,
[final] ).
cnf(c_0_772,plain,
lhs_atom14(X1),
c_0_613,
[final] ).
cnf(c_0_773,plain,
lhs_atom13(X1),
c_0_614,
[final] ).
cnf(c_0_774,plain,
lhs_atom12(X1),
c_0_615,
[final] ).
cnf(c_0_775,plain,
lhs_atom95,
c_0_616,
[final] ).
cnf(c_0_776,plain,
lhs_atom77,
c_0_617,
[final] ).
cnf(c_0_777,plain,
lhs_atom76,
c_0_618,
[final] ).
cnf(c_0_778,plain,
lhs_atom64,
c_0_619,
[final] ).
cnf(c_0_779,plain,
lhs_atom59,
c_0_620,
[final] ).
cnf(c_0_780,plain,
lhs_atom50,
c_0_621,
[final] ).
cnf(c_0_781,plain,
lhs_atom25,
c_0_622,
[final] ).
cnf(c_0_782,plain,
lhs_atom16,
c_0_623,
[final] ).
cnf(c_0_783,plain,
lhs_atom15,
c_0_624,
[final] ).
cnf(c_0_784,plain,
lhs_atom7,
c_0_625,
[final] ).
cnf(c_0_785,plain,
lhs_atom6,
c_0_626,
[final] ).
cnf(c_0_786,plain,
lhs_atom5,
c_0_627,
[final] ).
cnf(c_0_787,plain,
lhs_atom4,
c_0_628,
[final] ).
cnf(c_0_788,plain,
lhs_atom1,
c_0_629,
[final] ).
% End CNF derivation
cnf(c_0_630_0,axiom,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(sk1_esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom3]) ).
cnf(c_0_631_0,axiom,
( t != one_one_int
| plus_plus_int(power_power_int(sk1_esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom2]) ).
cnf(c_0_640_0,axiom,
( ~ ord_less_int(X1,X3)
| ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X4))
| ~ ord_less_eq_int(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom44]) ).
cnf(c_0_641_0,axiom,
( ~ ord_less_eq_int(X2,X3)
| ord_less_eq_int(plus_plus_int(X1,X2),plus_plus_int(X1,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom29]) ).
cnf(c_0_642_0,axiom,
( ~ ord_less_int(X1,X3)
| ord_less_int(plus_plus_int(X1,X2),plus_plus_int(X3,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom73]) ).
cnf(c_0_643_0,axiom,
( ord_less_int(X1,pls)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(plus_plus_int(X1,X2))
| ord_less_int(X2,pls) ),
inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom74]) ).
cnf(c_0_644_0,axiom,
( ~ ord_less_eq_int(number_number_of_int(X2),number_number_of_int(X1))
| ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom38]) ).
cnf(c_0_645_0,axiom,
( ~ ord_less_eq_nat(number_number_of_nat(X2),number_number_of_nat(X1))
| ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom36]) ).
cnf(c_0_646_0,axiom,
( ord_less_int(X1,pls)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ ord_less_int(X2,pls) ),
inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom74]) ).
cnf(c_0_672_0,axiom,
( ~ ord_less_int(X1,X2)
| ord_less_eq_int(plus_plus_int(X1,one_one_int),X2) ),
inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom90]) ).
cnf(c_0_673_0,axiom,
( ~ ord_less_eq_int(X1,X3)
| ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom29]) ).
cnf(c_0_674_0,axiom,
( ~ twoSqu526106917sum2sq(X1)
| twoSqu526106917sum2sq(times_times_int(X1,X2))
| ~ twoSqu526106917sum2sq(X2) ),
inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom96]) ).
cnf(c_0_675_0,axiom,
( ord_less_eq_int(number_number_of_int(X2),number_number_of_int(X1))
| ord_less_int(number_number_of_int(X1),number_number_of_int(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_675,def_lhs_atom39]) ).
cnf(c_0_676_0,axiom,
( ord_less_eq_nat(number_number_of_nat(X2),number_number_of_nat(X1))
| ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_676,def_lhs_atom37]) ).
cnf(c_0_677_0,axiom,
( ~ ord_less_eq_int(X1,X2)
| X1 = X2
| ~ ord_less_eq_int(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_677,def_lhs_atom30]) ).
cnf(c_0_678_0,axiom,
( ord_less_int(X1,X2)
| X1 = X2
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_678,def_lhs_atom28]) ).
cnf(c_0_679_0,axiom,
( ord_less_eq_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_679,def_lhs_atom156]) ).
cnf(c_0_680_0,axiom,
( ord_less_eq_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom154]) ).
cnf(c_0_681_0,axiom,
( ord_less_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom146]) ).
cnf(c_0_682_0,axiom,
( ord_less_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_682,def_lhs_atom144]) ).
cnf(c_0_683_0,axiom,
( ord_less_int(X1,plus_plus_int(X2,one_one_int))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom94]) ).
cnf(c_0_684_0,axiom,
( ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom92]) ).
cnf(c_0_685_0,axiom,
( ord_less_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom89]) ).
cnf(c_0_686_0,axiom,
( ord_less_int(bit0(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom87]) ).
cnf(c_0_687_0,axiom,
( ord_less_eq_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom85]) ).
cnf(c_0_688_0,axiom,
( ord_less_eq_int(bit1(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom83]) ).
cnf(c_0_689_0,axiom,
( ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom72]) ).
cnf(c_0_690_0,axiom,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom70]) ).
cnf(c_0_691_0,axiom,
( ord_less_eq_int(bit0(X1),bit0(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom68]) ).
cnf(c_0_692_0,axiom,
( ord_less_eq_int(bit0(X1),bit0(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom66]) ).
cnf(c_0_693_0,axiom,
( ord_less_int(bit0(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom63]) ).
cnf(c_0_694_0,axiom,
( ord_less_int(bit0(X1),bit0(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom61]) ).
cnf(c_0_695_0,axiom,
( ord_less_eq_int(bit1(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom58]) ).
cnf(c_0_696_0,axiom,
( ord_less_eq_int(bit1(X1),bit1(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom56]) ).
cnf(c_0_697_0,axiom,
( ord_less_int(bit1(X1),bit1(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom54]) ).
cnf(c_0_698_0,axiom,
( ord_less_int(bit1(X1),bit1(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom52]) ).
cnf(c_0_699_0,axiom,
( ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom43]) ).
cnf(c_0_700_0,axiom,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ~ ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom41]) ).
cnf(c_0_701_0,axiom,
( ~ ord_less_int(X1,pls)
| plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X2)) = number_number_of_nat(X2) ),
inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom75]) ).
cnf(c_0_702_0,axiom,
( ~ ord_less_eq_int(bit0(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom155]) ).
cnf(c_0_703_0,axiom,
( ~ ord_less_eq_int(bit0(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom153]) ).
cnf(c_0_704_0,axiom,
( ~ ord_less_int(bit1(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom145]) ).
cnf(c_0_705_0,axiom,
( ~ ord_less_int(bit1(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom143]) ).
cnf(c_0_706_0,axiom,
( ~ ord_less_int(X1,plus_plus_int(X2,one_one_int))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom93]) ).
cnf(c_0_707_0,axiom,
( ~ ord_less_eq_int(plus_plus_int(X1,one_one_int),X2)
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom91]) ).
cnf(c_0_708_0,axiom,
( ~ ord_less_int(bit0(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_708,def_lhs_atom88]) ).
cnf(c_0_709_0,axiom,
( ~ ord_less_int(bit0(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom86]) ).
cnf(c_0_710_0,axiom,
( ~ ord_less_eq_int(bit1(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom84]) ).
cnf(c_0_711_0,axiom,
( ~ ord_less_eq_int(bit1(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom82]) ).
cnf(c_0_712_0,axiom,
( ~ ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_712,def_lhs_atom71]) ).
cnf(c_0_713_0,axiom,
( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_713,def_lhs_atom69]) ).
cnf(c_0_714_0,axiom,
( ~ ord_less_eq_int(bit0(X1),bit0(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom67]) ).
cnf(c_0_715_0,axiom,
( ~ ord_less_eq_int(bit0(X1),bit0(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom65]) ).
cnf(c_0_716_0,axiom,
( ~ ord_less_int(bit0(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_716,def_lhs_atom62]) ).
cnf(c_0_717_0,axiom,
( ~ ord_less_int(bit0(X1),bit0(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom60]) ).
cnf(c_0_718_0,axiom,
( ~ ord_less_eq_int(bit1(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom57]) ).
cnf(c_0_719_0,axiom,
( ~ ord_less_eq_int(bit1(X1),bit1(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom55]) ).
cnf(c_0_720_0,axiom,
( ~ ord_less_int(bit1(X1),bit1(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_720,def_lhs_atom53]) ).
cnf(c_0_721_0,axiom,
( ~ ord_less_int(bit1(X1),bit1(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_721,def_lhs_atom51]) ).
cnf(c_0_722_0,axiom,
( ~ ord_less_eq_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_722,def_lhs_atom42]) ).
cnf(c_0_723_0,axiom,
( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom40]) ).
cnf(c_0_724_0,axiom,
( ~ ord_less_int(X1,X2)
| ord_less_eq_int(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_724,def_lhs_atom27]) ).
cnf(c_0_725_0,axiom,
( ord_less_eq_int(pls,bit1(X1))
| ~ ord_less_eq_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_725,def_lhs_atom152]) ).
cnf(c_0_726_0,axiom,
( ord_less_int(pls,bit0(X1))
| ~ ord_less_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_726,def_lhs_atom150]) ).
cnf(c_0_727_0,axiom,
( ord_less_int(bit0(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_727,def_lhs_atom148]) ).
cnf(c_0_728_0,axiom,
( ord_less_int(bit1(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_728,def_lhs_atom142]) ).
cnf(c_0_729_0,axiom,
( ord_less_int(pls,bit1(X1))
| ~ ord_less_eq_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_729,def_lhs_atom81]) ).
cnf(c_0_730_0,axiom,
( ord_less_eq_int(bit1(X1),pls)
| ~ ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_730,def_lhs_atom79]) ).
cnf(c_0_731_0,axiom,
( number_number_of_int(X2) = X1
| X1 != number_number_of_int(X2) ),
inference(unfold_definition,[status(thm)],[c_0_731,def_lhs_atom130]) ).
cnf(c_0_732_0,axiom,
( number_number_of_nat(X2) = X1
| X1 != number_number_of_nat(X2) ),
inference(unfold_definition,[status(thm)],[c_0_732,def_lhs_atom128]) ).
cnf(c_0_733_0,axiom,
( number_number_of_int(X2) != X1
| X1 = number_number_of_int(X2) ),
inference(unfold_definition,[status(thm)],[c_0_733,def_lhs_atom129]) ).
cnf(c_0_734_0,axiom,
( number_number_of_nat(X2) != X1
| X1 = number_number_of_nat(X2) ),
inference(unfold_definition,[status(thm)],[c_0_734,def_lhs_atom127]) ).
cnf(c_0_735_0,axiom,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_735,def_lhs_atom134]) ).
cnf(c_0_736_0,axiom,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_736,def_lhs_atom132]) ).
cnf(c_0_737_0,axiom,
( number_number_of_int(X1) = number_number_of_int(X2)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_737,def_lhs_atom126]) ).
cnf(c_0_738_0,axiom,
( ~ ord_less_int(X1,X2)
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_738,def_lhs_atom27]) ).
cnf(c_0_739_0,axiom,
( ~ ord_less_eq_int(pls,bit1(X1))
| ord_less_eq_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_739,def_lhs_atom151]) ).
cnf(c_0_740_0,axiom,
( ~ ord_less_int(pls,bit0(X1))
| ord_less_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_740,def_lhs_atom149]) ).
cnf(c_0_741_0,axiom,
( ~ ord_less_int(bit0(X1),pls)
| ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_741,def_lhs_atom147]) ).
cnf(c_0_742_0,axiom,
( ~ ord_less_int(bit1(X1),pls)
| ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_742,def_lhs_atom141]) ).
cnf(c_0_743_0,axiom,
( ~ ord_less_int(pls,bit1(X1))
| ord_less_eq_int(pls,X1) ),
inference(unfold_definition,[status(thm)],[c_0_743,def_lhs_atom80]) ).
cnf(c_0_744_0,axiom,
( ~ ord_less_eq_int(bit1(X1),pls)
| ord_less_int(X1,pls) ),
inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom78]) ).
cnf(c_0_745_0,axiom,
( bit0(X1) != bit0(X2)
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom133]) ).
cnf(c_0_746_0,axiom,
( bit1(X1) != bit1(X2)
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_746,def_lhs_atom131]) ).
cnf(c_0_747_0,axiom,
( number_number_of_int(X1) != number_number_of_int(X2)
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_747,def_lhs_atom125]) ).
cnf(c_0_632_0,axiom,
plus_plus_nat(plus_plus_nat(X4,X3),plus_plus_nat(X2,X1)) = plus_plus_nat(plus_plus_nat(X4,X2),plus_plus_nat(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom114]) ).
cnf(c_0_633_0,axiom,
plus_plus_int(plus_plus_int(X4,X3),plus_plus_int(X2,X1)) = plus_plus_int(plus_plus_int(X4,X2),plus_plus_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom113]) ).
cnf(c_0_634_0,axiom,
times_times_nat(times_times_nat(X4,X3),times_times_nat(X2,X1)) = times_times_nat(X4,times_times_nat(X3,times_times_nat(X2,X1))),
inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom102]) ).
cnf(c_0_635_0,axiom,
times_times_int(times_times_int(X4,X3),times_times_int(X2,X1)) = times_times_int(X4,times_times_int(X3,times_times_int(X2,X1))),
inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom101]) ).
cnf(c_0_636_0,axiom,
times_times_nat(times_times_nat(X4,X3),times_times_nat(X2,X1)) = times_times_nat(X2,times_times_nat(times_times_nat(X4,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom100]) ).
cnf(c_0_637_0,axiom,
times_times_int(times_times_int(X4,X3),times_times_int(X2,X1)) = times_times_int(X2,times_times_int(times_times_int(X4,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom99]) ).
cnf(c_0_638_0,axiom,
times_times_nat(times_times_nat(X4,X3),times_times_nat(X2,X1)) = times_times_nat(times_times_nat(X4,X2),times_times_nat(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom98]) ).
cnf(c_0_639_0,axiom,
times_times_int(times_times_int(X4,X3),times_times_int(X2,X1)) = times_times_int(times_times_int(X4,X2),times_times_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom97]) ).
cnf(c_0_647_0,axiom,
plus_plus_int(X3,plus_plus_int(X2,X1)) = plus_plus_int(X2,plus_plus_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom139]) ).
cnf(c_0_648_0,axiom,
plus_plus_int(plus_plus_int(X3,X2),X1) = plus_plus_int(X3,plus_plus_int(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom138]) ).
cnf(c_0_649_0,axiom,
times_times_int(times_times_int(X3,X2),X1) = times_times_int(X3,times_times_int(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom135]) ).
cnf(c_0_650_0,axiom,
plus_plus_nat(X3,plus_plus_nat(X2,X1)) = plus_plus_nat(X2,plus_plus_nat(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom122]) ).
cnf(c_0_651_0,axiom,
plus_plus_int(X3,plus_plus_int(X2,X1)) = plus_plus_int(X2,plus_plus_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom121]) ).
cnf(c_0_652_0,axiom,
plus_plus_nat(X3,plus_plus_nat(X2,X1)) = plus_plus_nat(plus_plus_nat(X3,X2),X1),
inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom120]) ).
cnf(c_0_653_0,axiom,
plus_plus_int(X3,plus_plus_int(X2,X1)) = plus_plus_int(plus_plus_int(X3,X2),X1),
inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom119]) ).
cnf(c_0_654_0,axiom,
plus_plus_nat(plus_plus_nat(X3,X2),X1) = plus_plus_nat(X3,plus_plus_nat(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom118]) ).
cnf(c_0_655_0,axiom,
plus_plus_int(plus_plus_int(X3,X2),X1) = plus_plus_int(X3,plus_plus_int(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom117]) ).
cnf(c_0_656_0,axiom,
plus_plus_nat(plus_plus_nat(X3,X2),X1) = plus_plus_nat(plus_plus_nat(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom116]) ).
cnf(c_0_657_0,axiom,
plus_plus_int(plus_plus_int(X3,X2),X1) = plus_plus_int(plus_plus_int(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_657,def_lhs_atom115]) ).
cnf(c_0_658_0,axiom,
times_times_nat(X3,times_times_nat(X2,X1)) = times_times_nat(X2,times_times_nat(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom110]) ).
cnf(c_0_659_0,axiom,
times_times_int(X3,times_times_int(X2,X1)) = times_times_int(X2,times_times_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom109]) ).
cnf(c_0_660_0,axiom,
times_times_nat(X3,times_times_nat(X2,X1)) = times_times_nat(times_times_nat(X3,X2),X1),
inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom108]) ).
cnf(c_0_661_0,axiom,
times_times_int(X3,times_times_int(X2,X1)) = times_times_int(times_times_int(X3,X2),X1),
inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom107]) ).
cnf(c_0_662_0,axiom,
times_times_nat(times_times_nat(X3,X2),X1) = times_times_nat(X3,times_times_nat(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom106]) ).
cnf(c_0_663_0,axiom,
times_times_int(times_times_int(X3,X2),X1) = times_times_int(X3,times_times_int(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom105]) ).
cnf(c_0_664_0,axiom,
times_times_nat(times_times_nat(X3,X2),X1) = times_times_nat(times_times_nat(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom104]) ).
cnf(c_0_665_0,axiom,
times_times_int(times_times_int(X3,X2),X1) = times_times_int(times_times_int(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom103]) ).
cnf(c_0_666_0,axiom,
power_power_int(X3,plus_plus_nat(X2,X1)) = times_times_int(power_power_int(X3,X2),power_power_int(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom47]) ).
cnf(c_0_667_0,axiom,
times_times_nat(power_power_nat(X1,X3),power_power_nat(X1,X2)) = power_power_nat(X1,plus_plus_nat(X3,X2)),
inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom46]) ).
cnf(c_0_668_0,axiom,
times_times_int(power_power_int(X1,X3),power_power_int(X1,X2)) = power_power_int(X1,plus_plus_nat(X3,X2)),
inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom45]) ).
cnf(c_0_669_0,axiom,
power_power_int(power_power_int(X3,X2),X1) = power_power_int(X3,times_times_nat(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom35]) ).
cnf(c_0_670_0,axiom,
power_power_nat(power_power_nat(X1,X3),X2) = power_power_nat(X1,times_times_nat(X3,X2)),
inference(unfold_definition,[status(thm)],[c_0_670,def_lhs_atom32]) ).
cnf(c_0_671_0,axiom,
power_power_int(power_power_int(X1,X3),X2) = power_power_int(X1,times_times_nat(X3,X2)),
inference(unfold_definition,[status(thm)],[c_0_671,def_lhs_atom31]) ).
cnf(c_0_748_0,axiom,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_748,def_lhs_atom140]) ).
cnf(c_0_749_0,axiom,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom136]) ).
cnf(c_0_750_0,axiom,
plus_plus_nat(X2,X1) = plus_plus_nat(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_750,def_lhs_atom124]) ).
cnf(c_0_751_0,axiom,
plus_plus_int(X2,X1) = plus_plus_int(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_751,def_lhs_atom123]) ).
cnf(c_0_752_0,axiom,
times_times_nat(X2,X1) = times_times_nat(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom112]) ).
cnf(c_0_753_0,axiom,
times_times_int(X2,X1) = times_times_int(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom111]) ).
cnf(c_0_754_0,axiom,
power_power_nat(X1,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X2)) = times_times_nat(power_power_nat(X1,X2),power_power_nat(X1,X2)),
inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom22]) ).
cnf(c_0_755_0,axiom,
power_power_int(X1,times_times_nat(number_number_of_nat(bit0(bit1(pls))),X2)) = times_times_int(power_power_int(X1,X2),power_power_int(X1,X2)),
inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom21]) ).
cnf(c_0_756_0,axiom,
power_power_int(plus_plus_int(X2,X1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom11]) ).
cnf(c_0_757_0,axiom,
power_power_nat(plus_plus_nat(X2,X1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(X1,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_757,def_lhs_atom10]) ).
cnf(c_0_758_0,axiom,
power_power_int(plus_plus_int(X2,X1),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(X2,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))),X1)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),X2),power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(X1,number_number_of_nat(bit1(bit1(pls))))),
inference(unfold_definition,[status(thm)],[c_0_758,def_lhs_atom9]) ).
cnf(c_0_759_0,axiom,
power_power_int(plus_plus_int(X2,X1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X2),X1)),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),
inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom8]) ).
cnf(c_0_760_0,axiom,
number_number_of_int(X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom137]) ).
cnf(c_0_761_0,axiom,
times_times_nat(X1,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_761,def_lhs_atom49]) ).
cnf(c_0_762_0,axiom,
times_times_nat(number_number_of_nat(bit0(bit1(pls))),X1) = plus_plus_nat(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom48]) ).
cnf(c_0_763_0,axiom,
power_power_nat(X1,one_one_nat) = X1,
inference(unfold_definition,[status(thm)],[c_0_763,def_lhs_atom34]) ).
cnf(c_0_764_0,axiom,
power_power_int(X1,one_one_nat) = X1,
inference(unfold_definition,[status(thm)],[c_0_764,def_lhs_atom33]) ).
cnf(c_0_765_0,axiom,
ord_less_eq_int(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_765,def_lhs_atom26]) ).
cnf(c_0_766_0,axiom,
plus_plus_int(number_number_of_int(X1),one_one_int) = number_number_of_int(plus_plus_int(X1,bit1(pls))),
inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom24]) ).
cnf(c_0_767_0,axiom,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(bit1(pls),X1)),
inference(unfold_definition,[status(thm)],[c_0_767,def_lhs_atom23]) ).
cnf(c_0_768_0,axiom,
power_power_nat(X1,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_768,def_lhs_atom20]) ).
cnf(c_0_769_0,axiom,
power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_769,def_lhs_atom19]) ).
cnf(c_0_770_0,axiom,
times_times_nat(X1,X1) = power_power_nat(X1,number_number_of_nat(bit0(bit1(pls)))),
inference(unfold_definition,[status(thm)],[c_0_770,def_lhs_atom18]) ).
cnf(c_0_771_0,axiom,
times_times_int(X1,X1) = power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),
inference(unfold_definition,[status(thm)],[c_0_771,def_lhs_atom17]) ).
cnf(c_0_772_0,axiom,
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(unfold_definition,[status(thm)],[c_0_772,def_lhs_atom14]) ).
cnf(c_0_773_0,axiom,
power_power_nat(number_number_of_nat(X1),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(X1),number_number_of_nat(X1)),
inference(unfold_definition,[status(thm)],[c_0_773,def_lhs_atom13]) ).
cnf(c_0_774_0,axiom,
power_power_int(number_number_of_int(X1),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(X1),number_number_of_int(X1)),
inference(unfold_definition,[status(thm)],[c_0_774,def_lhs_atom12]) ).
cnf(c_0_775_0,axiom,
zprime(number_number_of_int(bit0(bit1(pls)))),
inference(unfold_definition,[status(thm)],[c_0_775,def_lhs_atom95]) ).
cnf(c_0_776_0,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(unfold_definition,[status(thm)],[c_0_776,def_lhs_atom77]) ).
cnf(c_0_777_0,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(unfold_definition,[status(thm)],[c_0_777,def_lhs_atom76]) ).
cnf(c_0_778_0,axiom,
ord_less_eq_int(pls,pls),
inference(unfold_definition,[status(thm)],[c_0_778,def_lhs_atom64]) ).
cnf(c_0_779_0,axiom,
~ ord_less_int(pls,pls),
inference(unfold_definition,[status(thm)],[c_0_779,def_lhs_atom59]) ).
cnf(c_0_780_0,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(unfold_definition,[status(thm)],[c_0_780,def_lhs_atom50]) ).
cnf(c_0_781_0,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(unfold_definition,[status(thm)],[c_0_781,def_lhs_atom25]) ).
cnf(c_0_782_0,axiom,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(unfold_definition,[status(thm)],[c_0_782,def_lhs_atom16]) ).
cnf(c_0_783_0,axiom,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(unfold_definition,[status(thm)],[c_0_783,def_lhs_atom15]) ).
cnf(c_0_784_0,axiom,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom7]) ).
cnf(c_0_785_0,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),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom6]) ).
cnf(c_0_786_0,axiom,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom5]) ).
cnf(c_0_787_0,axiom,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(unfold_definition,[status(thm)],[c_0_787,def_lhs_atom4]) ).
cnf(c_0_788_0,axiom,
ord_less_eq_int(one_one_int,t),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
~ ! [X5] : 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),X5),
file('<stdin>',fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
fof(c_0_1_002,axiom,
! [X1,X2] :
( ord_less_int(X1,X2)
| X1 = X2
| ord_less_int(X2,X1) ),
file('<stdin>',fact_29_zless__linear) ).
fof(c_0_2_003,axiom,
! [X3,X4] :
( ord_less_eq_int(X3,X4)
| ord_less_eq_int(X4,X3) ),
file('<stdin>',fact_27_zle__linear) ).
fof(c_0_3_004,axiom,
~ ! [X5] : 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),X5),
c_0_0 ).
fof(c_0_4_005,axiom,
! [X1,X2] :
( ord_less_int(X1,X2)
| X1 = X2
| ord_less_int(X2,X1) ),
c_0_1 ).
fof(c_0_5_006,axiom,
! [X3,X4] :
( ord_less_eq_int(X3,X4)
| ord_less_eq_int(X4,X3) ),
c_0_2 ).
fof(c_0_6_007,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),esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7_008,plain,
! [X3,X4] :
( ord_less_int(X3,X4)
| X3 = X4
| ord_less_int(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_4]) ).
fof(c_0_8_009,plain,
! [X5,X6] :
( ord_less_eq_int(X5,X6)
| ord_less_eq_int(X6,X5) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
cnf(c_0_9_010,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),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10_011,plain,
( ord_less_int(X1,X2)
| X2 = X1
| ord_less_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11_012,plain,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12_013,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),esk1_0) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
c_0_9,
[final] ).
cnf(c_0_13_014,plain,
( ord_less_int(X1,X2)
| X2 = X1
| ord_less_int(X2,X1) ),
c_0_10,
[final] ).
cnf(c_0_14_015,plain,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
c_0_11,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_13_0,axiom,
( ord_less_int(X1,X2)
| X2 = X1
| ord_less_int(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_13_1,axiom,
( X2 = X1
| ord_less_int(X1,X2)
| ord_less_int(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_13_2,axiom,
( ord_less_int(X2,X1)
| X2 = X1
| ord_less_int(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_14_0,axiom,
( ord_less_eq_int(X1,X2)
| ord_less_eq_int(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_14_1,axiom,
( ord_less_eq_int(X2,X1)
| ord_less_eq_int(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_12_0,axiom,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),sk2_esk1_0) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(literals_permutation,[status(thm)],[c_0_12]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_016,conjecture,
? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
file('<stdin>',conj_0) ).
fof(c_0_1_017,negated_conjecture,
~ ? [X1,X2] : plus_plus_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_018,negated_conjecture,
! [X3,X4] : plus_plus_int(power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X4,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)],[c_0_1])]) ).
cnf(c_0_3_019,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)],[c_0_2]) ).
cnf(c_0_4_020,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),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_165,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_4) ).
cnf(c_281,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,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(copy,[status(esa)],[c_165]) ).
cnf(c_285,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,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(copy,[status(esa)],[c_281]) ).
cnf(c_286,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,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(copy,[status(esa)],[c_285]) ).
cnf(c_287,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,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(copy,[status(esa)],[c_286]) ).
cnf(c_736,negated_conjecture,
plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,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(copy,[status(esa)],[c_287]) ).
cnf(c_164,plain,
( plus_plus_int(power_power_int(sk1_esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_630_0) ).
cnf(c_734,plain,
( plus_plus_int(power_power_int(sk1_esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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(copy,[status(esa)],[c_164]) ).
cnf(c_735,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(power_power_int(sk1_esk3_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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(rewriting,[status(thm)],[c_734]) ).
cnf(c_741,plain,
~ ord_less_int(one_one_int,t),
inference(backward_subsumption_resolution,[status(thm)],[c_736,c_735]) ).
cnf(c_742,plain,
~ ord_less_int(one_one_int,t),
inference(rewriting,[status(thm)],[c_741]) ).
cnf(c_0,plain,
( ord_less_int(X0,X1)
| X0 = X1
| ord_less_int(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_13_0) ).
cnf(c_454,plain,
( ord_less_int(X0,X1)
| X0 = X1
| ord_less_int(X1,X0) ),
inference(copy,[status(esa)],[c_0]) ).
cnf(c_455,plain,
( ord_less_int(X0,X1)
| ord_less_int(X1,X0)
| X0 = X1 ),
inference(rewriting,[status(thm)],[c_454]) ).
cnf(c_749,plain,
( ord_less_int(t,one_one_int)
| t = one_one_int ),
inference(resolution,[status(thm)],[c_742,c_455]) ).
cnf(c_750,plain,
( ord_less_int(t,one_one_int)
| t = one_one_int ),
inference(rewriting,[status(thm)],[c_749]) ).
cnf(c_163,plain,
( plus_plus_int(power_power_int(sk1_esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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 ),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_631_0) ).
cnf(c_732,plain,
( plus_plus_int(power_power_int(sk1_esk1_0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sk1_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(copy,[status(esa)],[c_163]) ).
cnf(c_740,plain,
t != one_one_int,
inference(backward_subsumption_resolution,[status(thm)],[c_736,c_732]) ).
cnf(c_743,plain,
t != one_one_int,
inference(rewriting,[status(thm)],[c_740]) ).
cnf(c_756,plain,
ord_less_int(t,one_one_int),
inference(forward_subsumption_resolution,[status(thm)],[c_750,c_743]) ).
cnf(c_757,plain,
ord_less_int(t,one_one_int),
inference(rewriting,[status(thm)],[c_756]) ).
cnf(c_103,plain,
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_724_0) ).
cnf(c_612,plain,
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,X1) ),
inference(copy,[status(esa)],[c_103]) ).
cnf(c_613,plain,
( ~ ord_less_int(X0,X1)
| ord_less_eq_int(X0,X1) ),
inference(rewriting,[status(thm)],[c_612]) ).
cnf(c_759,plain,
ord_less_eq_int(t,one_one_int),
inference(resolution,[status(thm)],[c_757,c_613]) ).
cnf(c_762,plain,
ord_less_eq_int(t,one_one_int),
inference(rewriting,[status(thm)],[c_759]) ).
cnf(c_150,plain,
( ~ ord_less_eq_int(X0,X1)
| X1 = X0
| ~ ord_less_eq_int(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_677_0) ).
cnf(c_706,plain,
( ~ ord_less_eq_int(X0,X1)
| X1 = X0
| ~ ord_less_eq_int(X1,X0) ),
inference(copy,[status(esa)],[c_150]) ).
cnf(c_707,plain,
( ~ ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(X1,X0)
| X1 = X0 ),
inference(rewriting,[status(thm)],[c_706]) ).
cnf(c_769,plain,
( ~ ord_less_eq_int(one_one_int,t)
| t = one_one_int ),
inference(resolution,[status(thm)],[c_762,c_707]) ).
cnf(c_770,plain,
( ~ ord_less_eq_int(one_one_int,t)
| t = one_one_int ),
inference(rewriting,[status(thm)],[c_769]) ).
cnf(c_6,plain,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox/tmp/iprover_modulo_efc815.p',c_0_788_0) ).
cnf(c_465,plain,
ord_less_eq_int(one_one_int,t),
inference(copy,[status(esa)],[c_6]) ).
cnf(c_854,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_770,c_743,c_465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 14:59:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.41 % FOF problem with conjecture
% 0.19/0.41 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_ee1bd3.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_efc815.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_ef2238 | grep -v "SZS"
% 0.19/0.43
% 0.19/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ iProver source info
% 0.19/0.43
% 0.19/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.43 % git: non_committed_changes: true
% 0.19/0.43 % git: last_make_outside_of_git: true
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ Input Options
% 0.19/0.43
% 0.19/0.43 % --out_options all
% 0.19/0.43 % --tptp_safe_out true
% 0.19/0.43 % --problem_path ""
% 0.19/0.43 % --include_path ""
% 0.19/0.43 % --clausifier .//eprover
% 0.19/0.43 % --clausifier_options --tstp-format
% 0.19/0.43 % --stdin false
% 0.19/0.43 % --dbg_backtrace false
% 0.19/0.43 % --dbg_dump_prop_clauses false
% 0.19/0.43 % --dbg_dump_prop_clauses_file -
% 0.19/0.43 % --dbg_out_stat false
% 0.19/0.43
% 0.19/0.43 % ------ General Options
% 0.19/0.43
% 0.19/0.43 % --fof false
% 0.19/0.43 % --time_out_real 150.
% 0.19/0.43 % --time_out_prep_mult 0.2
% 0.19/0.43 % --time_out_virtual -1.
% 0.19/0.43 % --schedule none
% 0.19/0.43 % --ground_splitting input
% 0.19/0.43 % --splitting_nvd 16
% 0.19/0.43 % --non_eq_to_eq false
% 0.19/0.43 % --prep_gs_sim true
% 0.19/0.43 % --prep_unflatten false
% 0.19/0.43 % --prep_res_sim true
% 0.19/0.43 % --prep_upred true
% 0.19/0.43 % --res_sim_input true
% 0.19/0.43 % --clause_weak_htbl true
% 0.19/0.43 % --gc_record_bc_elim false
% 0.19/0.43 % --symbol_type_check false
% 0.19/0.43 % --clausify_out false
% 0.19/0.43 % --large_theory_mode false
% 0.19/0.43 % --prep_sem_filter none
% 0.19/0.43 % --prep_sem_filter_out false
% 0.19/0.43 % --preprocessed_out false
% 0.19/0.43 % --sub_typing false
% 0.19/0.43 % --brand_transform false
% 0.19/0.43 % --pure_diseq_elim true
% 0.19/0.43 % --min_unsat_core false
% 0.19/0.43 % --pred_elim true
% 0.19/0.43 % --add_important_lit false
% 0.19/0.43 % --soft_assumptions false
% 0.19/0.43 % --reset_solvers false
% 0.19/0.43 % --bc_imp_inh []
% 0.19/0.43 % --conj_cone_tolerance 1.5
% 0.19/0.43 % --prolific_symb_bound 500
% 0.19/0.43 % --lt_threshold 2000
% 0.19/0.43
% 0.19/0.43 % ------ SAT Options
% 0.19/0.43
% 0.19/0.43 % --sat_mode false
% 0.19/0.43 % --sat_fm_restart_options ""
% 0.19/0.43 % --sat_gr_def false
% 0.19/0.43 % --sat_epr_types true
% 0.19/0.43 % --sat_non_cyclic_types false
% 0.19/0.43 % --sat_finite_models false
% 0.19/0.43 % --sat_fm_lemmas false
% 0.19/0.43 % --sat_fm_prep false
% 0.19/0.43 % --sat_fm_uc_incr true
% 0.19/0.43 % --sat_out_model small
% 0.19/0.43 % --sat_out_clauses false
% 0.19/0.43
% 0.19/0.43 % ------ QBF Options
% 0.19/0.43
% 0.19/0.43 % --qbf_mode false
% 0.19/0.43 % --qbf_elim_univ true
% 0.19/0.43 % --qbf_sk_in true
% 0.19/0.43 % --qbf_pred_elim true
% 0.19/0.43 % --qbf_split 32
% 0.19/0.43
% 0.19/0.43 % ------ BMC1 Options
% 0.19/0.43
% 0.19/0.43 % --bmc1_incremental false
% 0.19/0.43 % --bmc1_axioms reachable_all
% 0.19/0.43 % --bmc1_min_bound 0
% 0.19/0.43 % --bmc1_max_bound -1
% 0.19/0.43 % --bmc1_max_bound_default -1
% 0.19/0.43 % --bmc1_symbol_reachability true
% 0.19/0.43 % --bmc1_property_lemmas false
% 0.19/0.43 % --bmc1_k_induction false
% 0.19/0.43 % --bmc1_non_equiv_states false
% 0.19/0.43 % --bmc1_deadlock false
% 0.19/0.43 % --bmc1_ucm false
% 0.19/0.43 % --bmc1_add_unsat_core none
% 0.19/0.43 % --bmc1_unsat_core_children false
% 0.19/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.43 % --bmc1_out_stat full
% 0.19/0.43 % --bmc1_ground_init false
% 0.19/0.43 % --bmc1_pre_inst_next_state false
% 0.19/0.43 % --bmc1_pre_inst_state false
% 0.19/0.43 % --bmc1_pre_inst_reach_state false
% 0.19/0.43 % --bmc1_out_unsat_core false
% 0.19/0.43 % --bmc1_aig_witness_out false
% 0.19/0.43 % --bmc1_verbose false
% 0.19/0.43 % --bmc1_dump_clauses_tptp false
% 1.99/2.28 % --bmc1_dump_unsat_core_tptp false
% 1.99/2.28 % --bmc1_dump_file -
% 1.99/2.28 % --bmc1_ucm_expand_uc_limit 128
% 1.99/2.28 % --bmc1_ucm_n_expand_iterations 6
% 1.99/2.28 % --bmc1_ucm_extend_mode 1
% 1.99/2.28 % --bmc1_ucm_init_mode 2
% 1.99/2.28 % --bmc1_ucm_cone_mode none
% 1.99/2.28 % --bmc1_ucm_reduced_relation_type 0
% 1.99/2.28 % --bmc1_ucm_relax_model 4
% 1.99/2.28 % --bmc1_ucm_full_tr_after_sat true
% 1.99/2.28 % --bmc1_ucm_expand_neg_assumptions false
% 1.99/2.28 % --bmc1_ucm_layered_model none
% 1.99/2.28 % --bmc1_ucm_max_lemma_size 10
% 1.99/2.28
% 1.99/2.28 % ------ AIG Options
% 1.99/2.28
% 1.99/2.28 % --aig_mode false
% 1.99/2.28
% 1.99/2.28 % ------ Instantiation Options
% 1.99/2.28
% 1.99/2.28 % --instantiation_flag true
% 1.99/2.28 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.99/2.28 % --inst_solver_per_active 750
% 1.99/2.28 % --inst_solver_calls_frac 0.5
% 1.99/2.28 % --inst_passive_queue_type priority_queues
% 1.99/2.28 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.99/2.28 % --inst_passive_queues_freq [25;2]
% 1.99/2.28 % --inst_dismatching true
% 1.99/2.28 % --inst_eager_unprocessed_to_passive true
% 1.99/2.28 % --inst_prop_sim_given true
% 1.99/2.28 % --inst_prop_sim_new false
% 1.99/2.28 % --inst_orphan_elimination true
% 1.99/2.28 % --inst_learning_loop_flag true
% 1.99/2.28 % --inst_learning_start 3000
% 1.99/2.28 % --inst_learning_factor 2
% 1.99/2.28 % --inst_start_prop_sim_after_learn 3
% 1.99/2.28 % --inst_sel_renew solver
% 1.99/2.28 % --inst_lit_activity_flag true
% 1.99/2.28 % --inst_out_proof true
% 1.99/2.28
% 1.99/2.28 % ------ Resolution Options
% 1.99/2.28
% 1.99/2.28 % --resolution_flag true
% 1.99/2.28 % --res_lit_sel kbo_max
% 1.99/2.28 % --res_to_prop_solver none
% 1.99/2.28 % --res_prop_simpl_new false
% 1.99/2.28 % --res_prop_simpl_given false
% 1.99/2.28 % --res_passive_queue_type priority_queues
% 1.99/2.28 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.99/2.28 % --res_passive_queues_freq [15;5]
% 1.99/2.28 % --res_forward_subs full
% 1.99/2.28 % --res_backward_subs full
% 1.99/2.28 % --res_forward_subs_resolution true
% 1.99/2.28 % --res_backward_subs_resolution true
% 1.99/2.28 % --res_orphan_elimination false
% 1.99/2.28 % --res_time_limit 1000.
% 1.99/2.28 % --res_out_proof true
% 1.99/2.28 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_ee1bd3.s
% 1.99/2.28 % --modulo true
% 1.99/2.28
% 1.99/2.28 % ------ Combination Options
% 1.99/2.28
% 1.99/2.28 % --comb_res_mult 1000
% 1.99/2.28 % --comb_inst_mult 300
% 1.99/2.28 % ------
% 1.99/2.28
% 1.99/2.28 % ------ Parsing...% successful
% 1.99/2.28
% 1.99/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 1.99/2.28
% 1.99/2.28 % ------ Proving...
% 1.99/2.28 % ------ Problem Properties
% 1.99/2.28
% 1.99/2.28 %
% 1.99/2.28 % EPR false
% 1.99/2.28 % Horn false
% 1.99/2.28 % Has equality true
% 1.99/2.28
% 1.99/2.28 % % ------ Input Options Time Limit: Unbounded
% 1.99/2.28
% 1.99/2.28
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 Compiling...
% 1.99/2.28 Loading plugin: done.
% 1.99/2.28 % % ------ Current options:
% 1.99/2.28
% 1.99/2.28 % ------ Input Options
% 1.99/2.28
% 1.99/2.28 % --out_options all
% 1.99/2.28 % --tptp_safe_out true
% 1.99/2.28 % --problem_path ""
% 1.99/2.28 % --include_path ""
% 1.99/2.28 % --clausifier .//eprover
% 1.99/2.28 % --clausifier_options --tstp-format
% 1.99/2.28 % --stdin false
% 1.99/2.28 % --dbg_backtrace false
% 1.99/2.28 % --dbg_dump_prop_clauses false
% 1.99/2.28 % --dbg_dump_prop_clauses_file -
% 1.99/2.28 % --dbg_out_stat false
% 1.99/2.28
% 1.99/2.28 % ------ General Options
% 1.99/2.28
% 1.99/2.28 % --fof false
% 1.99/2.28 % --time_out_real 150.
% 1.99/2.28 % --time_out_prep_mult 0.2
% 1.99/2.28 % --time_out_virtual -1.
% 1.99/2.28 % --schedule none
% 1.99/2.28 % --ground_splitting input
% 1.99/2.28 % --splitting_nvd 16
% 1.99/2.28 % --non_eq_to_eq false
% 1.99/2.28 % --prep_gs_sim true
% 1.99/2.28 % --prep_unflatten false
% 1.99/2.28 % --prep_res_sim true
% 1.99/2.28 % --prep_upred true
% 1.99/2.28 % --res_sim_input true
% 1.99/2.28 % --clause_weak_htbl true
% 1.99/2.28 % --gc_record_bc_elim false
% 1.99/2.28 % --symbol_type_check false
% 1.99/2.28 % --clausify_out false
% 1.99/2.28 % --large_theory_mode false
% 1.99/2.28 % --prep_sem_filter none
% 1.99/2.28 % --prep_sem_filter_out false
% 1.99/2.28 % --preprocessed_out false
% 1.99/2.28 % --sub_typing false
% 1.99/2.28 % --brand_transform false
% 1.99/2.28 % --pure_diseq_elim true
% 1.99/2.28 % --min_unsat_core false
% 1.99/2.28 % --pred_elim true
% 1.99/2.28 % --add_important_lit false
% 1.99/2.28 % --soft_assumptions false
% 1.99/2.28 % --reset_solvers false
% 1.99/2.28 % --bc_imp_inh []
% 1.99/2.28 % --conj_cone_tolerance 1.5
% 1.99/2.28 % --prolific_symb_bound 500
% 1.99/2.28 % --lt_threshold 2000
% 1.99/2.28
% 1.99/2.28 % ------ SAT Options
% 1.99/2.28
% 1.99/2.28 % --sat_mode false
% 1.99/2.28 % --sat_fm_restart_options ""
% 1.99/2.28 % --sat_gr_def false
% 1.99/2.28 % --sat_epr_types true
% 1.99/2.28 % --sat_non_cyclic_types false
% 1.99/2.28 % --sat_finite_models false
% 1.99/2.28 % --sat_fm_lemmas false
% 1.99/2.28 % --sat_fm_prep false
% 1.99/2.28 % --sat_fm_uc_incr true
% 1.99/2.28 % --sat_out_model small
% 1.99/2.28 % --sat_out_clauses false
% 1.99/2.28
% 1.99/2.28 % ------ QBF Options
% 1.99/2.28
% 1.99/2.28 % --qbf_mode false
% 1.99/2.28 % --qbf_elim_univ true
% 1.99/2.28 % --qbf_sk_in true
% 1.99/2.28 % --qbf_pred_elim true
% 1.99/2.28 % --qbf_split 32
% 1.99/2.28
% 1.99/2.28 % ------ BMC1 Options
% 1.99/2.28
% 1.99/2.28 % --bmc1_incremental false
% 1.99/2.28 % --bmc1_axioms reachable_all
% 1.99/2.28 % --bmc1_min_bound 0
% 1.99/2.28 % --bmc1_max_bound -1
% 1.99/2.28 % --bmc1_max_bound_default -1
% 1.99/2.28 % --bmc1_symbol_reachability true
% 1.99/2.28 % --bmc1_property_lemmas false
% 1.99/2.28 % --bmc1_k_induction false
% 1.99/2.28 % --bmc1_non_equiv_states false
% 1.99/2.28 % --bmc1_deadlock false
% 1.99/2.28 % --bmc1_ucm false
% 1.99/2.28 % --bmc1_add_unsat_core none
% 1.99/2.28 % --bmc1_unsat_core_children false
% 1.99/2.28 % --bmc1_unsat_core_extrapolate_axioms false
% 1.99/2.28 % --bmc1_out_stat full
% 1.99/2.28 % --bmc1_ground_init false
% 1.99/2.28 % --bmc1_pre_inst_next_state false
% 1.99/2.28 % --bmc1_pre_inst_state false
% 1.99/2.28 % --bmc1_pre_inst_reach_state false
% 1.99/2.28 % --bmc1_out_unsat_core false
% 1.99/2.28 % --bmc1_aig_witness_out false
% 1.99/2.28 % --bmc1_verbose false
% 1.99/2.28 % --bmc1_dump_clauses_tptp false
% 1.99/2.28 % --bmc1_dump_unsat_core_tptp false
% 1.99/2.28 % --bmc1_dump_file -
% 1.99/2.28 % --bmc1_ucm_expand_uc_limit 128
% 1.99/2.28 % --bmc1_ucm_n_expand_iterations 6
% 1.99/2.28 % --bmc1_ucm_extend_mode 1
% 1.99/2.28 % --bmc1_ucm_init_mode 2
% 1.99/2.28 % --bmc1_ucm_cone_mode none
% 1.99/2.28 % --bmc1_ucm_reduced_relation_type 0
% 1.99/2.28 % --bmc1_ucm_relax_model 4
% 1.99/2.28 % --bmc1_ucm_full_tr_after_sat true
% 1.99/2.28 % --bmc1_ucm_expand_neg_assumptions false
% 1.99/2.28 % --bmc1_ucm_layered_model none
% 1.99/2.28 % --bmc1_ucm_max_lemma_size 10
% 1.99/2.28
% 1.99/2.28 % ------ AIG Options
% 1.99/2.28
% 1.99/2.28 % --aig_mode false
% 1.99/2.28
% 1.99/2.28 % ------ Instantiation Options
% 1.99/2.28
% 1.99/2.28 % --instantiation_flag true
% 1.99/2.28 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.99/2.28 % --inst_solver_per_active 750
% 2.08/2.28 % --inst_solver_calls_frac 0.5
% 2.08/2.28 % --inst_passive_queue_type priority_queues
% 2.08/2.28 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.08/2.28 % --inst_passive_queues_freq [25;2]
% 2.08/2.28 % --inst_dismatching true
% 2.08/2.28 % --inst_eager_unprocessed_to_passive true
% 2.08/2.28 % --inst_prop_sim_given true
% 2.08/2.28 % --inst_prop_sim_new false
% 2.08/2.28 % --inst_orphan_elimination true
% 2.08/2.28 % --inst_learning_loop_flag true
% 2.08/2.28 % --inst_learning_start 3000
% 2.08/2.28 % --inst_learning_factor 2
% 2.08/2.28 % --inst_start_prop_sim_after_learn 3
% 2.08/2.28 % --inst_sel_renew solver
% 2.08/2.28 % --inst_lit_activity_flag true
% 2.08/2.28 % --inst_out_proof true
% 2.08/2.28
% 2.08/2.28 % ------ Resolution Options
% 2.08/2.28
% 2.08/2.28 % --resolution_flag true
% 2.08/2.28 % --res_lit_sel kbo_max
% 2.08/2.28 % --res_to_prop_solver none
% 2.08/2.28 % --res_prop_simpl_new false
% 2.08/2.28 % --res_prop_simpl_given false
% 2.08/2.28 % --res_passive_queue_type priority_queues
% 2.08/2.28 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.08/2.28 % --res_passive_queues_freq [15;5]
% 2.08/2.28 % --res_forward_subs full
% 2.08/2.28 % --res_backward_subs full
% 2.08/2.28 % --res_forward_subs_resolution true
% 2.08/2.28 % --res_backward_subs_resolution true
% 2.08/2.28 % --res_orphan_elimination false
% 2.08/2.28 % --res_time_limit 1000.
% 2.08/2.28 % --res_out_proof true
% 2.08/2.28 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_ee1bd3.s
% 2.08/2.28 % --modulo true
% 2.08/2.28
% 2.08/2.28 % ------ Combination Options
% 2.08/2.28
% 2.08/2.28 % --comb_res_mult 1000
% 2.08/2.28 % --comb_inst_mult 300
% 2.08/2.28 % ------
% 2.08/2.28
% 2.08/2.28
% 2.08/2.28
% 2.08/2.28 % ------ Proving...
% 2.08/2.28 %
% 2.08/2.28
% 2.08/2.28
% 2.08/2.28 % Resolution empty clause
% 2.08/2.28
% 2.08/2.28 % ------ Statistics
% 2.08/2.28
% 2.08/2.28 % ------ General
% 2.08/2.28
% 2.08/2.28 % num_of_input_clauses: 166
% 2.08/2.28 % num_of_input_neg_conjectures: 1
% 2.08/2.28 % num_of_splits: 0
% 2.08/2.28 % num_of_split_atoms: 0
% 2.08/2.28 % num_of_sem_filtered_clauses: 0
% 2.08/2.28 % num_of_subtypes: 0
% 2.08/2.28 % monotx_restored_types: 0
% 2.08/2.28 % sat_num_of_epr_types: 0
% 2.08/2.28 % sat_num_of_non_cyclic_types: 0
% 2.08/2.28 % sat_guarded_non_collapsed_types: 0
% 2.08/2.28 % is_epr: 0
% 2.08/2.28 % is_horn: 0
% 2.08/2.28 % has_eq: 1
% 2.08/2.28 % num_pure_diseq_elim: 0
% 2.08/2.28 % simp_replaced_by: 0
% 2.08/2.28 % res_preprocessed: 2
% 2.08/2.28 % prep_upred: 0
% 2.08/2.28 % prep_unflattend: 0
% 2.08/2.28 % pred_elim_cands: 0
% 2.08/2.28 % pred_elim: 0
% 2.08/2.28 % pred_elim_cl: 0
% 2.08/2.28 % pred_elim_cycles: 0
% 2.08/2.28 % forced_gc_time: 0
% 2.08/2.28 % gc_basic_clause_elim: 0
% 2.08/2.28 % parsing_time: 0.005
% 2.08/2.28 % sem_filter_time: 0.
% 2.08/2.28 % pred_elim_time: 0.
% 2.08/2.28 % out_proof_time: 0.001
% 2.08/2.28 % monotx_time: 0.
% 2.08/2.28 % subtype_inf_time: 0.
% 2.08/2.28 % unif_index_cands_time: 0.
% 2.08/2.28 % unif_index_add_time: 0.
% 2.08/2.28 % total_time: 1.862
% 2.08/2.28 % num_of_symbols: 52
% 2.08/2.28 % num_of_terms: 770
% 2.08/2.28
% 2.08/2.28 % ------ Propositional Solver
% 2.08/2.28
% 2.08/2.28 % prop_solver_calls: 1
% 2.08/2.28 % prop_fast_solver_calls: 3
% 2.08/2.28 % prop_num_of_clauses: 251
% 2.08/2.28 % prop_preprocess_simplified: 395
% 2.08/2.28 % prop_fo_subsumed: 0
% 2.08/2.28 % prop_solver_time: 0.
% 2.08/2.28 % prop_fast_solver_time: 0.
% 2.08/2.28 % prop_unsat_core_time: 0.
% 2.08/2.28
% 2.08/2.28 % ------ QBF
% 2.08/2.28
% 2.08/2.28 % qbf_q_res: 0
% 2.08/2.28 % qbf_num_tautologies: 0
% 2.08/2.28 % qbf_prep_cycles: 0
% 2.08/2.28
% 2.08/2.28 % ------ BMC1
% 2.08/2.28
% 2.08/2.28 % bmc1_current_bound: -1
% 2.08/2.28 % bmc1_last_solved_bound: -1
% 2.08/2.28 % bmc1_unsat_core_size: -1
% 2.08/2.28 % bmc1_unsat_core_parents_size: -1
% 2.08/2.28 % bmc1_merge_next_fun: 0
% 2.08/2.28 % bmc1_unsat_core_clauses_time: 0.
% 2.08/2.28
% 2.08/2.28 % ------ Instantiation
% 2.08/2.28
% 2.08/2.28 % inst_num_of_clauses: 139
% 2.08/2.28 % inst_num_in_passive: 0
% 2.08/2.28 % inst_num_in_active: 0
% 2.08/2.28 % inst_num_in_unprocessed: 166
% 2.08/2.28 % inst_num_of_loops: 0
% 2.08/2.28 % inst_num_of_learning_restarts: 0
% 2.08/2.28 % inst_num_moves_active_passive: 0
% 2.08/2.28 % inst_lit_activity: 0
% 2.08/2.28 % inst_lit_activity_moves: 0
% 2.08/2.28 % inst_num_tautologies: 0
% 2.08/2.28 % inst_num_prop_implied: 0
% 2.08/2.28 % inst_num_existing_simplified: 0
% 2.08/2.28 % inst_num_eq_res_simplified: 0
% 2.08/2.28 % inst_num_child_elim: 0
% 2.08/2.28 % inst_num_of_dismatching_blockings: 0
% 2.08/2.28 % inst_num_of_non_proper_insts: 0
% 2.08/2.28 % inst_num_of_duplicates: 0
% 2.08/2.28 % inst_inst_num_from_inst_to_res: 0
% 2.08/2.28 % inst_dismatching_checking_time: 0.
% 2.08/2.28
% 2.08/2.28 % ------ Resolution
% 2.08/2.28
% 2.08/2.28 % res_num_of_clauses: 224
% 2.08/2.28 % res_num_in_passive: 20
% 2.08/2.28 % res_num_in_active: 103
% 2.08/2.28 % res_num_of_loops: 16
% 2.08/2.28 % res_forward_subset_subsumed: 29
% 2.08/2.28 % res_backward_subset_subsumed: 1
% 2.08/2.28 % res_forward_subsumed: 1
% 2.08/2.28 % res_backward_subsumed: 0
% 2.08/2.28 % res_forward_subsumption_resolution: 4
% 2.08/2.28 % res_backward_subsumption_resolution: 2
% 2.08/2.28 % res_clause_to_clause_subsumption: 33
% 2.08/2.28 % res_orphan_elimination: 0
% 2.08/2.28 % res_tautology_del: 0
% 2.08/2.28 % res_num_eq_res_simplified: 0
% 2.08/2.28 % res_num_sel_changes: 0
% 2.08/2.28 % res_moves_from_active_to_pass: 0
% 2.08/2.28
% 2.08/2.28 % Status Unsatisfiable
% 2.08/2.28 % SZS status Theorem
% 2.08/2.28 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------